Full Module Description, 2006/07

Full Module Description, 2007/08 -click on the grey boxes to add content. You cannot alter the layout.

Module Title: Specialist Physics A Multiple Module Module Short Name: PH2M-SPA Module SITS ID (if known): PHY2024

Module Provider (AOU): PH00 Subject (3 letters): PHY Level: 2 Number of Credits: 30 Module Co-ordinator: DrR JL KeddieEDDIE Module Components: Additional Mechanics: (Professor Professor JA Tostevin JA Tostevin) Dr PD Stevenson Modelling Complex Systems: Professor BN Murdin Advanced Wave Physics: Dr JL Keddie Experimentation III (SS/TP): Dr PJ Sellin Experimentation IV (Physics): Dr RPL SearAdvanced Wave Computational Modelling: (Dr PD Physics (Professor BN Stevenson) Murdin) Experimentation III (SS/TP) (Professors WN Catford & W Gelletly &

Drs SJ Sweeney and JL Keddie)

Module Availability: Autumn and Spring Semester (Y)

Assessment Pattern Unit(s) of Assessment Weighting Towards Module Mark( %) Additional Mechanics (5 credits): Examination (End of Semester) 16.7%66 Modelling Complex Systems (5 credits): Coursework (Group Presentation) 8.35% Coursework (Written Report) 8.435%16.66 Advanced Wave Physics: (5 credits): Examination (End of Semester) 16.7%66 Experimentation III (SS/TP) (5 credits): Coursework (Laboratory Diary) 8.35% Coursework (Written Report) 8.35%16.66 Experimentation IV (Physics) (5 credits): Coursework (Laboratory Diary) 8.35% Coursework (Written Report) 8.35%16.66 Computational Modelling (5 credits): Coursework (Written Report) 16.7%66 Qualifying Condition(s): Physics programme regulations refer.

Pre-requisite/Co-requisites Additional Mechanics, Modelling Complex Systems and Advanced Wave Physics:

Date Last Revised: 26/04/2018 21 PH1M –Physics P-Principles of Physics PH1M--Mathematics I PH1-Mathematics II

Modelling Complex Systems: None.

Advanced Wave Physics: None.

Experimentation III (SS/TP) and Experimentation IV (Physics): PH1 - Practical I PH1 – Practical II or equivalentM-EXPP

Experimentation IV (Physics): PH1 - Practical I PH1 - Practical II or equivalent

Computational Modelling: PH1M - Mathematics 3 Mathematics & Quantum Physics I/II component of PH2 M-AMQP Mathematics and Quantum Physics I/II or equivalent

Module Overview Additional Mechanics (Professor J.A. Tostevin): This modulecomponent introduces a more sophisticated treatment of classical mechanics using analytical methods, covering Newton’s laws and their applications, plus Lagrangian and Hamiltonian methods.

Modelling Complex Systems (Dr P.D. Stevenson): An introduction to the basic concepts of complex systems, both natural and man-made, and to present a range of related mathematical methods such as neural networks, stochastic techniques, and fuzzy logic.

Advanced Wave Physics (Professor B.M. Murdin): A discussion of the key concepts in the propagation of waves and the associated mathemtcial treatment using a range of analytical and numerical problems.

Experimentation III (SS/TP) (Dr J.L. Keddie): Experimental class covering various aspects of solid state and thermal physics which supports a variety of Level HE2 material including waves, thermodynamics and the solid state.

Experimentation IV (Physics) (Dr P.J. Sellin): A range of fundamental and applied experiments covering mainly classical physics experiments, including optics and lasers.

Computational Modelling (Dr R.P.L. Sear): This module component comprises a six week computational physics/IT based project. This modulecomponent uses the students previous experience in computer literacy (from Level HE1, and 2MQP) to extend the students' experiences through a computer-based investigation of a topic of particular relevance to the chosen field of study or degree course.Through the Level HE1 (PH1 – Mathematics 3) and Level HE2 (PH2 – Mathematics and Quantum Physics 1/2) computational modules, all students will have acquired a good working knowledge of: - the Physics Department's computing facilities, - the use of the X-windows graphical user interface and the UNIX operating system,

Date Last Revised: 26/04/2018 22 - good keyboard and mouse skills, and - practice in the use of graphical and text based applications and utilities.

They will be able to use editors effectively and be competent in programming scientific problems in the FORTRAN 90 programming language. They will have knowledge of some useful numerical methods and recipes for modelling in physics and related fields. This module uses this investment in computer literacy to extend the students' experiences through a computer-based investigation of a topic of particular relevance to the chosen field of study or degree course.

Module Aims Additional Mechanics: To introduce the students to analytical classical mechanics and enable students to obtain equations of motion using more powerful and elegant methods than have been available previously.

