Title (Code) Fourier methods for solving the quantum well problem Degree: BSc in Physics (or Physics with any) Professor Ben Supervisor: Co-Supervisor None Murdin Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational Modelling

You have encountered the quantum well many times in physics. The solution for the wave-function is a simple sine wave, and the higher the frequency of the wave, the higher the energy. The boundary conditions mean that only waves with nodes at both sides of the well constructively interfere and live for a long time. The result is a series of allowed states with definite energy. You have already calculated the allowed states in quantum wells using these principles, and the solutions are relatively easy and are explained in many elementary quantum mechanics courses. The main practical example quoted in such courses is the semiconductor quantum well, where a very thin layer of one semiconductor with low potential is sandwiched between layers of a high potential semiconductor.

This model works well in some situations, but in real life, electrons in semiconductors are moving in a crystalline solid, with a periodic Project potential that has regular ups and downs, and the quantum well is description: usually formed by layers of different size peaks and troughs. The quantum physics problem in this case is harder to write down, and therefore harder to solve. There are many methods that have been described to solve it, and each has advantages and disadvantages. In this project you will use one of these methods, called the Fourier method. You will apply the calculation to model a research experiment being performed in the ATI on “spintronics”, where the shape of the quantum well will be used to control the electron spin. The type of quantum well in question is a new structure referred to as “the topological insulator” [see Big Bang Theory season 4 episode 14 for Sheldon’s lecture on this].

Prerequisites:

Ideally you should have some knowledge of Fortran programming or Matlab or some similar computing platform. Some pen and paper mathematical theory will be necessary. Last 14/11/16 Updated:

Title (Code) Nano-scale modeling of atom distributions Degree: BSc in Physics (or Physics with any) Supervisor: Professor Ben Murdin Co-Supervisor S Clowes Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational modelling

The smallest silicon transistors in use are about 14nm (in 2014). This is nearing the size of a single donor atom (3nm), and so we can now imaging devices where single atoms are at the heart. We can even begine to imagine devices where chains of individual atoms are used, and because there are many species of donor there are a great variety of chains that can be made. As part of the £multi-M COMPASSS project at Surrey/UCL we have developed a lithography technique to position individual donors exactly where desired, but we need to start developing an understanding of how the chains might be used. The classic transistor is made of n, p and n-type regions of semiconductor, but who knows how it will work when it is reduced to the atomic scale Project and it is made of a single donor-acceptor-donor chain? description: We need to understand the statistics of nearest-neighbours. The modelling will take randomly arranged donors and examine how current passes from one to the next, for different density profiles and different combinations of species. A prior MSc project is available as a basis on which to start.

Prerequisites:

Successful completion of level 2 solid-state physics and the final year Light and Matter module will be a great advantage. Some computational skill will be an advantage but specific language skills are not necessary. Last 14/11/16 Updated:

Title (Code) Electrical detection of atomic transitions in silicon Degree: BSc in Physics (or Physics with any) Supervisor: Professor Ben Murdin Co-Supervisor S Clowes Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: experiment

The donor in silicon is an analogue of hydrogen, with a ladder of 1s, 2p, states etc. The main difference between hydrogen and the donor is that the energy scale is in the infrared rather than the UV. We are trying to make electrical devices based on individual donors, which would be the smallest silicon devices. The devices are produced by implantation using the Surrey Ion Beam Centre, and we make electrical connections to the devices using the Advanced Technology Institute clean-room. These devices have many hundreds of implanted atoms, but we are working towards being able to use structures with only one atom at the heart. As part of the £multi-million COMPASSS project at Surrey/UCL we have developed a lithography technique to position individual Project donors exactly where desired, but we need to start developing an description: understanding of how to detect the state of the atoms electrically.

In this project you will investigate one method of detection of the atomic state in electrical devices. The state of the atom can be controlled with laser pulses, and the capacitance of the sample changes when the atoms’ state changes due to the laser pulses. You will investigate the response of the devices to infrared excitation of the atoms from the ground state to the excited states.

Prerequisites:

Successful completion of level 2 solid-state physics, and level 2 experimental labs. The final year Light and Matter module will be a great advantage. Last 14/11/16 Updated:

Title (Code) Quantum optical dynamics of a three level atom Degree: BSc in Physics (or Physics with any) Professor Ben Supervisor: Co-Supervisor None Murdin Room: 15ATI01 Email: b.murdin Address Phone: 9328 Group: Photonics Type: Computational Modelling

When a hydrogen-like atom, i.e. a mobile electron bound to a heavy positive ion, experiences an a.c. electromagnetic wave, it can be driven into the excited state, via a superposition state like Schrodinger’s cat. The equations governing this quantum optical control are relatively simple first-order differential equations. Their derivation is described in the final year Light and Matter course, although this is not neccesry to understand.

In the Photonics group we have recently been performing experiments involving driving atoms (phosphorus atoms in silicon) with pulses of light containing two different colours, and then watching the resulting motion of the electron. The orbital motion can be used to produce entanglement of the electron with the electrons on neighbouring atoms. Control over the trajectory will allow control over which atoms get entangled and how strong the entanglement is. Project description: We would like to visualise the wavefunction of the atom during the excitation, and explore the possibilities for driving the wave into useful orbits. In this project you will make a computer code to solve the quantum optical problem for two colour light pulses and three atomic levels, and follow this with rate equation solution to find which levels the electrons transfer to afterwards once the light has passed. The wavepackets will be visualised by creating movies. We will compare the results of your calculation with the experiments, and hopefully design new experiments that will be able to demonstrate the three-state superpositions that are possible.

Prerequisites:

Successful completion of the final year Light and Matter module will be an advantage, but is not required. You should have a good knowledge of Fortran or other programming platform. Some pen and paper mathematical theory will be helpful for checking limiting cases. Last 14/11/16 Updated:

Title: Flow instabilities in complex fluids

Co-Supervisor: Supervisor: James Adams None

Building/Room: 14BB03 Type of Project Theoretical/Computational Email: [email protected]

Project Description:

Newtonian fluids such as water have a simple internal structure, so their flow behaviour is relatively easy to understand and model. By comparison complex fluids like polymer solutions, and surfactant solutions, have more internal structure – the conformation of the polymer -- than simple Newtonian fluids such as water. However, a good understanding of the relation between the stress and their flow is important for applications such as injection moulding of plastics, and the flow of drilling fluid in boreholes.

Recent experiments have shown some unusual flow behaviour which has resulted in renewed interest in these materials. When subjected to a simple shear, some fluids will flow with a uniform shear rate. However, other fluids (notably polymer solutions) become unstable to the formation of shear bands. These bands can also form transiently, then decay away, and even chaotically.

This project will analyse the stability in an elongational flow of some constitutive models relating to polymer solutions and liquid crystalline polymers. This will require the student to break down the constitutive equation into a set of ordinary differential equations, and solve these equations numerically. The student will then determine the eigenvalues of the stability matrix, to determine whether the equations are stable. If time permits a spatial resolved model of the flow instability can be developed. Title: Reaction-diffusion models

Co-Supervisor: Supervisor: James Adams None

Building/Room: 14BB03 Theoretical/Computational/literat Type of Project ure review Email: [email protected]

Project Description:

Reaction-diffusion models describe many different physical processes including chemical reactions and the flow of complex fluids. More recently these models have been used to describe the behaviour of a financial market [1]. The market participants can place orders to buy or sell in the order book. These orders are then cleared when the participants agree a price. This can be modelled as a one dimensional grid of length L, with the buy and sell orders represented by two particle types that can diffuse in from either side. When the particles meet they annihilate each other.

In more sophisticated versions of this model the annihilation may result in the placing of an additional buy/sell order.

In this project the student will review the literature of these types of reaction-diffusion models [2], and their success in describing the statistical features of the financial market such as the relation between impact and volume of contracts traded. They will simulate the reaction-diffusion process and look at the effect of modifying the underlying reaction, or including a correlation between different order books.

[1] I. Mastrommateo et al. Anomalous Impact in Reaction-Diffusion Financial Models, Phys. Rev. Lett 113 268701 (2014).

[2] Stephen J. Cornell, Refined simulations of the reaction front for diffusion-limited two-species annihilation in one dimension, Phys. Rev. E 51, 4055 (1995).

Numerical description of resonances in nucleon-nucleus Title scattering (ResNA)

Co- Supervisor: Dr Carlo Barbieri None Supervisor Building/Room: 11BB03 Type of Nonlinear Physics/ Theory/ Email: [email protected] Project Computational Modelling Phone: (01483) 689327

Project Description:

In Quantum Mechanics, resonances are characterised by sizeable enhancements of reaction cross section for certain energies of incoming projectile. For example, these are seen in the elastic scattering of a nucleon (N)—which can be a proton or a neutron—against a target of nuclear mass A. This happens because of the existence of eigenstates that would describe specific orbits as there was a bound N-A system but they are instead at energies in the continuum (and therefore the two fragments cannot be tied forever). Nevertheless, at that given energy, the scattering wave function “resonates” with the “quasi-bound” orbit, which enhances the cross section.

Resonances are very important states in nuclear physics as they are often key indicators of nuclear structure in experiments and can influence astrophysical rates. On the other hand, their description in first principle calculation is very difficult due to the different nature that many-body basis need to describe both scattering and structure effects.

The project consist in addressing this issue by choosing a simple model for a given reactions and then expand the problem in different bases, such as spherical Bessel or Gamow basis, to study their performance.

Technical aspects. The project is mainly computational and mathematical. The student should be able to program a code in FORTRAN or C++ and will be using this to perform integrals and solve eigenvalue problems in in the complex plane. The student will gain experience in the study and calculations of nuclear reactions rates.

Title Sparse Neural Networks (SpNN)

Co- Supervisor: Dr Carlo Barbieri None Supervisor Building/Room: 11BB03 Type of Nonlinear Physics/ Theory/ Email: [email protected] Project Computational Modelling Phone: (01483) 689327

Project Description:

Most systems out of equilibrium, such as those encountered in plasma physics, turbulence or neuroscience, show organization of dynamical phenomena on different scales. For example, systems that are characterized by microscopically chaotic dynamics can give rise to collective behaviours. That is, even if each small component of the system behaves in an unpredictable and independent way, synchronized motion of the whole system still arise in certain conditions due to the interaction among the various components.

An interesting recent realization is that collective and oscillatory behaviours arise even in very sparse networks (i.e., where interactions among components are very small and close to negligible) [1]. This happens at certain critical values of the connectivity among various nodes and it is reminiscent of observation in neuronal cultures [2].

This project will consider the results of Ref. [1] and will attempt at taking them further by investigating the dependence of collective behaviours on other factors than connectivity, such as the coupling strength among nodes.

Technical aspects. The project is mainly computational and mathematical. The student should be able to program a code in FORTRAN or C++ to simulate the behaviour of coupled oscillators (needed). During the project he/she will develop software to simulate a large collection of coupled neurons and learn tools for the advanced analysis of the stability of complex systems.

References [1] S. Luccioni, et al., Physical Review Letter 109, 138103 (2012). [2] J. Soriano, et al., Proc. Nat. Acad. Sci. U.S.A. 105, 13758 (2008).

Title Feasibility study for an enhanced solar thermal collector

Supervisor: Steve Clowes Co-Supervisor

Email: [email protected] Building/Room: 12ATI02

Type of Project: Modelling & Experimental

Project Description:

A solar thermal collector captures solar radiation and transfers that heat efficiently to water thus providing a cheap and environmentally friendly source of hot water, or as commonly used in the US, a method for heating swimming pools. There are two types of solar thermal collectors: flat plate panels and evacuated tubes. Flat plate panels consist of an absorber plate in an insulated metal box. Lots of thin tubes carry water through the absorber plate heating it up as it passes through. Instead of a plate, evacuated tube collectors have glass tubes containing metal absorber tubes, through which water is pumped. Each tube is a vacuum (the air is ‘evacuated’ hence the name), which minimises heat loss.

Example of a commercial solar collector used for heating a pool

We have proposed a new method of increasing the performance of solar thermal collectors by modifying the optical properties of the absorber material. In this project you will model the physical properties of this proposed new absorber and optimise the parameters of the new design, such as the absorber geometry and water flow. There will also be a possibility to develop an experimental demonstrator of the proposed design depending on the results of the modelling and the availability of time. Title: The Angular Talbot Effect

Supervisor: Steve Clowes Co-Supervisor: Marian Florescu

Email: [email protected] Building/Room: 12ATI02

Type of Project: Modelling & Experiment

Project Description:

The Talbot effect is a near-field diffraction effect that is observed when monochromatic light passes through a grating. It was first observed in 1826 by Henry Fox Talbot, in which a planar wavefront is diffracted from a grating to form repeated self-images of the grating which are observed at periodic distances. The distance between these periodic distances is known as the Talbot length. At a distance in between these self-images, another image of the grating is observed at one-half Talbot length but this image is shifted by a half width of the grating spacing. Another image, half the original size, is seen at a quarter Talbot length, and at an eight of a Talbot length a quarter size image in seen, and so on forming what is called the Talbot carpet.

What is surprising is that not until 2014 (188 years after Talbot’s original work!) was the first report of the Talbot effect published in which pattern originated from a circular wavefront, such as that from a point source (Physical Review Letters 112, 213902). In this arrangement the near-field diffraction has a peculiar dependence on the distance between the grating and the source, and this was Figure 1 The angular Talbot effect coined The Angular Talbot Effect. In this project you will use finite-difference time-domain methods (using Lumerical software package) to model the Angular Talbot Effect with non-uniform gratings and with the introduction of additional optical components. You will also perform experiments to measure the Angular Talbot Effect and verify the simulations. Title: The chemistry of Andromeda's disk stars

Co-Supervisor: Supervisor: Dr. Michelle Collins None

Building/Room: 24 BC 03 Type of Project Data analysis Email: [email protected]

Project Description:

1. Summary By studying the abundance of different elements within stars, we can hope to learn about how an entire galaxy has formed. These elemental abundances are like chemical fingerprints, and they can help us identify when, where and how a given star formed. Many large surveys have focused on piecing together how our own Milky Way has formed over the past 14 billion years using this method, but it is only one galaxy amongst many. Ideally we would forensically study all galaxies in the cosmos this way, however most are beyond the reach of current instrumentation to study their individual stars so rigorously.

There is one other system for which such a detailed evolutionary portrait can be painted: our neighbouring spiral galaxy, Andromeda. By using spectra and imaging data taken as part of the Pan- Andromeda Archaeological survey, and a spectroscopic analysis tool developed by a Surrey Undergraduate student, you will measure the iron content for hundreds of stars in Andromeda to look for patterns, relations or differences in the chemical evolution throughout its vast, star-forming disk.

2. Method The main goal is to adapt the python routine developed by James Sawdy to process the hundreds of spectra with differing signal to noise ratios, and measure the metallicity distribution function for different regions of Andromeda's disk. Once these functions have been measured, you will analyse the results to determine whether there is a metallicity gradient in the disk, as is seen in our Galaxy, and identify any unusual regions that may have formed differently through e.g, mergers of smaller galaxies with Andromeda.

