The 60Th British Applied Mathematics Colloquium BAMC 2018
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Communications with Chaotic Optoelectronic Systems Cryptography and Multiplexing
COMMUNICATIONS WITH CHAOTIC OPTOELECTRONIC SYSTEMS CRYPTOGRAPHY AND MULTIPLEXING A Thesis Presented to The Academic Faculty by Damien Rontani In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology December 2011 Copyright c 2011 by Damien Rontani COMMUNICATIONS WITH CHAOTIC OPTOELECTRONIC SYSTEMS CRYPTOGRAPHY AND MULTIPLEXING Approved by: Professor Steven W. McLaughlin, Professor Erik Verriest Committee Chair School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor David S. Citrin, Advisor Adjunct Professor Alexandre Locquet School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Marc Sciamanna, Co-advisor Professor Kurt Wiesenfeld Department of Optical School of Physics Communications Georgia Institute of Technology Ecole Sup´erieure d'Electricit´e Professor William T. Rhodes Date Approved: 30 August 2011 School of Electrical and Computer Engineering Georgia Institute of Technology To those who have made me who I am today, iii ACKNOWLEDGEMENTS The present PhD research has been prepared in the framework of collaboration between the Georgia Institute of Technology (Georgia Tech, USA) and the Ecole Sup´erieured'Electricit´e(Sup´elec,France), at the UMI 2958 a joint Laboratory be- tween Georgia Tech and the Centre National de la Recherche Scientifique (CNRS, France). I would like to acknowledge the Fondation Sup´elec,the Conseil R´egionalde Lorraine, Georgia Tech, and the National Science Foundation (NSF) for their financial and technical support. I would like to sincerely thank my \research family" starting with my two advisors who made this joint-PhD project possible; Prof. -
Recurrence Plots for the Analysis of Complex Systems Norbert Marwan∗, M
Physics Reports 438 (2007) 237–329 www.elsevier.com/locate/physrep Recurrence plots for the analysis of complex systems Norbert Marwan∗, M. Carmen Romano, Marco Thiel, Jürgen Kurths Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany Accepted 3 November 2006 Available online 12 January 2007 editor: I. Procaccia Abstract Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system’s behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980’s. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system’s behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. -
A Translation Of
2011 A Translation of NJV 72^ dsgecr 1 2011 NJV 72^ dsgecr 2 2011 American Mathematical Society Providence, Rhode Island USA ISSN 0077-1554 TRANSACTIONS OF THE MOSCOW MATHEMATICAL SOCIETY Translation edited by Frances H. Goldman with the assistance of AMS staff A translation of TRUDY MOSKOVSKOGO MATEMATIQESKOGO OBWESTVA Editorial Board A. G. Sergeev (Editor in Chief) V. M. Buchstaber E.` B. Vinberg Yu. S. Ilyashenko A. A. Shkalikov A. V. Domrin (Corresponding Secretary) Advisory Board R. A. Minlos S. P. Novikov N. Kh. Rozov Library of Congress Card Number 65-4713 SUBSCRIPTION INFORMATION. Transactions of the Moscow Mathematical Society for 2011 will consist of one issue. Beginning in 2004, Transactions of the Moscow Mathematical Society is accessible from www.ams.org/journals/. The subscription prices for 2011 are US$532.00 list; US$425.00 institutional member. Upon request, subscribers to paper delivery of this journal are also entitled to receive electronic delivery. For paper delivery, subscribers outside the United States and India must pay a postage surcharge of US$6.00; subscribers in India must pay a postage surcharge of US$13.00. Expedited delivery to destinations in North America US$8.00; elsewhere US$17.00. Subscription renewals are subject to late fees. See www.ams.org/journal-faq for more journal subscription information. BACK NUMBER INFORMATION. For back issues see www.ams.org/bookstore. Subscriptions and orders should be addressed to American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904, USA. All orders must be accompanied by payment. Other cor- respondence should be addressed to 201 Charles St., Providence, RI 02904-2294, USA. -