Modelling Complex Systems: To characterize complex systems in nature and man-made systems. To introduce the student to the basic concepts behind neural networks, genetic algorithms, stochastic techniques, game theory and fuzzy logic. To highlight the range of application of these techniques in finance and in the physical sciences. To communicate scientific ideas orally.

Advanced Wave Physics: To impart to the student an understanding of how the principles of Wave Physics provide unifying concepts that help us interpret a wide range of physical phenomena.

Experimentation III (SS/TP): The module aims tTo provide the student with a detailed experience of solid state and thermal physics based experiments and how these relate to lecture-based material.

Experimentation IV (Physics): To provide the student with a detailed experience of general physics experimentation.

Computational Modelling: The aims are of this half-module is two-fold: i. To write a moderate-sized computer program to model a given physical process. ii. To use the program to investigate the underlying physics of the given process. iii.

Learning Outcomes Additional Mechanics: At the end of the half-modulecomponent, students should be able to - state, derive and use the Minimum Energy Principle, the Principle of Virtual work and D’Alembert’s Principle, as appropriate, to solve problems in classical mechanics, - state Lagrange’s equation and use the Lagrangian formalism to obtain equations of motion, - state Hamilton’s equations and use the Hamiltonian formalism to obtain equations of motion.

Modelling Complex Systems: At the end of the half-modulecomponent, students should - be able to identify the general characteristics of a complex system. - be able to describe the general structure of neural networks, explain the workings of a three- layer, feed-forward, fully connected network in detail and describe how neural networks can be trained - be able to explain the use of the genetic algorithm for optimization problems - understand how pseudo-random numbers are generated by a computer and how different distributions may be generated, explain the Metropolis algorithm and the principles of importance sampling - be able to qualitatively explain game theory, its relationship to group interaction and company

Date Last Revised: 26/04/2018 23 behaviour - be able to précis research papers and present the results orally.

Advanced Wave Physics: The students should be familiar with key concepts in the propagation of waves and be able to apply these concepts to solve analytical and numerical problems in both the systems studied and other analogous systems.

Experimentation III (SS/TP): The learning outcomes are manifold but include giving practical experience and appreciation of lecture-taught and/or text-book concepts which are realised in actual experiments. Other outcomes include experience with laboratory equipment, instrumentation and practices including safety practices in dealing with potential hazards, appreciation of electronics, cryogenics, computers, interfacing, optics, lasers, spectroscopy, sensors etc.

Experimentation IV (Physics): The student should be able to perform an experiment of intermediate difficulty, either involving practical or computational skills, by following written instruction. The student should be able to keep a comprehensive diary of the activity and to complete a full but selective report, based on the diary, in the style of a scientific paper. The specific practical skills gained will vary according to the choice of the experiments. Students should gain experience of experimental techniques and application of theoretical knowledge and be able to suitably document the experimental procedure in a lab diary and to present the work in a report.

Computational Modelling: The students should have: - developed their ability to write moderate-sized computer programs to model physical processes; - An improved confidence in developing and writing computer programs for scientific applications - an awareness of the value and also of the limitations of numerical methods in the simulation of physical systems - a deeper understanding of the physical processes and principles underlying the system they have modelled.

Module Content Additional Mechanics: A more sophisticated treatment of classical mechanics including the concept of generalised coordinates and introducing the Lagrangian and Hamiltonian formulations.

Introduction and Review: Newton's Laws, motion of a system of N particles, conservation laws, energy, the Minimum Energy Principle, constraints, degrees of freedom, the Principle of Virtual work and D’Alembert’s Principle (with applications to simple systems).

Lagrangian Formulation and Applications: Generalised coordinates, velocities and forces leading to the derivation of Lagrange’s equation. Application of the Lagrangian method to the projectile, simple pendulum, motion under the action of central forces, and motion in a rotating frame of reference (Coriolis and centrifugal forces).

Hamiltonian Formulation: Generalised momenta, derivation of Hamilton’s equations. Application to the simple pendulum and central forces leading to a discussion of orbits.

Modelling Complex Systems: This module provides aAn introduction to some computational techniques widely used in management, finance and in the physical sciences.

Date Last Revised: 26/04/2018 24 Module Content: - Properties of complex systems; emergent behaviour, scale-invariance. - Artificial Neural Networks (ANN): general concepts, focus on the three-layer, feed-forward, fully connected ANN. Training an ANN by back propagation. - Genetic algorithms (GA): reproduction, cross-over and mutation. Linking GAs to ANNs. - Stochastic simulation and Monte Carlo methods: pseudo-random numbers, manipulating of stochastic variables, simple Monte Carlo including importance sampling and the Metropolis algorithm. - Game theory: non-cooperative game theory, the Prisoner’s dilemma.