You will be using python for the bulk of the analysis work, so familiarity with this programming language is key.

Fig 1: The PandAS imaging of M31 (left) with locations of Keck spectroscopic fields shown as red points. On the right, we show spectra for individual stars within these fields. Understanding the fuel driving star formation in Andromeda

Co-Supervisor: Supervisor: Dr. Michelle Collins None

Building/Room: 24 BC 03 Type of Project Literature review Email: [email protected]

Project Description:

The stars of a galaxy can tell us much and more about its evolutionary history, but what about the fuel driving the formation of stars? Given that almost all elements heavier than hydrogen and helium are formed within stars, and then spread to the rest of the galaxy through supernovae explosions, we are all made up of star dust. In modern astronomy, it is not enough to simply study the stars that are burning now. We must also understand the gas and dust that make up the interstellar medium of a system. This component can tell us about the stars that have come and gone before our time, and the future evolution of a galaxy. By piecing together information from all the components of a galaxy, we can hope to understand its evolution more fully.

The goal of this literature review is to bring together information from several different, large scale astronomical surveys of the Andromeda galaxy, across a variety of wavelengths, so that we can put together a global picture for the current state and future fate of a star-forming galaxy. Key questions include what is the current star formation rate of Andromeda? How long will it continue to form stars for? What is the composition and role of gas and dust in Andromeda at present?

Some of the key surveys you will need to read about and understand include:

The Pan-chromatic Hubble Andromeda Treastury (e.g. Dalcanton et al. 2012, Lewis et al. 2015) The Herschel Exploitation of Local Galaxy Andromeda (e.g.,Fritz et al. 2012, Smith et al. 2012, Groves et al. 2012) Spitzer surveys of Andromeda (e.g., Gordon et al. 2006, Rafiei et al. 2016a,b) HI surveys of Andromeda (e.g. Kerp et al. 2016, Lehner et al. 2015, Lewis et al 2013, Chemin et al 2009, Corbelli et al. 2010)

Title (Code) Negative Refraction in Micro-Structured Photonic Materials Degree: BSc in Physics Supervisor: Marian Florescu Co-Supervisor : None Room: 26ATI02 Advanced Technology Institute Faculty of Engineering & Physical Email: [email protected] Address Sciences, University of Surrey Phone: (01483) 686813 GU2 7XH, United Kingdom Group: Theory and Advanced Computation Type: Theory/Computational Modelling

One of very interesting phenomena demonstrated in the last decades is the negative refraction of light. While the original demonstration employed metamaterials whose structural properties have been designed to achieve negative values for the electric and magnetic susceptibilities and this negative index of refraction, a rigorously defined negative index-of-refraction may not necessarily be a prerequisite for negative refraction phenomena. An alternate approach to attaining negative refraction uses the properties of ‘photonic crystals. Photonic crystalsnear photonic bandgap frequencies behave as if they have a certain effective refractive index which is not limited by the refractive index of composing materials and is determined by the photonic band structure. Such an index can be smaller than unity and also can be negative without absorption, and still we can use Snell’s law to describe the light propagation. This conclusion is interesting in two aspects: one is that this is contrary to intuitive understandings because generally we cannot define adequate refractive index in periodic structures as we will see below; second aspect is that it means that we can realize artificial dielectric materials having negative refractive index.

The focus of the project will be on exploring negative refraction in micro-structured dielectric materials, based on periodic, quasiperiodic and disordered distributions. The project will also analyse advanced functionalities enabled by negative refraction phenomena, such as superlensing and superprism phenomena. Project Description

Negative refraction. (a) Refraction in a conventional material (left). Negative refraction (center). Focusing by negative refraction (right). (b) Negative refraction in a hexagonal GaAs pillar photonic crystal (numerical simulation). (c) Focusing by negative refraction in a photonic crystal (numerical simulation) [1].

Prerequisites: The project would be suitable for students on any degree pathway with good grades in computational laboratories, mathematics and optics.

References:

[1] M. Notomi, “Theory of Light Propagation in Strongly Modulated Photonic Crystals: Refraction-like Behavior in the Vicinity of the Photonic Band Gap,” Phys. Rev. B 62, 10705, (2000). [2] M. Notomi, “Manipulating Light by Photonic Crystals”, NTT Technical Review 7, 9 (2009).

Title (Code) Single-Photon Sources Degree: BSc in Physics Supervisor: Marian Florescu Co-Supervisor : None Room: 26ATI02 Advanced Technology Institute Faculty of Engineering & Physical Email: [email protected] Address Sciences, University of Surrey Phone: (01483) 686813 GU2 7XH, United Kingdom Group: Theory and Advanced Computation Type: Theory/Computational Modelling

In recent years, quantum optical information processing has attracted much attention, mostly for its applications to secure communication protocols and the possibility of solving efficiently computational tasks impossible to solve on a classical computer. It was demonstrated that efficient quantum computing can be implemented using only single-photon sources, passive linear optical elements, and detectors. The optical approaches to quantum computation benefit from the lack of decoherence of photons and the relative ease of photon manipulation.

Single-photon sources [1] are thus essential ingredients in any optical implementation of quantum computing. A single photon source emits in a deterministic way one photon at a time, with each photon being indistinguishable from the others [2]. Identifying the optimal system able to generate “on demand”, unidirectional pulses of single photons with a high repetition rate (in a so-called "photon gun" device) [3] has proven to be a complex task and is a subject of great interest to the scientific community. Present-day research considers photon emission from single atoms or molecules, quantum dot structures, or chemical compounds.

This project will investigate the possibility of achieving single-photon emission in suitably designed optical cavities and waveguides on a photonic-crystal platform. You will perform an extensive literature review on implementations of single-photon guns, and investigate the influence of photonic density of states, slow light, and light localization on the emission of photons in an optical cavity coupled to a photonic-crystal waveguide. Project Description

Cavity in a 2D photonic crystal slab [2]. Photonic-crystal structure for “single-photon gun” [3].

This project will give you a good understanding of modern photonics, quantum optics and advanced computational methods for microstructured photonic structures and will use in- house developed, open-source and commercially available software.

Prerequisites: The project would be suitable for students on any degree pathway with good grades in computational laboratories, mathematics and optics.

References [1] P. Yao, V.S.C. Manga Rao, and S. Hughes, "On-chip single photon sources using planar photonic crystals and single quantum dots", Laser and Photonics Reviews 4, 499-516 (2010). [2] Y. Akahane, T. Asano, B. Song, S. Noda, "High-Q photonic nanocavity in a 2-dimensional photonic crystal”, Nature 425, 944 (2003). [3] M. Florescu, S. Scheel, H. Haeffner, H. Lee, P. L. Knight, J. P. Dowling, "Single photons on demand from 3D photonic band-gap structures", Europhysics Letters 69 (6), 945 (2005).

Title (Code) Thermal Radiation Control with Microstructured Photonic Materials Degree: BSc in Physics Supervisor: Marian Florescu Co-Supervisor : None Room: 26ATI02 Advanced Technology Institute Faculty of Engineering & Physical Email: [email protected] Address Sciences, University of Surrey Phone: (01483) 686813 GU2 7XH, United Kingdom Group: Theory and Advanced Computation Type: Theory/Computational Modelling

Photonic band-gap (PBG) materials are a new class of periodic materials that allow precise control of all electromagnetic wave properties. A PBG occurs in a periodic dielectric or metallic media, similarly to the electronic band gap in semiconductor crystals. In the spectral range of the PBG, the light cannot propagate regardless of direction or polarization. Moreover, the ability to tailor the properties of the electromagnetic radiation in a prescribed manner through the engineering of the photonic dispersion relation enables the design of systems that accurately control the emission and absorption of light.

The modifications of the spontaneous emission rate of atoms inside the photonic crystal structure determine, in turn, important alterations of thermal radiative processes. Thermal radiation is just spontaneous emission thermally driven and in thermal equilibrium with its material surroundings. In the PBG spectral range the thermal emission of radiation is strongly suppressed, whereas for specific frequencies in the allowed photonic bands (corresponding to transmission resonances of the photonic crystal), the thermal emission of radiation is resonantly enhanced up to the black-body limit [1]. Previous studies suggest that by optimizing the multi-mode radiation field of a PBG material, it is possible to achieve dramatic modifications of Planck's blackbody radiation spectrum [2], which are highly relevant to high- efficiency solar cells and thermophotovoltaic energy converters [3]. Project Description

Solar cell panels on a satellite. Thermal emission in a PBG material [2].

In this project you will investigate the relevant physical thermal phenomena in microstructured photonic materials and develop computational tools for identifying suitable choices of materials and structures with high conversion efficiency and maximum power extraction. This project will give you a good understanding of modern photonics, thermal radiation and advanced computational methods for microstructured photonic materials, and you will use in-house developed, open-source and commercially available software.

Prerequisites: The project would be suitable for students on any degree pathway with good grades in computational laboratories, mathematics and quantum physics.

References [1] J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three- dimensional photonic crystals with a large infrared bandgap," Nature 417, 52 (2002). [2] C. Schuler, C. Wolff, K. Busch, and M. Florescu, "Thermal radiation from finite photonic crystals", Applied Physics Letters 95, 241103 (2009). [3] A. W. Rodriguez et al., "Frequency-Selective Near-Field Radiative Heat Transfer between Photonic Crystal Slabs", Phys. Rev. Lett. 107, 114302 (2011).

Title: Einstein–Smoluchowski relation for a coalescing random walk

Degree: Any Physics degree Supervisor: J. Allam Co-Supervisor: None Building/Room: 13ATI01 Email: [email protected] Type of Project: Computational modelling Phone: 01483 686799 Project Description: This is one of three projects that use a similar FORTRAN programme as the starting point. Students can help each other to understand the programme and get it running, but will then perform independent investigations. Diffusion is an important process in the physical sciences, and beyond. According to Einstein and Smoluchowski, diffusion is described by a random walk whose mean square displacement increases linearly with time. In 1D this could be written as d z2 dt  2D and is sometimes referred to as the Einstein-Smoluchowski relation. What happens when diffusing particles are allowed to interact? The simplest example is coalescence A A A, which has been studied for 100 years. For instant short- range reactions in 1D, the problem is exactly solvable and has become a paradigm for far-from-equilibrium systems that show emergent behaviour such as self-organisation. Traditionally, reaction kinetics have been expressed in term of the concentration decay, or equivalently the growth of the mean pair separation d x dt, but reaction- induced spatial ordering mean that a simple universal expression cannot be found. We have derived a simple expression for the mean-square separation that we regard as an Einstein-Smoluchowski relation modified for concentration decay d x2 dt  4D x2  where  is the characteristic reaction time. This approach provides a framework for the interpretation of our recent experimental studies of exciton-exciton reactions on carbon nanotubes. In this project you will investigate the validity of Eq. (1) using a Monte Carlo simulation, for the following scenarios (as time permits) (i) Instantaneous short-range coalescence where Eq. (1) is ‘exact’. (ii) Non-instant reactions where an approximate modified form of Eq (1) is known. (iii) Long-range reactions, where a modification of Eq (1) is not yet known. (iv) The related annihilation reaction A A 0 where an exact solution is not known. You will be provided with a Monte Carlo programme written in Fortran, which can be used for investigation (i) and (with small modifications) for investigations (ii) – (iv). Earlier versions of this programme have been used by several undergraduate project students in recent years. You will develop skills in computer simulation and knowledge of phenomena that impact on many areas of science. Title: Critical dynamics: the computational cost of realistic simulation

Degree: Any Physics degree Supervisor: J. Allam Co-Supervisor: None Building/Room: 13ATI01 Email: [email protected] Type of Project: Computational Modelling Phone: 01483 686799

Project Description:

This is one of three projects that use the same programme as the starting point. Students can help each other to understand the initial programme and get it running, but will then perform independent investigations. Unlike the other projects, this one requires substantial new code and is intended for a confident computational modeller. Any language can be used, but only if Fortran is used will I be able to give limited help with the actual coding.

Processes that involve the motion of particles and their interaction when sufficiently close are common in physical and biological sciences. In certain conditions (most simply, low spatial dimensionality), for sufficiently large systems (many particles) and at sufficiently long times, behaviour emerges that resembles continuous phase transitions in the vicinity of a critical point. This ‘critical’ behaviour is challenging to simulate because many particles must be tracked over long times. Typically, highly simplified “toy” models are used to extract the main behaviours, but these do not reproduce all the phenomena observed experimentally, for example in out recent studies of exciton-exciton interactions on carbon nanotubes.

The purpose of this project is to perform a pilot study to assess the viability of introducing different levels of physical complexity to simulations of critical phenomena. For example

(1) Random walk on a lattice. A Fortran Monte Carlo programme is available and has been used by previous project students. (2) Langevin dynamics, where a random force simulates the thermal motion.

(3) Full Newtonian kinetics, as used in molecular dynamics simulations of chemical reactions and Monte Carlo simulation of electron transport in semiconductors.

To make the simulations feasible, very simple interactions of small numbers of particles in one spatial dimension will be performed. An investigation of the scaling with systems size will be used to assess the simulation of large systems. According to the interest of the student, a projection could be made of the usefulness of computational clusters or GPUs. Title: The coalescing random walk: how do long-range interactions modify the spatial distribution of particles? Degree: Any Physics degree Supervisor: J. Allam Co-Supervisor: None Building/Room: 13ATI01 Email: [email protected] Type of Project: Computational Modelling Phone: 01483 686799

Project Description:

This is one of three projects that use the same programme as the starting point. Students can help each other to understand the initial programme and get it running, but will then perform independent investigations.

For many-body systems in thermal equilibrium, we have a reasonable understanding of collective processes such as phase transitions and other “critical phenomena”. However many systems of interest (including most aspects of life) are far from equilibrium: here, no generic theory exists, and well-controlled experiments are “deplorably rare”. In order to make some progress, theory and simulation have used highly simplified models of particle interactions, and have shown rich critical kinetics in non-equilibrium systems. However, real-world processes do not have instant reactions and zero reaction range, so the question arises: what critical phenomena are observable in realistic experimental systems?

This project considers the effects of finite reaction time and interaction range on the kinetics of the Coalescing Random Walk (CRW). You will be provided with a Fortran programme that calculates the concentration of diffusing particles which coalesce with a certain probability at a given range. You will modify this programme to calculate the spatial distribution of nearest-neighbour pairs, and examine how this change as a function of reaction probability and range. The results may show us how to construct approximate analytical models of the CRW in the presence of long-range interactions, which would be useful for the interpretation of our recent experimental results on exciton-exciton reactions on carbon nanotubes.