Advanced Wave Physics: This course extends the Level HE1 course Waves in Physicsmaterial and introduces a number of more advanced wave concepts, such as Fraunhofer diffraction, and non-linearity. It balances the theoretical element with numerous practical examples from a wide range of subject areas, but with particular reference to Medical Physics. Given the breadth of the material, in a number of cases, only an overview of the topics will be given. Wave propagation: The (linear) wave equation in 3-D: Cartesian and spherical polar representations; plane and spherical waves Examples of waves and introduction of the corresponding conjugate variables: ultrasound (p, u), transmission lines (V, I), electromagnetic (E, H), string (-Tdy/dx, y) Non-linear propagation and applications Impedance as a unifying concept: relationship of impedance to wave speed and refractive index; general treatment of reflection at boundaries; Snell’s Law; impedance matching and examples from medical ultrasound, transmission lines and optics. Diffraction: Making Huygens’ wavelets quantitative: the Kirchoff scalar theory of diffraction (simplified version); Fraunhofer diffraction; single and double slits and diffraction grating revisited using the Fourier formalism.

Experimentation III (SS/TP): A six half-day laboratory-based half-modulecourse. Two extended experimental investigations are chosen from a number of topics available.

Two three-week experiments selected from (typically): - pn Junctions - Brownian Motion - Hall Effect in semiconductors - Heat Engine - Semiconductor lasers - Thermal diffusivity of solids - Infra-red spectroscopy of semiconductors - Thermal Radiation - Photoluminescence of solids - Adiabatic compression of gases - X-ray diffraction from crystals

Experimentation IV (Physics): A six half-day laboratory based half-modulecourse. An extended experimental investigation chosen from a number of topics available.

Two three-week experiments selected from (typically): - Optical fibres - Vibration interferometry - Chaos - Chromatic resolving power - Laser speckle - Channelled spectrum

Computational Modelling: A six half-day computational modelling project on a topic of particular relevance to the chosen field of study or degree course. The precise nature of the projects will vary from year to year, and the student will have a degree of choice. Typical project topics include Waves in an Annular Drum, Schrödinger Equation for the Harmonic Oscillator, Three-Body Interactions, Fourier Analysis of an EEG, Neural Networks, Chaotic Billiards and The Travelling Salesman Problem.

Date Last Revised: 26/04/2018 25 Methods of Teaching/Learning Additional Mechanics: 12 hours of lecture classes.

Modelling Complex Systems: The course is presented using uLearn, the university's e-learning system. 12 hours are scheduled for lecturer-assisted sessions.

Advanced Wave Physics: 12 hours of formal lectures that integrate with a number of experiments in the Experimentation I module (Electromagnetism).

Experimentation III (SS/TP): Six four-hour laboratory sessions.

Experimentation IV (Physics): Six four-hour laboratory sessions.

Computational Modelling: 24 hours of computer laboratory, timetabled as 4 hours per week. The computing laboratory is also available to students outside timetabled periods.

Selected Texts/Journals Additional Mechanics: i. T L Chow, Classical Mechanics, Wiley.

Modelling Complex Systems: No single text covers all the material contained in this half-module, although many texts in the library explain the principles of one technique. The following are suggested. i. Beltratti, Margarita and Terns, Neural networks for Economic and Financial Modelling, Thomson Computer Press. [for neural networks and genetic algorithms]. ii. Frenkel and Smit, Understanding Molecular Simulation, Academic Press [for Monte Carlo Modelling]. iii. Beale and Jackson, Neural Computing: an introduction, Institute of Physics Press iv. [for Neural Networks]. v. Goldberg, Genetic Algorithms in Search, Optimisation and Machine Learning, vi. Addison-Wesley [for Genetic Algorithms]. vii. Each month, the journal Physica A publishes articles using the techniques explored in this course. Most do not require knowledge beyond an undergraduate level to be understood. viii. Lui Lam, Nonlinear Physics for beginners, World Scientific [for overview of typical Complex Systems and methods of their description]. ix. Challet, Minority Games, Oxford University Press [for Game Theory].

Advanced Wave Physics: i. Module handouts. ii. H J Pain, The Physics of Vibrations and Wave, [Fifth Edition], Wiley, 1999.

Experimentation III (SS/TP): Laboratory instruction sheets provided.

Experimentation IV (Physics):

Date Last Revised: 26/04/2018 26 Laboratory instruction sheets provided some of which contain references to or copies of required reading.

Computational Modelling: Specific to the individual project undertaken.

Date Last Revised: 26/04/2018 27