This project is for someone with enough knowledge of Fortran to understand and modify the provided code: note that 7 undergraduate students worked on similar projects in recent years and all were able to handle the programming. You will develop skills in computer simulation and develop knowledge of phenomena that impact on many areas of science. Title The production of 14C in the atmosphere

Degree: Physics / Physics with Nuclear Astrophysics Supervisor: Zsolt Podolyák Co-Supervisor Building/Room: 05BB03 Type of Project Lit. review Email: [email protected] Phone: 6811

Project Description:

The 14C isotope of carbon is used for dating organic matter (carbon dating). The idea is that the isotopic ratio of 12C/14C in the environment is constant during the years. While the animal/plant is alive this isotopic ratio in the atmosphere and the animal/plant is the same. After death there is no more carbon intake and the amount of 14C nuclei start to reduce due to their decay. Therefore, by measuring the 12C/14C ratio in organic matter, its age can be determined.

But how is 14C, with a half-life of ~5730 years, is created in the first instance? And how much? 14C is cosmogenic isotope, meaning that it is produced when cosmic rays interacts with matter in atmosphere or soils and rocks. Other example of cosmogenic isotopes are 7Be (used for measuring erosion, dating ice etc.), 41Ca (dating carbonate rocks), 129I (groundwater).

The aim of the project is to understand how cosmogenic isotopes are produced. It will focus on 14C, but other nuclei could also be considered. A good start is to read G.A. Kovaltsov et al., Earth and Planetary Science Letters 337 (2012) 114. The important factors influencing the production and the main uncertainties in determining the amount of 14C created will be investigated. Title High-order deformation in atomic nuclei

Supervisor: Paul Stevenson Co-Supervisor Building/Room: 12BB03 [email protected] Type of Computational Modelling/ Email: k Project Theoretical Phone: 6796

Project Description:

Atomic nuclei come in a variety of shapes. Even in their ground states, some nuclei are spherical (such as most of those with magic numbers of protons or neutrons), while others are deformed, with the most common shape being a prolate spheroid (rugby ball).

The standard way to characterise nuclear shape is in an expansion of spherical harmonics, with the leading order being spherical, and the first non-trivial order of deformation giving the spheroids. There is some evidence (from observed excitation spectra) that some nuclei may possess a much higher-order deformation [1]. In this project you will review and understand selected literature on nuclear shape and the link between it and observable spectra, and use existing codes [2,3] to make new explorations of shape properties of some key nuclei to attempt to substantiate or repudiate the claims that their spectra may be due to their unusual shape.

While the codes exist, some post-processing of the output will be required, involving at least a little coding of ones own, so this would suit someone happy with computing. Aside from that, the bias is on the theoretical side.

[1] P. M. Walker, H. L. Liu, and F. R. Xu, Bulg. J. Phys. 42, 382 (2015) [2] W. Ryssens, V. Hellemans, M. Bender, and P.-H. Heenen, Comput. Phys. Comm. 187, 175 (2015). [3] J. A. Maruhn, P.-G. Reinhard, P. D. Stevenson, and A. S. Umar, Comput. Phys. Commun. 185, 2195 (2014) Toroidal nuclear excitations Title

Supervisor: Paul Stevenson Co-Supervisor 12BB03 Building/Room: Type of Project Computational / Theoretical Email: [email protected] Phone:

Project Description:

Giant resonances are excitation modes of atomic nuclei that are the dominant response of nuclei to excitation by photons over a wide energy range. The most basic mode is the giant dipole resonance in which the electric field in the photon drags all the protons in one direction with respect to the neutrons, causing a dipole between the centre of charge and the centre of mass. After absorbing the photon the nucleus relaxes by undergoing damped dipole oscillations. There is evidence to suggest that for low-energy photon absorption, the excitation pattern looks less like a dipole, but is actually a toroidal oscillation in which the nucleons swirl round in a loop [1]. In this project you will make calculations of this phenomenon using an existing code, though you will need to be confident with programming to post-process the output and make a rigorous analysis. An example of the flow of nucleons is shown in the figure [2].

[1] A. Repko. P.–G. Reinhard, V. O. Nestorenko, and J. Kvasil, Phys. Rev. C 87, 024305 (2013), arXiv:1212.2088 [2] P. D. Stevenson, EPJ Web of Conferences, 107, 08001 (2016), arXiv:1510.03017 (2015) Title Quantum Weak Measurements

Supervisor: Paul Stevenson Co-Supervisor 12BB03 Building/Room: Type of Project Literature Review Email: [email protected] Phone: 6796

Project Description:

In a paper published in 1988, Aharonov, Albert and Vaidman, proposed a technique to make a kind of "weak" measurement of a quantum system which does not collapse the system to an eigenvalue or otherwise appreciably disturb the wave function [1]. This procedure seems contradictory to the standard understanding of quantum mechanics, but has been exploited to follow the trajectory of a single photon in the two-slit experiment [2].

This project is a literature review project geared at understanding these weak measurements; how they work, the experimental implementation of them, and the debate as to whether they are in fact really quantum [3].

While a literature review, it will be necessary to work through the mathematics and the quantum mechanics to fully understand the technique and make a cogent description of it.

[1] Yakir Aharonov, David Z. Albert, and Lev Vaidman, Phys. Rev. Lett. 60, 1351 (1998) [2] Sacha Kocsis et al., Science 332, 1170–1173 (2011) [3] Christopher Ferrie and Joshua Combes, Phys. Rev. Lett. 113, 120404 (2014) Title Statistical uncertainty in nuclear models

Supervisor: Paul Stevenson Co-Supervisor 12BB03 Building/Room: Type of Project Theoretical / Computational Email: [email protected] Phone: 6796

Project Description:

A widely-used approach to give a quantum description of nuclei uses phenomenological effective interactions to model the nucleon-nucleon forces as felt inside a nucleus between protons and neutrons. These model interactions are supposed to be simplified versions of a full nuclear interaction, featuring only the parts needed to reproduce low energy nuclear data. They consist of terms motivated by physical considerations, with coefficients fitted to data.

The fitting procedure, when done properly, gives information about the uncertainties inherent in the model, about correlations between different data and any redundancies in the parameters of the interaction. These statistical techniques have only recently been applied to the nuclear interactions (e.g. in [1]), and have begun to shed considerable light on a large sub-field of nuclear physics.

The purpose of this project is to apply these techniques to analyse the success of a simplified nuclear model, the statistical reliability of its predictions, as well as to gain expertise with the nuclear model and the statistical techniques.

[1] P.–G. Reinhard and W. Nazarewicz, Phys. Rev. C 93, 051303(R) (2016) Can Quantum Mechanics Describe Physical Reality? The EPR Title paradox and Bell’s Theorem

Degree: Physics / Physics with Nuclear Astrophysics Supervisor: Daniel Doherty Co-Supervisor Alexis Diaz-Torres Building/Room: Lit. review/ 14BC04 theoretical/ Type of Project Email: [email protected] experiment Phone: 6811 design Project Description:

In 1935 the so-called EPR paper of Albert Einstein, Boris Podolsky and Nathan Rosen [1] a thought experiment was proposed that some thought brought into question the completeness of quantum mechanics. For this thought experiment they consider a particle at rest in the lab which then decays into a pair of back-to-back photons. This pair of photons is then described by a single, two-particle wave function. Once separated, the two photons are still described by the same wave function and a measurement of one observable of system one will determine the measurement of the observable in system two. Thus, a measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling (i.e. quantum entanglement). This is a puzzling situation as the first measurement of one system has "poisoned" the first measurement of the other system, no matter what the distance between them (in violation of special relativity). To account for this the EPR paper of Einstein, Podolsky and Rosen postulated that the existence of "hidden variables" of the system, violating the Copenhagen interpretation of quantum mechanics.

In a seminal 1964 paper, Irish physicist John Stewart Bell proposed a mechanism to test for these so­called hidden variables developing his now famous inequality as the basis for such a test which argued against the hidden variable theory presented in the EPR paper.

For a good introduction to this perhaps unfamiliar topic see Ref [4] and references therein. Or for those that are interested it is possible to find some good resources on YouTube (e.g. [5]). See also https://xkcd.com/1591/

This project should begin with a consultation of the literature including the original EPR and Bell papers in order to understand the relevant mathematics, then a review of the experimental progress to date (including potential problems) and then, finally, investigation and planning for how one would perform a simple test of Bell’s inequality with equipment similar to that which could be found in the undergraduate laboratory.

[1] A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 41, 777 (1935). [2] J. Bell, Physics 1, 195 (1964).

[3] J. Bell, Reviews of Modern Physics 38 447 (1966).

[4] http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html

[5] https://www.youtube.com/watch?v=v657Ylwh-_k Title: Modelling Climate Change

Co-Supervisor: Supervisor: Wilton Catford None

Building/Room: 04BC04 Modelling/Experiment/Lit Type of Project review/etc Email: [email protected]

Project Description:

Global circulation models that seek to describe and understand climate change are complex and time consuming to run on supercomputers. Before such computer power existed, climate change effects were already predicted and modelled using vastly simpler models that nevertheless included the key effects, typically in a simple vertical column model of the atmosphere. This project is part literature survey and part based on running simple climate simulations. As a start, a spreadsheet formulation of a climate model can be used, and its reaction to the changing of the input parameters can be explored. There will be a requirement to search the literature so as to be able to write a good description of the physics and the formulation of the sort of model that is represented in the spreadsheet. The project should include an assessment of the importance of these early mathematical descriptions in laying the foundations for the present day global circulation modelling, and also should try to identify and summarise the limitations of the early approaches in terms of the strength or extent of their predictions. Title: Crackling Noise

Co- Supervisor: David Faux Supervisor: None

Building/Room: 18BC04 Type of Modelling Project Email: [email protected]

Project Description:

Crackling noise occurs when a system suddenly responds to some external condition. The response can span a broad range of sizes. Examples are the cracking of paper when scrunched, earthquakes, avalanches and (possibly) the movement of financial markets.

The first task is to use an Ising-type model (Monte Carlo) to simulate crackling noise conditions. This corresponds, physically, to the formation and decay of magnetic domains. The student, if so inclined, could then analyse market data (for example, the FTSE 100 index) and analyse in terms of crackling noise statistics.

This is a computational project and the student should be content to program in FORTRAN or an alternative language of their choice.

Image from: Castellano et al (2009)

References Castellano et al, Statistical physics of social dynamics, Rev. Modern Phys., 81, 591 (2009) Bouchaud, The Unfortunate Complexity of the Economy, Physics World, April 2009 Sethna et al, Crackling Noise, Nature, 410, 242 (2001) Title: Quantum 2D cellular automata

Co- Supervisor: David Faux Supervisor: None

Building/Room: 18BC04 Type of Modelling Project Email: [email protected]

Project Description:

This project is related to the interdisciplinary field of quantum information.

Imagine a two-dimensional square lattice in which each square is labelled 0 as “live” or 1 as “dead”. A set of rules is applied to every square in the lattice simultaneously to determine whether a live cell stays alive or becomes dead, or whether a dead cell remains dead or becomes alive

The rules are simple yet give rise to complex behaviour. The student would explore and attempt to describe the complex behaviours. The student may be able to adapt the 2D quantum game to a 3G system involving quantum gates.

This is a computational project and the student should be content to program in FORTRAN or an alternative language of their choice.

Reference 1. The Quantum game of Life, article by Pablo Arrighi and Jonathan Grattage, Physics World June 2012. Title: Energy Resolution in Nuclear Transfer Reactions

Co-Supervisor: Supervisor: Wilton Catford None

Building/Room: 04BC04 Modelling/Experiment/Lit Type of Project review/etc Email: [email protected]

Project Description:

One of the key areas of nuclear physics experimental research at Surrey involves the study of neutron transfer reactions to add neutrons to radioactive nuclei that are accelerated to suitable energies to initiate such a reaction. It is vitally important in the experimental design to be able to quantify the energy resolution that can be achieved in terms of the excitation energy in the final nucleus. The main reaction of interest is (d,p) i.e. a deuteron is hit, and a proton emerges after the neutron is transferred. The main contributions in the resolution for these reactions are the energy loss of the proton as it leaves the reaction target, the energy resolution of the detectors used to record the protons and the angular resolution with which the protons can be detected. All of these sensitivities can be calculated, once the energy of the proton is calculated using relativistic kinematics equations, and the results will depend on the energy and mass of the beam particles, the thickness of the target and the angle of detection and the excitation energy of the final nucleus, etc. The project is to write a new fortran program or excel spreadsheet to do all of these calculations for (d,p) reactions using any given incident beam. A range of existing programmes is available in order to cross check the relativistic kinematics and to calculate and parametrise processes such as the energy loss of protons when escaping the target. Whilst elaborate Monte Carlo simulations of our experiments have been developed, the relatively simple approach of this project will lead to a useful, convenient and intuitive analysis that can inform the design of our future experiments. As well as the programming, the project report will need to describe the underlying physics that is being calculated. Title Waking-up to Photonics

Supervisor: Dr K Hild Co-Supervisor : Prof S Sweeney 08ATI02 Building/Room: Type of Lit review/modelling Email: [email protected] Project Phone: 6108

Project Description:

The white light produced by modern solid-state LED lighting is produced from a combination of a blue-emitting (460nm) Gallium nitride (GaN) semiconductor and a yellow-emitting phosphor. This combination is perceived as white light. Such light sources are very energy efficient compared to conventional light bulbs thus LED lights are gradually replacing conventional lighting, including streetlights. Alongside the interesting development in semiconductor technology (that led to the development of the GaN LED which was awarded the Nobel Prize in 2015) it has also been recently shown that blue light (at exactly the wavelength of the commercially available GaN LEDs) is responsible for the regulation of our body clock and our wake sleep cycle. Consequently, too much of the blue light (which is now in most homes) in the evening disrupts this natural cycle.

This project is an initial literature review into the alternatives of producing white light without relying on the 460nm pump source. This will range from the combinations of red, green blue LEDs to other pump sources, other phosphors and other ways of providing down conversion (e.g. quantum dots). The aim of the literature review is to find the advantages and short comings of existing technologies to be able to develop efficient light sources that work better with human physiology. Alongside the literature review the project will involve some computation modelling of white light and semiconductor LED structures.

The project is suitable for anyone that is interested in some real life applications and in learning more about lighting and human health. Title Bad Science and Imaginary Weapons: The hafnium bomb

Degree: Physics / Physics with Nuclear Astrophysics Supervisor: Daniel Doherty Co-Supervisor Building/Room: 14BC04 Type of Project Lit. review Email: [email protected] Phone: 6811 Project Description:

In the late 90s, University of Texas professor Carl Collins and his team claimed, with the use of a simple dental X-ray machine and other simple apparatus, that they were able to trigger the release of an enormous amount of energy from a trace of the isomer of hafnium-178 [1]. Such a result, if correct, would have substantial technological consequences: including use a so-called nuclear battery and perhaps most crucially the potential to build a weapon by arranging the hafnium in such a way as to trigger a chain reaction. It is, therefore, no great surprise that such a development attracted significant interest from the US military in particular as such a device would circumvent all existing non-proliferation treaties which were aimed at controlling access to fissile material. However, despite significant interest (and financial investment) these results have to date not been confirmed.

An isomer is a “metastable” excited state of a nucleus. Their half lives span a range from 10-9 seconds up to years. In fact, for the isomer of interest in hafnium-178 is approximately 31 years (~109 seconds).

The literature review will begin with an investigation of the physics underpinning nuclear isomerism before moving on to look at the possible energy release mechanisms. The next stage will then be to critically assess the original Collins experiments and subsequent follow up work which have failed to reproduce the original results. Finally, a review of the future (if any) for technology based on nuclear isomerism should be explored.

An excellent starting point for this project would be to consult the book “Imaginary Weapons” by Sharon Weinberger.

[1] C. B. Collins et al, Phys. Rev. Lett. 82, 695 (1999) Spectroscopy of 34Cl and its influence on the astrophysical 33S(p,γ)34Cl reaction

Supervisor: Gavin Lotay Co-Supervisor Building/Room: 22BC04 Type of Project Experiment Analysis Email: [email protected] Phone: 01483 689589

Project Description:

Gamma-ray spectroscopy is a powerful tool for extracting the excitation energies and spins of nuclear levels. These properties are essential ingredients for our understanding of the nuclear shell model and can play a key role in determining stellar reaction rates.

Recently, a gamma-ray spectroscopy study of the nucleus 34Cl was performed at Argonne National Laboratory, USA, using the large germanium detector array Gammasphere [1]. In this project, you will analyse the latest dataset with a goal to extract the energies and spins of excited levels in 34Cl that exist above the proton-emission threshold. These states determine the rate of the astrophysical 33S + p  34Cl + γ reaction in stellar environments, as well as the abundance of 33S found in presolar grains [2].

Figure 1 - The Gammasphere detector array

[1] I.Y. Lee, Nucl. Phys. A520, 641c (1990. [2] A. Parikh et al., Phys. Lett. B737, 314 (2014). The Impact of Nuclear Reaction Rate Uncertainties on the Path of Nucleosynthesis in Classical Novae

Supervisor: Gavin Lotay Co-Supervisor Building/Room: 22BC04 Type of Project Modelling Email: [email protected] Phone: 01483 689589

Project Description :

Investigations of classical novae represent a cornerstone of nuclear astrophysics research [1]. These astronomical events, which comprise of a main sequence star and a white dwarf star in a close binary system, are among the most frequent and violent stellar explosions to occur in our Galaxy, leaving imprints on our observed Universe in the form of chemical elements. Recently, remarkable advances in astronomy have established detailed elemental abundance distributions for the ejecta of nova explosions and as such, provide a major new challenge for the field. However, large uncertainties in the underlying nuclear physics processes that govern the path of nucleosynthesis in classical novae make it extremely difficult to capitalize on the latest observational data.

Figure 1 - Artist impression of a classical nova

In this project, you will utilize the computational code NuGrid [2] to model classical nova explosions. In particular, you will investigate the potential impact of varying specific nuclear reaction rates on the final ejected abundances of elements.

[1] J. Jose, M. Hernanz, and C. Iliadis, Nuclear Physics A 777, 550 (2006). [2] P.A. Denissenkov et al., Monthly Notices of the Royal Astronomical Society 442, 2058 (2014).

Title: Year 3 final project: Resolved Star Formation History

Co-Supervisor: Supervisor: Dr. Noelia E. D. Noël None

Building/Room: Type of Project Lit review Email: [email protected]

Project Description: In this project the student will explain how the star formation history (SFH) of a galaxy in the Local Group of galaxies (the galaxies around the Milky Way and Andromeda) can be derived from the colour-magnitude diagrams (CMDs) of its resolved stars.

The project should include a description of the procedures to build synthetic CMDs and how to exploit them to derive the SFHs, as well as the uncertainties. The student should also discuss the SFHs of resolved dwarf galaxies of all morphological types, obtained from the application of the synthetic CMD method. Which galaxies show evidence of long interruptions in the SFH? Are late-type dwarf galaxies’ SFHs rather continuous? Is there any galaxy in the Local Group observed to be currently experiencing its first star formation episode?

The implications of this investigation should be discussed.

Title: Year 3 final project: Obtaining Colour-Magnitude Diagrams

Co-Supervisor: Supervisor: Dr. Noelia E. D. Noël None

Building/Room: Type of Project Modelling Email: [email protected]

Project Description: The aim of this project is to construct a colour-magnitude diagram using data for a simulated galaxy.

The Hertzprung-Rusell (H-R) diagram is a plot of the luminosities of stars (or absolute magnitudes) against their surface temperatures (or spectral types). In particular, if the horizontal variable is expressed as the radiation difference measured from two different wavelengths (the colour index), such a diagram is called colour-magnitude diagram (CMD). All stars evolve at different rates depending on their masses. But independently of the mass, from birth up to 99% of its lifetime, each star evolves in a similar manner. Stars spend most of their lives burning hydrogen slowly in a state of stable points over the entire CMD, but mostly concentrated on the Main Sequence (MS) that goes from the upper left (hot, blue, luminous stars) to the bottom right (cool, dim, red stars). When the hydrogen supply in the core of a star is depleted, hydrogen burning is no longer possible. This ends the MS phase of a star’s life. The star moves out form the MS to the Red Giant Branch (RGB), where the initial stages of helium burning phase begin.

The CMD of a stellar system the best fossil record on the system evolution, because it preserves the imprinting of all the relevant evolution parameters (age, mass, chemical composition, initial mass function).

The synthetic CMD method allows us to derive all the star formation histories (SFH) parameters within the lookback time reached by the available photometry. To do this, a synthesizer works with classical ingredients:

• Star formation law and rate, SFR(t), which regulate the mass at each time t; • Initial mass function (IMF), which gives the number N of stars in each generation per unit stellar mass interval. A useful form is a power-law

(1)

• The IMF is usually assumed to be independent of time; • Chemical enrichment: due to the galaxy chemical evolution, the metallicity of the gas from which stars form changes with time. This is described by an age-metalicity relation (AMR) Z(t); • Stellar evolution tracks, giving the temperature and luminosity of stars of given mass and metallicity at any time after their birth; • Stellar atmosphere models, to transform the bolometric magnitudes and temperatures into the observational plane; • Binary fraction and mass ratio.

The standard procedure is the following. Using a Monte Carlo algorithm, masses and ages are extracted according to the IMF and the star formation law (e.g. constant or exponentially decreasing with time, proportional to some power of the gas density, etc.). The metallicity follows suitable AMRs. The extracted synthetic stars are placed in the CMD by interpolation among the adopted stellar evolution tracks of the assumed metallicity. In order to take into account the presence of unresolved binary stars, a chosen fraction of stars are assumed to be binaries and coupled with a companion star. The fake population is put at the distance of the galaxy we want to analyse, simultaneously correcting for reddening and extinction.

Figure 1: Synthetic CMD simulated for a galaxy assuming a constant SFH throughout its whole lifetime from 13.5 Gyr ago until now. The different evolutionary phases are shown too.

The shape of an atomic nucleus: “spherical aren’t they? And why Title do we care anyway?”

Degree: Physics / Physics with Nuclear Astrophysics Supervisor: Daniel Doherty Co-Supervisor Building/Room: 14BC04 Lit. review/ data Type of Project Email: [email protected] analysis Phone: 6811 Project Description:

Along with the mass the shape is one of the most fundamental properties of an atomic nucleus, yet it is one of the least well understood. It is governed by the interplay of macroscopic, ‘liquid-drop’ like properties of the nuclear matter and microscopic shell effects.

The somewhat naive picture of spherical nuclei is far from reflecting the reality of nuclear structure, indeed nuclei which are spherical in their ground state should be regarded as special cases. In fact, a variety of shapes are observed (often in the same atomic nucleus) with the most comment being a rugby ball (prolate deformed) or a water melon (oblate deformed). More exotic shapes have also been identified including recent the observation of so-called ‘pear shaped’ (or octupole deformed) nuclei [1]. The literature survey part of this project will address the underlying nuclear structure physics that drives these fascinating phenomena and the various experimental probes being employed to observe them, including laser spectroscopy and Coulomb excitation. Finally, the implications for both nuclear physics and beyond will be considered.

Sphereical, oblate and prolate shapes observed in the radioactive nucleus Pb-186. This figure is taken from Ref [2].

Depending on interest and progress this project can also contain a small data analysis component, where the student will analyze real Coulomb excitation data recently obtained at the HIE­ISOLDE facility, CERN. The goal of this analysis will be to extract a “quadrupole moment” which is closely related to the charge distribution and thus the nuclear shape. This software used to perform this analysis is written in Fortran so some basic knowledge of this language would be advantageous.

[1] L. P. Gaffney et al. Nature 497, 199 (2013) [2] A.N. Andreyev et al, Nature 405, 186 (2000) Title: Measurement of Naturally Occurring Radioactive Materials Using High Resolution Gamma-ray Spectrometry.

Co-Supervisor: Supervisor: P.H.Regan None

Building/Room: 05BC04 Type of Project Experiment Email: [email protected]

Project Description: This project will use gamma-ray spectrometry to assess the levels and activity concentrations of various radionuclides in environmental samples. In particular, discrete line gamma-ray spectroscopy will be used to identify transitions associated with decays from the Thorium and Uranium decay chains and from potassium-40. The project will involve the detailed calibration and operation of a hyper-pure germanium detector set-up and the analysis of gamma-ray spectra taken in the Environmental Radioactivity Laboratories at the University of Surrey.

The main objectives will be to a) calibrate and characterise the HpGe detection system; b) carry out a radiological assay of prepared environmental samples using gamma-ray spectrometry; c) evaluate the results using a weighted mean analysis to calculate the activity concentrations and relative isotopic abundances of uranium in these samples. Title: Quantifying and Correlating Nuclear Deformation and Masses

Co-Supervisor: Supervisor: Prof. P.H.Regan None

Building/Room: 05BC04 Type of Project Modelling & Lit review Email: [email protected]

Project Description:

Most atomic nuclei are not spherical in shape, but have some degree of deviation from sphericity. This can be inferred by looking at a number of nuclear structure observables, including the energy of the first spin/parity 2+ state in even-even nuclei and also by the energy differences between successive nuclear excited states within the same nucleus (i.e. the energy difference between two successive gamma- rays).

This project is in 2 parts: (a) a literature survey to form a data base linking nuclear energy levels, nuclear mass differences (Vpn) and decay lifetimes of excited states in even- even nuclei,

(b) looking for correlations between these observables to determine nuclear deformations based on simple parameters such as the energy of the first excited state and the number of nucleons in the nucleus; also possibly looking for deviations between measured nuclear masses and predictions from the simple, Semi-empirical mass formula to also identify regions of nuclear deformation and shape evolution.

From these new insights into nuclear structure, including the shifting and evolution of nuclear shell closures and magic numbers may be observed. Some basic nuclear structure (i.e. physics undergraduate) knowledge / interest would be an advantage, as would basic experience in use of data-base systems, such as Excel Title: Thorium Based Nuclear Reactors

Co-Supervisor: Supervisor: Prof. P.H.Regan None

Building/Room: 05BC04 Type of Project Lit review. Email: [email protected]

Project Description:

This is a literature survey project which will examine the pluses and minuses (and viability) of Thorium-based nuclear reactors. It will also weigh up radiochemistry aspects against nuclear proliferation, plus the historical and technical aspects of the thorium nuclear fuel cycle. Why do we use Uranium-based reactors instead of thorium based one in the UK ? Title Effect of the nuclear physics input on the r process abundances

Degree: Physics with Nuclear Astrophysics/Physics Supervisor: Zsolt Podolyák Co-Supervisor Building/Room: 05BB03 Type of Project Modelling Email: [email protected] Phone: 6811

Project Description:

Half of the isotopes heavier than iron are produced in the so called rapid neutron capture process. The r process takes place in extreme neutron rich environments, such as supernovae explosions and/or neutron star mergers. The r-process abundance calculations assume knowledge of both the astrophysical site and the nuclear physics properties of the nuclei involved. Nuclear physics input are the half-lives, Q-values, neutron emission probabilities.

The majority of the r-process waiting point nuclei cannot be studied experimentally at the moment. Progress was made during recent years at radioactive beam facilities regarding nuclei around N~82. However no experimental information is available on heavier, e.g. N~126, r-process path nuclei.

The aim of the project is to quantify the effect of the nuclear physics uncertainties on the r process abundances. For example, abundance calculations will be performed considering different theoretical beta-decay lifetime calculations. Namely, new calculations consider so called forbidden transition when predicting half-lives, while the old ones do not account for these. The inclusion of forbidden transitions shortens half-lives considerably (sometimes by a factor of 2-5), which affects the r process path and the abundances. The nuclear physics input is tabulated. The abundances of nuclei produced via the r process will be calculated using publicly available software (see https://sourceforge.net/p/nucnet-tools/home/Home/). Programming knowledge is necessary. Title: Data science applied to the structure of nanocrystals

Co-Supervisor: Supervisor: Richard Sear None

Building/Room: 10BB03 Type of Project Modelling Email: [email protected]

Project Description:

Many crystalline materials are composed not of one or a few macroscopic crystals, but of many nanocrystallites, i.e., crystals that may be only of order 10 nm across. These materials include important materials, such as the organic crystals used in the next generation solar cells we want to develop to produce cheap green electricity. In these materials the size of the crystals matters as it affects properties such as conductivity, so we need to measure it.

This is often difficult, as the crystals are so small, but one way is to use the fact that the crystal size affects the width of the peaks observed in the crystal’s structure factor S(q); the structure factor can be measured in experiment via X-ray diffraction. The bigger the crystal, the higher and sharper are the peaks. This is illustrated in the S(q)s shown at the right. There the dashed curve is for a crystals with twice the number of molecules, as the S(q) plotted as the solid curve.

This project is a computational project, and will use data science techniques, such as regression (= fitting), studies of correlation, and possibly some neural nets. These techniques will be applied to structure factors and features in structures factors (such as peak heights and widths). The objective is to see how best to obtain crystal sizes plus robust error estimates on this size. We will also see if crystal temperatures can be estimated from S(q)s. Thus, this project would suit a student who likes computation. Regarding languages, the student will be expected to write their own code in Fortran or python or ….

The data science techniques will be applied to an existing set of S(q)s, which are of a nanocrystals generated in computer simulations. As the nanocrystals have been generated in simulations, the exact size of the crystals is known, and these known sizes will be used to validate predictions of the data analysis of the S(q)s. Title: Computer simulation off the crystallisation of mixtures

Co-Supervisor: Supervisor: Richard Sear None

Building/Room: 10BB03 Type of Project Modelling Email: [email protected]

Project Description: Crystals are, by definition, composed of ordered periodic arrangements of molecules or atoms. Simple one component systems such as pure iron, pure argon, etc, often crystallise easily into very well ordered, i.e., few defects in the ordering, crystals. Mixtures often crystallise with more difficulty. For example, if the molecules crystallising are of different sizes, then if a molecule of the larger species gets stuck in lattice position where a smaller molecule should be, this can mess up crystallisation. In mixtures there are ways crystallisation can fail that only occur in mixtures, i.e., that never happen in single component systems.

This project will use computer simulation to study the crystallisation of a simple model mixture, and then look at the resulting crystals, which we expect will be poorly ordered, to see what is going wrong. An example configuration is shown to the left. We will quantify how bad the ordering is and attempt to understand what the cause is, and how we can avoid these problems and produce well- ordered crystals in mixtures.

As a computer simulation project this will suit a student with computational skills. The mixtures will be simulated using DynamoMD, which is free software, and the student will be given code (Fortran or Python) to analyse crystalline ordering. The student will then run the simulations and modify the code, and write new code, to analyse the results. Once we have ideas for what controls the poor ordering, further simulations will be performed to test these ideas.

There are many applications for the crystallisation of mixtures, for example some solid state memories rely on the ultrafast crystallisation of nanosized domains. But despite this importance, a fundamental understanding of why some mixtures crystals in nanoseconds while others never do, or form very poorly ordered crystals, is poorly understood. Title: Data analysis of the shapes of glycine crystals

Co-Supervisor: Supervisor: Richard Sear None

Building/Room: 10BB03 Type of Project Modelling Email: [email protected]

Project Description: Crystals are, by definition, composed of ordered periodic arrangements of molecules or atoms. Their growth is perhaps surprisingly, rather complex. Liquid droplets can grow simply by pairs of droplets coming into contact and coalescing, or simply by absorbing molecules. As crystals have to preserve their ordered lattices, these mechanisms are not available. This complexity has observable consequences, for example, two crystals growing in identical conditions can grow at very different rates, and form crystals of very different shapes.

On the left is a circular well containing 0.l ml of solution of a molecule called glycine. So the circular features in the image are the walls of the well, but the needle-like object at the top left of the well is a glycine crystal. On the right is another well, where the conditions are the same, but the crystal that can be seen in the bottom right of the well has a very different shape. We do not know why. A PhD student, Laurie Little, working in the Soft Matter group has obtained hundreds of images of these crystals, including time sequences of their growth.

This project will use involve writing code to automatically analyse these images, i.e., to read them in, and then to extract and quantify crystal shapes, including during their growth. So it will suit a student with computational skills. The actual analysis of the images could be done in Fortran, Python etc, although some non-Fortran work would be required to input the images. Analysis of crystal shapes will require subtracting before-crystallisation from post-crystallisation images, to identify the crystals, then the set of pixels of the image identified as the crystal will be analysed. The data on crystal shapes will then be studied to look for patterns that we can use to understand why crystals form these shapes, i.e., what the mechanism is that determines these shapes.

Crystallisation is of fundamental interest, as crystals are everywhere from our bones to the computer chips in our mobile phones. Crystal shape is often of interest in those industries that make crystalline products. An example is the pharmaceutical industry. Most drugs (aspirin etc) are made by compacting powders of crystals, and it is notoriously difficult to make tablets from powders of needle-like crystals. Thus there is considerable interest in controlling crystal shape, in addition to our interest in understanding how crystals growing under identical conditions can have such diverse shapes.

Title: Radiation modelling with Geant4

Co-Supervisor: Supervisor: Paul Sellin Michael Hubbard None

Building/Room: N/A Type of Project Modelling Email: [email protected]

Description: This project will model an AmBe neutron-gamma source in a water tank using Geant4 [1]. Geant4 is the leading Monte Carlo radiation physics simulation program which is used in all areas of radiation physics such as high energy physics, nuclear physics and medical physics. The simulation will investigate the neutron and gamma-ray flux within that is produced from the department’s “water tank” AmBe neutron source. Neutron detectors made from plastic scintillators (EJ-209 and EJ-299 [2,3]) will also be modelled to expamine their response to neutron and gamma radiation, and any background radiation from the water tank. As this project focuses on modelling an aptitude for computing is required. No prior experience is required of the Geant4 Monte Carlo software, however you should be willing to learn new computing skills during the project, eg. to carry out some basic data analysis using python. This project will aid the development of pulse shape discrimination (PSD) of neutron and gamma-rays in plastic scintillators using silicon photomultipliers (SiPMs), which is currently being carried being carried out in the radiation and medical physics group.

Skills you will acquire from this project:  Monte Carlo simulation using Geant4.  Statistical and Data analysis using Python  An understanding of the radiation physics of neutron sources.

References [1] S. Agostinelli et al, “Geant4 - A simulation toolkit”, Nuclear Instruments and Methods in Physics Research A 506 (2003) 250-303. [2] N. Zaitseva et al, “Plastic scintillators with efficient neutron/gamma pulse shape discrimination”, Nuclear Instruments and Methods in Physics Research A 668 (2012) 88-93. [3] Z. Hartwig and P. Gumplinger, “Simulating response functions and pulse shape discrimination for organic scintillation detectors with Geant4”, Nuclear Instruments and Methods in Physics Research A 737 (2014) 155-162.

Title: Performance of a Gamma-ray pinhole imaging camera

Co-Supervisor: Supervisor: Paul Sellin Matthew Taggart None

Building/Room: 41BC04 Type of Project Experiment Email: [email protected]

Description: In this project you will measure the imaging performance of a prototype gamma ray imaging camera which has been developed at Surrey for use in localising the position of radioisotope sources. Typical applications of this device include environmental radioactivity measurements, or any other situation where the position of an unknown source needs to be identified. The pinhole imaging camera uses recent developments in photomultiplier tube (PMT) technology which include the implementation of multiple readout anodes, giving a gamma ray detector with a coarse degree of position sensitivity. The project will investigate the properties of a Hamamatsu position- sensitive PMT with a 6 x 6 anode readout. Studies will measure the relative response of each anode by performing gamma spectroscopy studies on standard laboratory sources (241-Am, 22-Na, 60-Co, 137-Cs) using a plastic scintillator. Once the initial detector characterisation has been completed, a pinhole collimator will be used to investigate the imaging performance of the detector for sources positioned at known locations from the sensor.

The student will become familiar with the basic principles of radiation detection, and gain experience using the Maestro Easy-MCA system performing gamma spectroscopy and imaging measurements.

Title: Electrical Conductivity of Polymer Sensors

Co-Supervisor: Supervisor: Paul Sellin Prodromos Chatzispyroglou None

Building/Room: 41BC04 Type of Project Experiment Email: [email protected]

Description: In recent years more and more attention is focused on using organic materials as the active component in various electronic devices, such as light emitting diodes and radiation sensors. Organic electronics benefit from being able to be produced in large scale, with low fabrication cost and low environmental impact. Although their performance cannot yet be compared to conventional inorganic devices that mostly use silicon and germanium, recent studies demonstrate that a better understanding of their electrical properties will boost their performance and will realize organic electronic and photonic devices spanning from field effect transistors, solar cells, light-emitting displays, smart tags and molecular sensors.

The scope of this project is the characterisation and investigation of the electrical properties of polymer sensors which are designed to be used as nuclear radiation detectors. The project includes data acquisition and data processing. The student will conduct current and voltage measurements on the polymer sensors at different temperatures varying from low to room temperature. During the experiment, the polymer sensor will be placed in a thermal insulated enclosure with controlled temperature. A Keithley pico-ammeter will be used to measure the voltage and the current while the low temperature will be achieved by cooling the sensor with cold nitrogen gas. The data will be captured using LabView software and will be processed in Python. No previous experience of computing in either LabView or Python is required, although there will be scope to further develop the supplied software if you wish.

References S.R. Forrest, “The path to ubiquitous and low-cost organic electronic appliances on plastic”, Nature, 428/6986 (2004) 911. V.A. Coropceanu et al, “Charge transport in organic semiconductors”, Chemical Reviews 107 (2007) 926-952. B. Fraboni et al, “Solution‐ Grown, Macroscopic Organic Single Crystals Exhibiting Three‐ Dimensional Anisotropic Charge‐ Transport Properties”, Advanced Materials, 21(18) (2009) 1835-1839.

Title: Characterisation of a compact neutron detector

Co-Supervisor: Supervisor: Paul Sellin Matthew taggart None

Building/Room: 41BC04 Type of Project Experiment Email: [email protected]

Description: In recent years there has been a significant breakthrough in scintillator based radiation detectors – two major advances in detector technology have occurred simultaneously. The first of these is the fabrication of a new class of plastic scintillators which are capable of distinguishing between neutrons and gamma rays through the technique of pulse shape discrimination. The second new technology is the replacement of traditional photomultiplier tubes (PMTs) with solid state devices called silicon photomultipliers (SiPM). The SiPM provides a much smaller optical sensor with similar high gain performance to a traditional PMT, but with some interesting and unique physical properties.

In this project you will be experimentally characterising the performance of a compact scintillator/SiPM detector which can separately measure neutrons and gamma rays. This detector has been produced by an MPhys student last year, and needs to be characterised in details. You’ll learn about the physics of SiPM detectors, the pulse shape discrimination performance of plastic scintillators, and how to use high-speed waveform digitisers to capture pulse shapes from the detector. The data analysis is carried out using python programs which have been written already, although there will be an opportunity to further develop the python data analysis codes.

References [1] N. Zaitseva et al, “Plastic scintillators with efficient neutron/gamma pulse shape discrimination”, Nuclear Instruments and Methods in Physics Research A 668 (2012) 88-93. [2] L. Hermsdorf et al, “Silicon photomultipliers for medical imaging and dosimetry”, Radiation Protection Dosimetry 169 (2016) 430-435.

Title: Hyperspectral imaging for mammography applications

Co-Supervisor: Supervisor: Dr Silvia Pani None

Building/Room: 18BB03 Type of Project Modelling

Email: [email protected]

Project Description:

Hyperspectral imaging, i.e., an imaging modality where the information relative to the energy of the detected photons is retained, is becoming a reality thanks to the availability of position-sensitive spectroscopic detectors.

In X-ray imaging, one of the uses of hyperspectral imaging is the one-shot acquisition of images at several energies, to be combined, by solving a set of simultaneous linear equations, to highlight different component of an object: for instance, bone and soft tissue, or soft tissue and contrast agent.

This project will address, trough modelling, the possibility of using the same technique to decouple the glandular component of breast tissue from the adipose one, thus addressing an important problem in mammography, the fraction of glandular tissue being an indicator of breast cancer risk.

The student will address the optimum energy selection as well as the statistics/dose requirements for structure visualisation. Finally, they will design a test object to validate the model and image it.

Title: The centre of the Milky Way galaxy

Co-Supervisor: Supervisor: Dr Alessia Gualandris Prof Mark Gieles None

Building/Room: 19BC03 Type of Project Literature review

Email: [email protected]

Project Description:

This project is a literature review on the topic of the Galactic centre and what we have learned about its formation and evolution in the past 20-30 years, since the first evidence for a supermassive black hole at the centre appeared. The Galactic Centre is a very rich and dynamical environment, an ideal laboratory to study the physical processes that take place in the vicinity of a supermassive black hole. The student will be required to read recent articles on the composition of the Galactic Centre (the black holes, stars and gas structures) and the physical processes that drive the evolution of the region.

Figure 1. Image of the Milky Way and a laser guide pointed at the Galactic Centre.

Figure 2. Infrared image of the Galactic Centre region around the supermassive black hole SgrA*.

Title: Gravitational waves: sources and detectors

Co-Supervisor: Supervisor: Dr Alessia Gualandris Prof Justin Read None

Building/Room: 19BC03 Type of Project Literature review

Email: [email protected]

Project Description:

This project is a literature review on the topic of gravitational waves, and in particular on the astrophysical sources that are expected to provide measurable signals and the detectors that can be used to identify them. Relevant sources include binaries of neutron stars, stellar mass black holes and supermassive black holes. Gravitational waves from these different sources are expected in different ranges of frequencies and therefore different types of detectors are required to measure their signals. The student will be required to read relevant articles on gravitational waves sources, focussing on the predicted rates of coalescence expected from each class, as well as on detectors and observational techniques.

Figure 1. Binary of black holes emitting gravitational waves.

Figure 2. First gravitaional wave detection by the Advanced LIGO interferometer. Title Dosimetry for Hand radiotherapy

Degree: all BSc in Physics, especially PNA

Supervi Co- Annika Lohstroh None sor: Supervisor

Room: 17BB03 Department of Physics Faculty of Engineering & Email: [email protected] Physical Sciences Address University of Surrey Phone: (01483) 689419 GU2 7XH United Kingdom

Group: RAM Type: Experiment

The interaction mechanism of X-ray photons depends on the atomic number of the material they interact with. Hence, the dose deposited into bonny tissues or tissue near bones will differ from the dose deposited near soft tissue, due to the higher atomic number elements present in the bone material.

Conventional dosimetry approaches often assume soft tissue Project equivalence of the irradiated material and hence may underestimate descript the delivered dose to the bones and in the vicinity of bones, which ion: may play a significant role at the kV energy range employed during radiotherapy treatment of tumours located on fingers/hands.

Hence, the aim of this project is to develop a suitable phantom to simulate the Hand geometry and subsequently carry out irradiations and analysis of dose deposition for a number of geometries and irradiation conditions.

Last Updated 10th October 2016 :

Title Bohmian Trajectories in Quantum Scattering

Degree: All programmes

Supervisor: Jim Al-Khalili

Building/Room: 08BB03 Type of Modelling/ Email: [email protected] Project: Mathematical

Project Description

In spite of the undoubted success of the quantum formalism, its interpretation continues to present difficulties. The two most popular are the Copenhagen view, which denies the existence of an objective reality in the absence of measurement, and the Many Worlds interpretation, which assumes a deterministic objective reality and is based on very few assumptions, but hypothesises an infinite number of parallel universes in which all possible outcomes for a quantum system are realised. Bohmian mechanics offers an alternative the these two. It is often referred to as a non-local hidden variables approach.

The essential feature of the approach due to Bohm is to reformulate quantum mechanics in a language which is closer to that of classical physics. For instance, here particles have both definite position AND momentum, although these cannot be measured simultaneously. By assuming wave function satisfies the Schrödinger equation one can obtain two real equations, one of which is a classical equation of motion supplemented by an additional potential term (called the quantum potential) that is responsible for the novel quantum behaviour. The second equation is a continuity equation corresponding to the conservation of probability. The solutions of the equation of motion give rise to a set of individual particle trajectories arising from various initial conditions.

The project requires the student to apply this approach to a 1-D scattering problem such as quantum tunnelling Bohmian trajectories in the two slit through a potential barrier, or to find an alternative experiment. Particles go through description of what happens in the famous two-slit one slit or the other but the experiment. We have been taught that each particle quantum potential pervades both. somehow goes through both slits at once. Not necessarily, according to the Bohmian view.

The work will involve algebraic development of the formalism as well as numerical (computational) calculations with the results displayed graphically.

Title Testing semi-classical approximations to quantum scattering

Degree: All programmes

Supervisor: Jim Al-Khalili

Building/Room: 08BB03 Type of Modelling/ Email: [email protected] Project: Mathematical

Project Description

Modelling quantum scattering in atomic, nuclear and particle physics at high energies can be simplified considerably by using semi-classical approximation approaches, such as the Eikonal and WKB methods.

To obtain observables (quantities that can be measured in an accelerator for example) we need to calculate not the wave function, but the scattering amplitude. In semi-classical approaches such as the eikonal model this involves numerically evaluating an integral:

. � � = −�� � �� � 2�� sin � 2 � − 1

In this equation, � is the zeroth order Bessel function, k is the incident wave number, b is the impact parameter between projectile and target and � � is the eikonla phase shift function which depends in a simple way on the interaction potential between the two interacting particles.

This project involves writing a fortran program that calculates the elastic scattering cross section using both the eikonal and WKB models. It is planned that a comparison of the cross sections can be made for a variety of energies and nuclear projectiles and targets to study when the methods are valid and under what conditions they break down.

Title Testing the Quantum Zeno and Anti-Zeno effects in proton tunnelling

Degree: All programmes

Supervisor: Jim Al-Khalili

Building/Room: 08BB03 Type of Modelling/ Email: [email protected] Project: Mathematical/ Computational

Project Description

According to the quantum Zeno effect, frequent observations of a quasi-stable quantum system will inhibit its evolution, whether this involves nuclear decay, quantum tunneling or simply propagation of a particle, since each observation collapses the wave function, removing those components that had begun to explore the regions of space where, for example, decay may take place. Conversely, the anti-Zeno effect happens when the act of measurement actively encourages the evolution of the quantum state. In proton tunneling through a barrier separating two potential wells, it is not clear which of the two effects will win since the result depends on the shape of the double well, the height of the barrier and The quantum Zeno hence the distribution of the energy eigenvalues. effect is commonly known as ‘the watched This project involves setting up a simple 1-D double pot never boils’. well potential in which a particle is placed initially on one side. By numerically solving the time dependent Master Equation with a dissipative term (equivalent to the Schrödinger equation, but with coupling to an external environment) the effect of measurement on the likelihood of the particle tunneling through to the other well can be determined.

Energy eigenstates in an asymmetric double well potential. Only a few have amplitudes in the shallow well and contribute to tunnelling.

Title Crystallisation in Elastomers: Hardening Soft Matter

Supervisor: Prof. J.L. Keddie Co-Supervisor 4 BB 03 Building/Room: Type of Experimental Email: [email protected] Project Phone: 6803

Project Description:

Elastomers are made from crosslinked polymer networks. Their elasticity makes them useful in everyday objects such as car tyres, rubber bands, and laboratory gloves. At the molecular level, they have randomly coiled polymer segments between the crosslinking points that act as tiny springs. Elastomers are able to be strained to high values before failing, but they typically have a low elastic modulus. Crystallisation of the polymers provides a way to adjust the viscoelastic properties. The presence of crystals in an elastomer raises the elastic modulus.

In this project, crystallisation in poly(chloroprene) elastomers will be investigated experimentally. This polymer slowly crystallises at room temperature, which is below the crystal melting temperature of approximately 38 °C. The rate of crystallisation increases with decreasing temperatures below this point.

The student will use dynamic mechanical analysis to evaluate the elastomers as a function of their aging time and temperature, both of which determine the level of crystallinity. The effect of crystal melting on the viscoelastic properties will be determined. The student will measure hardness of poly(chloroprene) films using a König hardness tester at regular intervals of time as crystallisation occurs. The increase in hardness will be correlated with the extent of crystallisation determined via differential scanning calorimetry. The project will aim to find the optimum thermal treatments to obtain partially crystallised elastomers with a high elastic modulus.

The project would particularly suit a student with a background knowledge of soft matter physics who is seeking practical work. A PhD student and a technician will provide support in the laboratory, which is in the AZ Building. Title Beating the Diffraction Limit with Super-Resolution Microscopy

Supervisor: Prof. J.L. Keddie Co-Supervisor 4 BB 03 Building/Room: Type of Literature Review Email: [email protected] Project Phone: 6803

Project Description:

Ever since the work of Abbé, it had been assumed by physicists that optical microscopes could not provide image resolution at length scales below about one-half of the wavelength of light. Starting in the 1990s, super-resolution optical microscopy techniques were developed to increase the spatial resolution beyond the so-called classical diffraction limit by using novel optical and computational methods1 or by exploiting the photochemistry of specific fluorescent dyes.2 Development of the family of super-resolution optical microscopy techniques culminated in the award of the 2014 Nobel Prize in Chemistry to the primary inventors.

Over the past two decades, super-resolution techniques have primarily been applied to cellular biology. This project’s particular focus will be on soft matter systems. The project will review the literature to determine the extent to which super-resolution microscopy techniques have been used previously to study colloids, polymers, and liquid crystals. Of special interest are two particular techniques: dSTORM and SIM.

Direct stochastic optical reconstruction microscopy (dSTORM),3 which is a super- resolution technique based on single molecule localisation, provides the highest resolution images achievable using far-field optical imaging (down to 15–20 nm at a speed of approximately one image per minute). In contrast, structured illumination microscopy (SIM)4 allows for the observation of processes in (near) real time (currently 14 frames per second) with a more modest resolution enhancement down to ~100 nm.

The strengths and limitations of the various techniques of super-resolution microscopy will be determined through careful assessment of published results. After gaining a deeper understanding of the techniques, the student will identify opportunities for using them to answer questions in soft matter physics.

References

[1] E. J. Rees, M. Erdelyi, D. Pinotsi, A. Knight, D. Metcalf and C. F. Kaminski, Optical Nanoscopy, 2012, 1, 1-10. [2] G. T. Dempsey, M. Bates, W. E. Kowtoniuk, D. R. Liu, R. Y. Tsien and X. Zhuang, Journal of the American Chemical Society, 2009, 131, 18192-18193. [3] M. J. Rust, M. Bates and X. Zhuang, Nature Meth, 2006, 3, 793-796. [4] M. G. L. Gustafsson, Journal of Microscopy, 2000, 198, 82-87. Title Lightning

Degree: all BSc in Physics

Supervis Co- Annika Lohstroh None or: Supervisor

Room: 17BB03 Department of Physics Faculty of Engineering & Email: [email protected] Physical Sciences Address University of Surrey Phone: (01483) 689419 GU2 7XH United Kingdom

Group: CNRP Type: Literature review

The aim of this literature review is to establish and summarise the optical signatures emitted during lightning in order to inform a future lightning detection system based on the visible light signatures. For this purpose, the student will be asked to establish

- an overview of lightening occurrences and “hot spots” around the world. - the state of the art of current lightning detectors (including less Project successful approached may potentially not be pursued at the descripti current time). on: - An overview of the known optical emissions (spectral and temporal) associated with lightening and the challenges in their detection (modifications by clouds/atmosphere/rain etc).

The information gathered shall then be used in order to make recommendations regarding the advantages and disadvantages in lightening detection, the information that can be gained from it and minimum requirements in order to exclude terrestrial interference.

Last Updated 6th October 2016 : Title The NMR relaxation characteristics of drying wood. BSc in Physics/Physics with All Degree: Particularly suited to students taking PHY3045: Medical Imaging Co- Supervisor: Professor P.J. McDonald Supervisor Room: 19BB03 Dept. of Physics Faculty of Engineering Email: [email protected] Address & Physical Sciences Phone: 6798 Group: M: Soft Matter / Materials Type: Experimental Nuclear magnetic resonance is the technology underpinning Magnetic Resonance Imaging (MRI). The contrast in medical MR

images arises from differences in nuclear spin T2 relaxation times between tissue types. This project uses bench-top nuclear magnetic resonance (NMR) equipment to measure the NMR spin-spin relaxation times of water hydrogen in wood. This project is interesting as we have an on-going research programme with Forest Research (part of Forestry Commission) to introduce NMR / MRI to Forestry as a high-tech tool for the management of UK wood resources. The relaxation time distribution in wood is complex. Water chemically bound into wood fibers has a very short relaxation time (microseconds). Free water absorbed into cell walls has a slightly longer relaxation time (millisecond). The relaxation time of water within the cells is longer still (10-100 ms). However, these times are Project very moisture content dependent and are dependent also on whether description: the sample is late or early wood (i.e which part of the tree ring) or sapwood or heartwood. We now believe that the relaxation times also depend on whether the wood sample has ever been dried out. In other words, there is hysteresis around the sorption cycle. The objective of this project is to measure the relaxation time distribution in a piece of “never dried” wood of known type, then progressively dry the wood and then re-hydrate the wood, measuring

the T2 distribution all the way around. We will look for reversible / irreversible effects and try to correlate these with sample mass and what is known about changes to wood cell structures as they dry: e.g. capillary forces collapsing cells. If sufficient time is available it may be interesting to compare fast and slow drying as this has an effect in other material systems and also to investigate whether there are irreversible effects on a second sorption cycle (we expect not).  To measure the T2 distribution of wood. This will require some dexterity in terms of sample handling and experiment design and learning to use a bench top NMR spectrometer.  To measure this distribution around a sorption cycle. This will Main require careful experimental planning and attention to detail as the experiment will take 2 to 3 weeks to complete if the Objectives wood is dried slowly and so cannot easily be repeated.  To analyse the data using exponential fitting and inverse Laplace transform software.  To interpret the data through gained understanding of wood science (guided reading / literature survey). Training in the use of the NMR spectrometer and in the data analysis Technical can be provided. The analysis is likely harder / more time consuming Aspects than actually taking the data if the experiment is (i) well planned and (ii) the analysis is done carefully. Title Fluid dynamics: Lattice Boltzmann simulations of liquid/vapour in partially permeable materials. Degree: BSc in Physics/Physics with All Supervisor: Professor P.J. McDonald Co-Supervisor Room: 19BB03 Faculty of Engineering Email: [email protected] & Physical Sciences Address University of Surrey Phone: 6798 GU2 7XH United Kingdom Group: M: Soft Matter / Materials Type: Numerical modelling In 2014/15 Michael Turner in his Final Year Project showed that it as possible to combine two established Lattice Boltzmann methods to describe the condensation of liquid and vapour in partially permeable materials using effective media methods: McDonald, PJ and Turner, MN (2015), Modelling and Simulation in Materials Science and Engineering, 24 pp. 1-15.

However, the so called Shan-Chen potential that he used in his simulations was a very simple one that really only allowed a factor of 10 or so difference in density between the liquid and vapour. This is, Project of course, a serious limitation for real, practical, applications involving water. description: A number of alternate potentials are now proposed in the literature. The objective of this project is to research these different potentials and to discover by experiment which of them is the best from the perspective of allowing Turner’s model to continue to work while at the same time allowing a very much greater density ratio between the liquid and vapour.

Once the best potential is identified and the model and code is validated, the idea is to create a more realistic numerical simulation of the sorption cycle of a wood cell than has hitherto been possible.  To conduct a literature survey of recent Shan-Chen like potentials that allow a greater liquid – vapour density ratio. Main  To adapt Turner’s MATLAB code to use these new potentials. Objectives  To test if they work in an effective media model.  To create a more realistic numerical simulation of the sorption cycle of a wood cell than has hitherto been possible. Technical Some knowledge of MATLAB is an advantage. The LB algorithm is fairly straightforward to understand and learn with plenty of good Aspects introductory texts and on-line materials. Title Design and Build an MRI Magnet Demonstrator Degree: BSc in Physics/Physics with All Supervisor: Professor P.J. McDonald Co-Supervisor Room: 19BB03 Faculty of Engineering Email: [email protected] & Physical Sciences Address University of Surrey Phone: 6798 GU2 7XH United Kingdom Group: M: Soft Matter / Materials Type: Experiment + modelling The University and a local company are seeking Government funding to build a magnetic resonance imaging (MRI) magnet suitable for imaging water inside large concrete structures with a view to diagnosing degradation: concrete cancer. Since you cannot wrap a bridge in a magnet, the magnet must be “one sided” and “work” when it is placed on the concrete surface. This is a so-called “Sweet-Spot” design. A magnet of this kind can be constructed out on many little bar magnets glued together in an appropriate, but hopefully simple, geometry – the LEGO approach to magnet design. The aim of this project is to make a mock-up of the real thing out of little bar magnets to check the design is OK, to look for any obvious flaws or difficulties in the construction process, and to get a feel for how sensitive the design is to slight manufacturing errors. Project Within this project you will first optimize the design of the magnet description: using numerical modelling. In particular, you will need to write a finite element computer code to solve the Laplace equation for the magnetic potential as described in module PHY2065. The boundary conditions are that the potential is zero at infinity and a constant over the magnetic poles. You can then add and move your LEGO bricks of magnetic material around in the simulation until the magnetic field “shape” is as good as you can get – you have a nice “Sweet Spot” of uniform field displaced from the structure surface. Then, you will make a mock-up of the magnet by gluing together a large number (of the order 50) small bar magnets. This will take a bit of ingenuity since the magnets will naturally try and join together in one long string. You will need to hold them in place until the epoxy sets! Finally, you can measure the magnetic field using a Hall Probe and compare it to your simulation.

 To write a finite element modelling code to solve Laplace Equation.  Use the code to optimise the magnet design, bearing in mind Main that you will need to make it for real, so the design cannot be Objectives too complex.  Make a mock-up of the design with small bar magnets.  Use a Hall probe to measure the field created and compare to the simulation. You will need reasonable numerical modelling skills as developed in Technical year 2. You can use any language, but as supervisor I like MATLAB for Aspects this. You will need good experimental / practical skills to actually make the magnet. Title The Vacuum Bazooka Degree: BSc in Physics/Physics with All. Co- Supervisor: Professor P.J. McDonald Supervisor Room: 19BB03 Faculty of Engineering Email: [email protected] & Physical Sciences Address University of Surrey Phone: 6798 GU2 7XH United Kingdom Numerical modelling Group: Type: and experiment. Dependent on your point of view, the Vacuum Bazooka is an executive toy or a School Physics teaching aid. Using 3 tubes, a T- Piece connector and a syringe, a ball bearing is turned into a deadly projectile. You can find YouTube demonstrations of fancy versions with vacuum cleaners very easily. Only this year, in School Year 10, is Einstein’s great-great- grandchild who has inherited his inspirational genes and who starts to ask more challenging questions. Project “Can you make the projectile show simple harmonic motion?” the 14 year old child asks, then worse “I think you can, but how much description: damping is there?”. In order to answer the questions, you need a better analysis and numerical simulation of the Vacuum Bazooka to discover what happens when you vary its use somewhat. The purpose of this project is to make a detailed analysis and from that a numerical simulation of the Vacuum Bazooka in order to answer the questions. Ideally, there will be sufficient time at the end to build a bazooka and to test your results experimentally.

 To write down the equations of motion for the projectile in a vacuum bazooka including a careful consideration of the damping terms.  To write a computer program to solve the equations of motion and to investigate carefully what happens under different boundary conditions. Main  To discover the conditions necessary for simple harmonic Objectives motion.  To build a simple practical bazooka that demonstrates this “unusual” behaviour for a bazooka and to compare experimental data to the results of the numerical simulation.  Hence, to measure as many basic parameters that describe the tubes and ball bearing as possible in what will undoubtedly be an unorthodox way. Technical Reasonable programming skills, ability to fashion a Bazooka from Aspects “odds and ends” and imagination!

Title: How simple are simple stellar populations?

Co-Supervisor: Supervisor: Prof Mark Gieles Dr. Eduardo Balbinot

Building/Room: 18 BC 03 Type of Project Lit review

Email: [email protected]

Project Description:

Globular clusters (GCs) are old (10-13 Gyr) stellar systems containing 10^5 – 10^6 stars. The stars are all believed to have formed at the same time and the iron abundances of stars in a GC are very similar. This has led people to believe that all stars formed from the same gas cloud that was well mixed before the stars formed. These properties have made GCs the archetypical “simple stellar populations” (SSP) against which almost every stellar evolution model is tested.

In the last decade, however, it was found that a large fraction (sometimes up to 70-80%) of the stars in GCs have strange abundances (Carretta et al. 2009). They are enriched in certain elements (mainly Na) and depleted in others (mainly O). The Na-O anti-correlation is the result of hydrogen burning at high temperatures. At the same time, the main sequence of many GCs are broadened, or even split in multiple distinct main sequences (e.g. Piotto et al. 2007). The bluer main sequence is thought to be the result of He enrichment, another result of H burning.

The stellar populations of GCs can not be understood from age and iron abundance alone, which has been known since the 60s: some clusters are very similar in age and iron abundance, and have very different stellar populations (such as M3 and M13, e.g. Arp 1955). This is the so-called “second parameter” problem.

In this project you will do a literature review and show how the multiple population phenomena evolved from a curiosity, to a major scientific problem. There have been various theoretical “scenarios” that could explain this. You will compare them and discuss where they succeed and where they fail.

Arp 1955, AJ, 60, 317 Carretta et al. 2009, A&A, 505, 117 Piotto et al. 2007, ApJ, 661, 53

Title: Comparing velocity anisotropy of Milky Way dwarf galaxies and globular clusters

Co-Supervisor: Supervisor: Prof Mark Gieles Dr. Eduardo Balbinot

Building/Room: 18 BC 03 Collect data from literature and Type of Project some statistics Email: [email protected]

Project Description:

Galaxies grow via accretion of smaller structures and mergers with other galaxies. Traces of this are found in the Milky Way stellar halo in the form of stellar streams from disrupted dwarf galaxies.

This merger scenario predicts a clear signal in the velocity structure of accreted stars/systems, namely a bias towards radial orbits, meaning that there is preferred direction for the velocity vector towards the centre of the Galaxy. If we look at the orbits of dwarf galaxies, then it appears that they are less radial than expected from predictions from cosmological models (Lux et al. 2010).

One possible explanation for this is that the dwarf galaxies on radial orbits have been destroyed because they experience stronger tidal fields when they move close to the Galactic centre. If that is true then the stars that came from the disrupted dwarf galaxies should be on more radial orbits. However, it is hard/impossible to get a census of all disrupted dwarf galaxies!

The more massive dwarf galaxies may have brought in globular clusters (GCs) and for these systems we can determine the orbits. In this project you will compare the velocity anisotropy as determined by Dinescu et al. (1999) of GCs that are classified as accreted and formed in-situ (Leaman et al. 2013) and compare this to the results of dwarf galaxies. Some python programming and statistics is needed for this project.

Dinescu, Girard & van Altena 1999, ApJ, 117 Leaman, Vandenberg & Mendel 2013, MNRAS, 436, 122 Lux, Read & Lake 2010, MNRAS, 406, 2312

Title Liquid exfoliation of novel two-dimensional nanomaterials

Supervisor: Dr. Izabela Jurewicz Co-Supervisor Prof. J.L. Keddie

Building/Room: 03BB03 Type of Experimental Email: [email protected] Project Phone: 4196

Project Description:

12 years after separating atomically thin graphene sheets from graphite using Scotch Tape1, and 8 years after liquid separation of graphite to make individual atomically thin graphene sheets on large scale was introduced2, two new types of layered

materials, MoS2 and WS2 have been added to the already broad family of 2D nanomaterials.3,4 They can undergo remarkable changes in their electronic structures depending on the number of layers: from indirect-band-gap bulk semiconductors to direct-band-gap monolayer semiconductors thus have a great potential in various applications ranging from optoelectronic devices, transistors to solar cells, etc.

The project will be focused on the optimisation of liquid phase exfoliation of bulk materials to produce predominantly

individual sheets of MoS2 and Ws2 respectively in surfactant- assisted dispersions using ultrasonication and centrifugation procedures. The characterisation procedures will involve using modern analytical techniques such as Atomic Force Microscopy, Raman spectroscopy and UV-Vis spectroscopy to relate the

changes in electronic structure and properties of MoS2 and Ws2 Fig. Microscopic characterization of size- nanosheets with thickness. selected WS2 nanosheets. (A−D) TEM (A,B) and AFM (C,D) images of nanosheets, size selected with upper and lower centrifugation 1. K. S. Novoselov et al., Science 306, 666 (2004) speeds of (A,C) 1.5 krpm and 2 krpm and 2. Y. Hernandez et al., Nature Nanotechnology 3, 563 - 568 (B,D) 6 krpm and 7.5 krpm, respectively (2008) (adapted from from ref. 4). 3. C. Backes et al., Nature Communications, 4576 (2014) 4. C. Backes et al., ACS Nano 10, 1589−1601(2016)

Title Spinning conducting and strong polymer fibres with carbon nanotubes for smart textile applications Supervisor: Dr. Izabela Jurewicz Co-Supervisor Prof. J.L. Keddie

Building/Room: 03BB03 Type of Experimental Email: [email protected] Project Phone: 4196

Project Description:

Carbon nanotubes (CNTs) are cylindrical molecules that have a diameter in the nanoscale, one hundred times the tensile strength of steel, thermal conductivity better than diamond, and electrical conductivity similar to copper, but with the ability to carry much higher currents. This makes them potentially useful in many applications ranging from structural composites to optoelectronics. It is extremely difficult however, to translate the fascinating nanoscale properties to the macroscopic level of objects that are large enough to be practically visible with the naked eye. This can be potentially achieved, by the incorporation of CNTs to the macroscopic continuous polymer fibres which are of great interest to textile 1-4 manufactures. CNTs could be used to make lightweight Fig. (A) Stable SWNT suspension in a multifunctional textiles for smart clothing that integrate medical lithium dodecyl sulfate/dionized water solution. These suspensions are used as the sensors, antennas, and other devices. ‘‘ink’’ for spinning nanotube gel fibers. (B) The ink in (A) is injected into a glass pipe (where the coagulation solution is coaxially flowing) to form the The aim of the project is to develop a composition-property diagram gel fiber, which travels along the glass pipe and is eventually collected on a rotating mandrel in a water bath. A hundred meters showing the change in mechanical strength and electrical of gel state fiber tightly wrapped on a mandrel is shown. (C) These pictured gel conductivity of macroscopic polymer fibres as a function of fibers act like a rubber, reversibly elongating up to 400% before breaking. polymer/CNT ratio. The project will involve the fabrication of (D) The gel is subsequently drawn out of the bath, passed over a series of godets and polymer/CNT dispersions at various ratios and coagulation-spinning through an acetone washing bath during a drying process, and finally wound onto a of macroscopic long fibres using built-in-house spinning apparatus. spool (pictured, with a wound nanotube fiber). (E) Scanning electron micrograph of You will also perform electrical conductivity and stress-strain the end of an undrawn composite carbon nanotube fiber, showing carbon nanotubes measurements on resulting fibres. in a polyvinyl alcohol matrix(adapted from ref. 4)

1. Ijima et al., Nature 354, 56–58 (1991) 2. Dalton et al. Nature 423, 703 (2003) 3. Mercader et al. J. Appl. Polym. Sci., 125: E191–E196 (2012) 4. Dalton et al. J. Mater. Chem., 14, 1-3 (2004)

Title Fusion dynamics of light exotic nuclei using classical mechanics and stochasticity Supervisor: Dr. Alexis Diaz-Torres Co-Supervisor Building/Room: 01BB03 Type of [email protected] Modelling Email: Project k Phone: 01483689855

Project Description:

Reactions between atomic nuclei are a driving force in nature. Low-energy fusion reactions in stars and supernovae create the elements we see around us. Nuclear physics research has entered a new era with developments of new generation exotic beam facilities such as FAIR in Europe with which the UK nuclear physics community is closely collaborating. This project aims at learning about the fusion dynamics of weakly-bound light nuclei at low collision energies. These nuclei are very fragile and can be easily dissociated into fragments when they interact with other nuclei. A Fortran code will be provided which simulates the reaction dynamics of a weakly-bound two-body projectile on a stable heavy target [1]. It exploits the concepts of a classical Newtonian trajectory as well as the Monte Carlo sampling of a probability density [2,3].

[1] A. Diaz-Torres, Computer Physics Communications 182 (2011) 1100-1104. [2] A. Diaz-Torres, Journal of Physics G 37 (2010) 075109-1-10. [3] A. Diaz-Torres et al., Physical Review Letters 98 (2007) 152701-1-4.

Some reaction processes when a light exotic (two-body) projectile interacts with a stable heavy target Title Quantum tunnelling in low-energy nuclear fusion

Supervisor: Dr. Alexis Diaz-Torres Co-Supervisor Building/Room: 01BB03 Type of [email protected] Modelling Email: Project k Phone: 01483689855

Project Description:

Low-energy fusion reactions in stars and supernovae create the elements we see around us. Although the stars can be very hot (~109 Kelvin), the kinetic energy of the fusing nuclei is relatively small (~keV) in the energy scale of nuclear physics (~MeV). Fusion happens by quantum tunnelling that is a quantum phenomenon where a particle tunnels through a barrier that it classically could not overcome. The aim of this project is to learn how two complex atomic nuclei fuse at low collision energies. A Fortran code will be provided to understand and quantify the fusion probability and its dependence on the structure of the fusing nuclei [1].

[1] K. Hagino et al., Computer Physics Communications 123 (1999) 143-152.

Potential energy as a function of the internuclear separation (black curve) during the fusion process of two nuclei. Quantum tunnelling happens when the collision energy is smaller than the height of the Coulomb barrier and the nuclei are trapped at the potential pocket forming a compound nucleus. Life on Mars…?

Supervisor: Professor Stephen Sweeney Co-Supervisor

Building/Room: 07BB03 and 12ATI01 Literature Type of Project Review and Email: [email protected] Modelling Phone: 6800

Project Description:

How can we tell if there is life elsewhere in the Universe? The markers of life can be found in the chemical composition of an atmosphere, with CO2, CH4 and other gases being indicative of living processes. Spectroscopy is a powerful technique that we can use to understand the properties of matter and is routinely used to discover information about materials. Practical examples of spectroscopy include environmental sensing; whereby the absorption of light in the air can be used to measure greenhouse and pollutant gases or to simply determine whether fruit is ripe. In the search for life, this technique can be used on-board satellites and other probes to remotely measure the concentration of gases such as CO2 or CH4 or locally to measure vegetation and deforestation on Earth. For Space exploration, spectroscopy can be used to probe the make-up of non-terrestrial atmospheres and rocks. Such techniques are currently being used by the Curiosity rover to explore Mars and have been used to detect the presence of water. One of the main challenges in spectroscopy is that spectrometer technology is often large and cumbersome making it expensive to produce. This project focuses on developing compact, low mass approaches to spectroscopic sensing which can easily be included in a mission payload.

In this project you will look at new approaches to making solid-state spectrometers/sensors that are so small that they can easily be transported in quantity on-board satellites or planetary probes or rovers. Your aim will be to explore the literature and potential technological approaches that show the most promise. For your chosen approach you will then look into the feasibility and requirements of the system and undertake preliminary modelling of how the solution should behave for your target environment (e.g. Mars or a moon).

This project is ideally suited to someone with an interest in applying physics knowledge to new technology. This project involves being creative and is suitable for students with an interest in photonics and Space research. The weighting of the literature review, vs. modelling of the project will largely be determined by project progress and the student’s strengths, interests and abilities in each area.

Curiosity Rover © NASA Enabling Medical Diagnosis with Mobile Phones

Supervisor: Professor Stephen Sweeney Co-Supervisor

Building/Room: 07BB03 and 12ATI01 Literature Type of Project Review and Email: [email protected] Modelling Phone: 6800

Project Description:

Spectroscopy is a powerful technique to understand the properties of matter and is routinely used to discover information about materials. Practical examples of spectroscopy include environmental sensing; whereby the absorption of light in the air can be used to measure greenhouse and pollutant gases or to simply determine whether fruit is ripe. Recent studies have shown that the chemical markers in exhaled breath can contain early indicators of diseases such as various forms of cancer. These markers have characteristic absorption lines in the mid-infrared part of the spectrum giving rise to optical “fingerprints” for disease. There is consequently a strong interest in developing compact mid- infrared photonic technologies (lasers, LEDs, photodetectors, spectrometers etc.) that could be used to detect these fingerprints non-invasively. The long-term goal of this work is to develop compact, e.g. mobile phone based, sensors that can detect traces of illness using only exhaled breath.

In this project you will undertake an in-depth literature based study to determine the mid-infrared fingerprints of various diseases. You will then explore the technological solutions available to enable the detection of these fingerprints. This will combine a survey of the literature with modelling of the typical requirements of a detection system. It will show what can be achieved with current technology and investigate how technologies such as Quantum Cascade Lasers may be developed to make portable sensors possible. Depending on the direction that the project takes, there is also the possibility to undertake photonic device modelling.

This project is ideally suited to someone with an interest in applying physics knowledge to new technology. This project involves being creative and is suitable for students with an interest in photonics and medical physics. The weighting of the literature review, vs. modelling vs. experimental parts of the project will largely be determined by project progress and the student’s strengths and interests in each area. Title: Photon-assisted quantum transport in a single-atom transistor

Supervisor: E Ginossar Co-Supervisor S Clowes Building/Room: Type of Computer modelling Email: [email protected] Project Phone:

Project Description

Silicon-based devices at the atomic scale are central to nanotechnology and solid state quantum computers. Recent advanced fabrication techniques such as ion beam implantation and scanning tunnelling microscope lithography have paved the way to experimental realizations of these devices, with the first demonstration of a single- atom transistor in 2012 [Fuechsle1 et al., Nature Nanotechnology 7, pp 242-246]. In these devices the conventional scheme for controlling the electrical current is utilizing a gate voltage which has to be fabricated in the sample. We wish to carry out a theoretical analysis of the possibility of using an external THz laser to control the charge transport. This method of optical control might prove to be useful not only for nanoelectronics but also quantum computing with dopants in Silicon. The project is closely related to the ongoing experimental efforts in the Photonics and Quantum sciences group at the University of Surrey.

The system under study is a single Phosphorous dopant implanted in Silicon (c.f. figure). This dopant is coupled to two electrical leads called the source and the drain, and an external optical field used for the control purpose. Electrons can tunnel through the dopant resulting in an electric current flowing between the source and the drain. The tunnelling current depends strongly on the quantum state of the dopant, which can be altered by shining THz photons on it. In this project you will simulate the steady state of a dopant interacting with the optical field and the two electrical leads, and from this information estimate the amplitude of the current across the channel.

Figure 1: A Phosphorous dopant implanted in Silicon. The tunnelling current of the electrons through the dopant can be controlled by changing the quantum state of the dopant, which is accomplished by an external THz laser. Title: High energy states in superconducting cavity quantum electrodynamics

Supervisor: E Ginossar Co-Supervisor Building/Room: Type of Analytical+Computer Email: [email protected] Project modelling Phone:

Project Description

Future quantum computing relies on reliable realisations of artificial highly coherent ‘qubit’ (quantum bit) systems. IBM, Google, Intel are currently supporting the development of large scale quantum processors based on the technology of superconducting circuits. In this project we will use the Hamiltonian of such a system to explore the yet poorly understood properties of high energy states. In particular we will focus on the energy exchange mechanism between the qubit and its environment, a key to understanding fast efficient measurement of quantum states. The research hypothesis is that this mechanism could explain the yet not understood nonlinear response of the system as measured in recent experiments. The project will include analysing the quantum mechanical solution of the Hamiltonian and calculations will be performed with the software Mathematica. A good grounding in quantum mechanics is recommended.

The nonlinear response as a function of frequency

and power

A superconducting processor (Google) 1

Year 3 final project: Dark Matter Supervisor: Prof. J. I. Read | [email protected] Project type: Astrophysics, Theory/Computation Degree: Physics with Astronomy Desirable skills: Strong work ethic; good literature review skills

1 Project description Dark matter is a mysterious substance that appears to make up most of the mass of the Universe, yet we do not know what it is. Our best guess so far is that it is some new particle of nature, with popular candidates including ‘sterile neutrinos’, ‘axions’ and super-symmetric ‘WIMPs’. A model in which the dark matter fluid is non-relativistic when it decouples from the expansion – so-called ‘cold’ dark matter – gives a remarkable match to a wide array of data, from the cosmic microwave background (CMB) radiation to the clustering of galaxies. However, on smaller scales there have been long-standing tensions that might hint to more complex dark matter, or a problem with our numerical models. Finally, there are significant world-wide efforts to create or detect these dark matter particles. Each type of particle requires its own strategy. For example, WIMPs could be created at the Large Hadron Collider in Cern, detected in experiments deep underground, or spotted through their annihilation into gamma-rays, using gamma-ray telescopes like the FERMI satellite. By contrast, sterile neutrinos would not be created at the LHC nor produce gamma-ray emission, but could be detected through their decay into X-ray photons. Axions require another suite of experiments again. So far, apart from interesting hints, no smoking gun signature for dark matter has yet been found. This has led some to question the paradigm, exploring alternative theories of gravity or even more exotic possibilities. In this literature review project, you will explain the classical evidences for dark matter (rotation curves and the mo- tion of galaxies inside galaxy clusters) and the more modern evidence that comes from the CMB, gravitational lensing and other cosmological probes. You will sum- marise what we know about its nature to date and any outstanding puzzles. You will discuss alternative gravity theories and compare and contrast these with par- ticle dark matter candidates, critically as- sessing which is more likely given the cur- rent data. Finally, you will assess the prospects for detecting or ruling out dark matter particles in the next 5-10 years.

Figure 1: The remarkable “bullet cluster”, 1E 0657-56. This composite image shows the galaxies seen in optical light, the hot X-ray emitting gas (red contours) and the total mass distribution derived from weak grav- itational lensing (blue contours). The cluster is really two clusters that are in the processes of merging. The smaller of the two (right) has just ploughed through the larger (left) leaving behind a cone of hot X-ray gas. Like all galaxy clusters, most of the mass is in a mysterious dark matter component, but what is special is that the bulk of the visible mass (red) is in a physically distinct location from the two peaks in the gravitational field (blue). This is very hard to explain unless dark matter is a dynam- ical ‘collisionless’ fluid, most likely made up from weakly interacting massive particles (WIMPs) that lie beyond the standard model of particle physics. The race is on to either detect or create such particles in labora- tory experiments all over the world. Credit: X-ray: NASA/CXC/CfA/M. Markevitch et al.; Lensing: NASA/STScI; ESO WFI; Magellan/U. Ari- zona/D. Clowe et al.; Optical: NASA/STScI; Magellan/U. Arizona/D. Clowe et al. Title: The Physics of Cycling

Co-Supervisor: Supervisor: Dr Arnau Rios Huguet None

Building/Room: 13BB03 Literature review and/or Type of Project Modelling Email: [email protected]

Project Description:

Bicycles are complex mechanical objects [1,2]. Their behaviour can be described using simple Newtonian mechanics, but the reach of bicycle science is actually wider. Details of material science in frame construction, the hydrodynamics of air resistance and mechanical stability all matter in the cycling performance, for instance [3,4,5]. One can build and use physical models to describe bicycles, their dynamics, and even the optimal performance of riders in wind conditions [6].

In this project, you will focus on the physics aspects of cycling, through an extensive literature review. You will choose a topic; look up relevant literature and extract key points from it; describe the reasoning behind any equations and approximations. If necessary, you will set up numerical models to reproduce previous literature, and possibly extend the reach of previous research. This project might require some numerical skills – and a love for the ride.

[1] A. Sharp, Bicycles & Tricycles: An Elementary Treatise on Their Design and Construction, Cambridge, MA : MIT (1979). ISBN 0262690667. [2] J.P. Meijaard, J. M. Papadopoulos, A. Ruina and A. L. Schwab, Proc. R. Soc. A 463, 1955 (2007). [3] D. G. Wilson, Bicycling Science, MIT Press (2004), ISBN 026223237. [4] M. Glaskin, Cycling Science: How rider and machine work together, Frances Lincoln Eds. (2013), ISBN 0711233594. [5] F. Theilmann and C. Reinhard, Phys. Educ. 51 015001 (2016). [6] A. Brad Anton, Optimal time-trial bicycle racing with headwinds and tailwinds, http://arxiv.org/abs/1309.1741. Title: Nodal structure of wave functions with non-local potentials

Co-Supervisor: Supervisor: Dr Arnau Rios Huguet None

Building/Room: 13BB03 Type of Project Modelling Email: [email protected]

Project Description:

The Schrodinger equation is a cornerstone of quantum mechanics:

2 −ℏ 2 ∇ +V ( r ) φ ( r ) =E φ ( r ) . [ 2m ] n n n

For a given local potentials, V ( r ) , one solves the previous equations to find eigenenergies, En ,

and wavefunctions, φn ( r ) [1]. The zeros of the wavefunctions,

φn (ri )=0,i=1,⋯ ,N

determine its so-called nodal structure, and contain useful information about the eigenstates [2]. For local interactions producing bound states, for instance, there are well-known relations between the number of nodes, N , and the quantum number of a state, n .

In several cases of interest, particularly in nuclear physics, the Schrodinger equation involves non-local potentials, because the potential energy at r depends on the behavior of the wave function at neighboring points, r' ,

2 − ℏ 2 ' ' ' ∇ φ ( r )+ dr V ( r ,r ) φ (r )=E φ ( r ) . 2m n ∫ n n n

For these non-local interactions, early studies demonstrated that the number of nodes in the bound state wavefunctions change [4]. This project will continue these early explorations using matrix numerical techniques.

In particular, in this project, you will:

1) Explore the literature about wavefunctions and their nodes; 2) Solve the Schrodinger equation, using standard matrix techniques for a local potential, and extend the numerical routines to the non-local case; 3) Find the nodes of the wavefunctions for different quantum numbers; 4) Study in detail how non-locality affects the nodes in the wavefunctions.

The conclusions will be relevant for a number of applications in nuclear and electronic structure physics. Skills in coding and numerical analysis (Matlab, Fortran, Mathematica) will be necessary.

[1] A. Messiah, Quantum Mechanics, Dover (1999). [2] M. Bajdich, L. Mitas, G. Drobny and L. K. Wagner, Phys. Rev. B 72, 075131 (2005). [3] R. H. Hooverman, Nucl. Phys. A 186, 155 (1972). [4] R. H. Hooverman, Nucl. Phys. A 189, 161 (1972).

Title (Code) Quantum systems of bosons with soft van der Waals potentials Degree: BSc in Physics/Physics with All Co- Supervisor: Dr N.K. Timofeyuk Supervisor Room: 15BB03 Faculty of Email: [email protected] Engineering & Physical Sciences Address University of Surrey Phone: 6795 GU2 7XH United Kingdom Group: N Type: Theoretical

Quantum many-body systems made of very weakly-interacting bosons (such as helium droplets) have universal features in their spectra. Their spectra plotted as functions of the two-body scattering length look like a tree with regularly spaces branches. Each branch representing an n-th excited state of N- body system is “attached” to the branch corresponding to (n-1)th excited state of the N-1-body system. Recently the study of universality of these spectra has Project been carried out with simple Gaussian potentials [1]. The aim of the project is description: to extend this study for a different class of two-body potentials which have realistic van der Waals behavior at large inter-atomic distances. The project will use hyperspherical functions method [2] as a means to solve many-body Schrödinger equation for bosons.

[1] A. Kievsky, M. Gattobigio and N.K. Timofeyuk, Few-body Syst. 55, 945 (2013) [2] N.K. Timofeyuk, Phys. Rev. A86, 032507 (2012)

Difficulty Level (1-5):

The main objective is to incorporate soft van der Waals force into existing code that solves the Schrödinger equation for many-boson Main systems in hyperspherical coordinates (4). Then calculations will be Objectives carried out for a range of many-body systems and their behaviour with respect to the strength of the van der Waals potential will be studied.

The student will have to derive analytical expression for hyperrarial potential for soft van der Waals potential in the lowest order (4). Then a Fortran subroutine will be written and incorporated into the existing Technical code that solves the Schrödinger equation in hyperspherical coordinates Aspects (3). Ability to code in Fortran will be needed. The new code will be used to calculate binding energies of helium droplets. The student will present the results obtained graphically and will need to interpret these.

Title (Code) Matter density distribution in helium drops Degree: BSc in Physics/Physics with All Co- Supervisor: Dr N.K. Timofeyuk Supervisor Room: 15BB03 Faculty of Email: [email protected] Engineering & Physical Sciences Address University of Surrey Phone: 6795 GU2 7XH United Kingdom Group: N Type: Theoretical

Helium is an inert gas that does not make compounds. However, at extremely low temperatures, helium can self-assemble into drops that contain two helium atoms or more. There exist many theoretical models to describe helium drops as systems of interacting many-body quantum objects. Usually, such models are very complicated but it has been shown in [1] that very similar results for the helium drop’s binding energies can be obtained in a simple model that uses hyperspherical coordinates and that has only one dynamical degree of freedom Project – the hyperradius. This project will aim to calculate the matter density description: distribution in helium drops within the hyperspherical approach. The density will be obtained for the ground state of helium drops and for one of their excited states, in which they “breathe”. The theoretical technique of density calculation developed in this project will become an important first step towards using the hyperspherical approach in calculating various kinds of densities in atomic and nuclear systems.

[1] N.K. Timofeyuk, Phys. Rev. A86, 032507 (2012)

Difficulty Level (1-5): The method will use the link between the hyperspherical and harmonic oscillator models. Therefore, as a first step, expressions for density of bosonic systems will be obtained in the harmonic oscillator model (2), corrected for centre-or mass motion (3). These results will be used to Main obtain an analytical expression for the density in the hyperspherical Objectives approach (4). There is a simple Fortran code that calculates the many- body wave functions for bosonic system in the lowest order approximation. A subroutine will be written that uses these wave functions to calculate the corresponding densities (4).

The project will need understanding of the basic QM harmonic oscillator model and the quantum-mechanical definition of density. Technical Understanding Fourier-transforms will be developed. Ability to develop Aspects analytical expressions and to code in Fortran will be needed. The student will present the results obtained graphically and will need to interpret these.

Title (Code) Quantum many-body systems in one dimension Degree: BSc in Physics/Physics with All Co- Supervisor: Dr N.K. Timofeyuk Supervisor Room: 15BB03 Faculty of Email: [email protected] Engineering & Physical Sciences Address University of Surrey Phone: 6795 GU2 7XH United Kingdom Group: N Type: Literature review

The world we live in is three-dimensional. Therefore, realistic models of Project various systems of particles must be based on quantum-mechanical equations description: defined in 3D. However, quite often physicists consider lower-dimension many-body models, such 1D. The aim of this project is to investigate why one- dimensional models are of any interest. Is it just pure curiosity or can some systems of atoms align in a chain and effectively behave as 1D objects?

The main objective of this project is to give a synopsis of modern literature on the quantum-mechanical description of many-body systems in one dimension and to explain what kinds of questions are tackled when 1D problems are considered. What has been already solved and Main what questions still await a solution? Why unsolved questions are Objectives important? What methods are used to solve many-body equations in 1D? Is there any use of 1D many-body models?

The student will have to search the literature and then to select and arrange material in a way to give a snapshot of a modern 1D research. Technical The student should be able to explain the motivation of this research Aspects and to comment both on current achievements and presently unsolved problems.

Title (Code) Many-body forces in quantum systems of bosons Degree: BSc in Physics/Physics with All Co- Supervisor: Dr N.K. Timofeyuk Supervisor Room: 15BB03 Faculty of Email: [email protected] Engineering & Physical Sciences Address University of Surrey Phone: 6795 GU2 7XH United Kingdom Group: N Type: Theoretical

Two weakly-interacting bosons (such as helium atoms) often attract each other when they are far apart but strongly repel when they “touch” each other. Such a strong short-range repulsion creates difficulties for a quantum description of many-body systems made of very weakly-interacting bosons (such as helium droplets). However, it was found that the numerical methods used to describe a few of such bosons (less then ten) converge fast if, instead of a two-body force with repulsion at short range, an attractive only force is used while, to compensate to the absence for two-body repulsion, a purely repulsive three- Project body force is used [1,2]. But for more than 10-20 bosons the convergence gets description: worse again [3]. The project will look at the introduction of simple n-body forces in droplets that contain N helium atoms (n < N). Can such forces generate an averaged N-body potential which does not contain short-range repulsion, and will not cause any problems for many-body quantum models? Using a model based on hyperspherical coordinates it will be checked if the introduction of such n-body forces can describe the known energies of helium droplets.

[1] A. Kievsky, M. Gattobigio and M.Viviani, Phys. Rev. A 84, 052503 (2011) [2] N.K. Timofeyuk, Phys. Rev. A 86, 032507 (2012) [3] N.K. Timofeyuk, Phys. Rev. A 91, 042513 (2015)

Difficulty Level (1-5):

The main objective is to incorporate n-body forces into an existing code that solves the N-body Schrödinger equation, written in hyperspherical Main coordinates, in the lowest order (4). Then calculations will be carried out Objectives for a range of N-body helium droplets with different parameters for the n-body force with the aim to fit these parameters to reproduce the known energies of helium droplets.

Then a Fortran subroutine will be written and incorporated into the existing code that solves the Schrödinger equation in hyperspherical Technical coordinates (3). Ability to code in Fortran will be needed. The new code Aspects will be used to calculate binding energies of helium droplets. The student will present the results obtained graphically and will need to interpret these.