SHOCKS, TURBULENCE, and PARTICLE ACCELERATION
SHOCKS, TURBULENCE, and PARTICLE ACCELERATION MYKOLA GORDOVSKYY University of Manchester STFC Introductory Solar System Plasma Physics Summer School, 12 September 2017 Outline . Basic phenomenology . Shocks - Basic physics (conservation laws etc) - Shocks in the solar corona and collisionless SW plasma - Fermi I particle acceleration . Turbulence - Basic physics in different regimes (collisionless, HD) - Existing misconceptions and non-existent controversies - Turbulence in the corona and SW - Fermi II particle acceleration . Particle acceleration - Mechanisms of particle acceleration - Outstanding problems . Summary and open questions Outline . Basic phenomenology . Shocks - Basic physics (conservation laws etc) - Shocks in the solar corona and collisionless SW plasma - Fermi I particle acceleration . Turbulence - Basic physics in different regimes (collisionless, HD) - Existing misconceptions and non-existent controversies - Turbulence in the corona and SW - Fermi II particle acceleration . Particle acceleration - Mechanisms of particle acceleration - Outstanding problems . Summary and open questions T&Cs, basic phenomenology etc Thermal Non-thermal . Collisional . Collisionless . Particle distribution . No reason for quickly becomes Maxwellian distribution Maxwellian . Behaves like a N-body . Behaves like a fluid system . Magnetohydrodynamics . Kinetics . Fluid lectures: . Kinetic lectures: - Philippa Browning: MHD; - David Tsiklauri: Plasma - Gunnar Hornig: kinetics; Magnetic reconnection; - Eduard Kontar: High- - Valery Nakariakov: -
![Arxiv:1708.06571V1 [Nlin.AO] 22 Aug 2017 the Generating Unit, Which Is the Pressure Reservoir Be- Coupling: Neath the Pipe at a Basically Constant Rate](https://docslib.b-cdn.net/cover/3025/arxiv-1708-06571v1-nlin-ao-22-aug-2017-the-generating-unit-which-is-the-pressure-reservoir-be-coupling-neath-the-pipe-at-a-basically-constant-rate-313025.webp)
Arxiv:1708.06571V1 [Nlin.AO] 22 Aug 2017 the Generating Unit, Which Is the Pressure Reservoir Be- Coupling: Neath the Pipe at a Basically Constant Rate
SAW16, dated September 28, 2018 Synchronization of organ pipes 1, 2 1 Jakub Sawicki, ∗ Markus Abel, and Eckehard Schöll 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany 2Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Straße 24, 14476 Potsdam Germany We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators appear to be a good model for the occurring dynamical phenomena. Here the coupling is realized as distance-dependent, or time-delayed, equivalently. Analytically, we investigate the synchronization frequency and bifurcation scenarios which occur at the boundaries of the Arnold tongues. We successfully compare our results to experimental data. PACS numbers: 05.45.Xt, 05.45.-a Introduction - The physics of organ pipes is an in- we investigate the bifurcation scenarios in the context of terdisciplinary topic where many fields of science meet. two delay-coupled Van-der-Pol oscillators as a represen- It is highly interesting as it includes elements of non- tation of the system of two coupled organ pipes, such linear dynamical system theory [4, 6, 11], aeroacoustic as in the experimental setup of Bergweiler et al. [5]. modeling [13] and synchronization theory [17]. The fo- In extension of previous work, we study the dependence cus of these different research areas is the “queen of in- of Arnold tongues under variation of the time delay τ struments” which captivates through the grandeur of her and the coupling strength κ, to explore how undesired sight and majesty of her sound. -
2016 UK MHD – National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics
2016 UK MHD – National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics Glasgow, 12 and 13 May 2016 Radostin D. Simitev David MacTaggart David R. Fearn — Programme — A long version of this programme including abstracts is available online at http://www.gla.ac.uk/schools/mathematicsstatistics/events/conferences/ukmhd2016. — Thursday, 2016-05-12 — Welcome and Registration 9:00 – 10:25 Arrival, registration, set-up of posters. Refreshments available. 10:25 – 10:30 PROF ADRIAN BOWMAN Head of School Welcome message Invited Lecture Chairperson: Keke Zhang 10:30 – 11:10 PHILIPPA BROWNING Relaxation modelling and MHD simulations of energy release in kink-unstable coronal loops Session 1: Solar Applications I Chairperson: Alan Hood 11:10 – 11:25 TONY ARBER, C. Brady Simulations of Alfven wave driving of the solar chromosphere - efficient heating and spicule launching. 11:25 – 11:40 BEN SNOW, G. Botha, J. McLaughlin, A. Hillier Onset of 2D reconnection in the solar photosphere, chromosphere and corona 11:40 – 11:55 ANDREW HILLIER, Shinsuke Takasao, Naoki Nakamure Investigating slow-mode MHD shocks in a partially ionised plasma 11:55 – 12:10 JAMES THRELFALL, J. E. H. Stevenson, C. E. Parnell, T. Neukirch Particle dynamics at reconnecting magnetic separators 12:10 – 12:25 NIC BIAN, E. Kontar, J. Watters, G. Emslie Turbulent reduction of parallel transport in magnetized plasmas and anomalous cooling of coronal loops Lunch Break 12:25 – 14:00 Lunch is provided at “One A The Square”. The restaurant is located at the North-West corner of the Main University Building. Lunch vouchers enclosed in delegates’ conference wallets. Session 2: Solar Applications II Chairperson: David Hughes 14:00 – 14:15 DAVID PONTIN, G. -
Magnetohydrodynamics of the Sun Eric Priest Frontmatter More Information
Cambridge University Press 978-0-521-85471-9 - Magnetohydrodynamics of the Sun Eric Priest Frontmatter More information Magnetohydrodynamics of the Sun Magnetohydrodynamics of the Sun describes the subtle and complex interaction between the Sun’s plasma atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters cover the generation of the Sun’s magnetic field by dynamo action, magnetoconvection and the nature of photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection, the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence. Developed for a graduate course at St Andrews University, this advanced textbook provides a detailed account of our progress towards answering the key unsolved puzzles in solar physics. It is essential reading for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719. Eric Priest was elected Fellow of the Royal Society of Edinburgh in 1985, of the Norwegian Academy of Sciences and Letters in 1994, of the Royal Society in 2002 and of the European Academy of Sciences in 2005. He has delivered many named lectures, including the James Arthur Prize Lecture at Harvard and the Lindsay Memorial Lecture at the Goddard Space Flight Center. He was awarded the Hale Prize of the American Astronomical Society, only the second time it has been awarded to a British scientist, and the Gold Medal of the Royal Astronomical Society. -
Modulational Instability in Optical Fibers with Randomly-Kicked Normal
Modulational instability in optical fibers with randomly-kicked normal dispersion G Dujardin, A Armaroli, Simona Nodari, A Mussot, A Kudlinski, S Trillo, M Conforti, Stephan de Bièvre To cite this version: G Dujardin, A Armaroli, Simona Nodari, A Mussot, A Kudlinski, et al.. Modulational instability in optical fibers with randomly-kicked normal dispersion. Physical Review A, American Physical Society, 2021, 103 (5), pp.053521. 10.1103/PhysRevA.103.053521. hal-03157350v2 HAL Id: hal-03157350 https://hal.archives-ouvertes.fr/hal-03157350v2 Submitted on 10 Jun 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICAL REVIEW A 103, 053521 (2021) Modulational instability in optical fibers with randomly kicked normal dispersion G. Dujardin ,1 A. Armaroli ,2 S. Rota Nodari ,3 A. Mussot,2 A. Kudlinski,2 S. Trillo,4 M. Conforti ,2,* and S. De Bièvre 1,† 1Univ. Lille, CNRS UMR 8524 - Laboratoire Paul Painlevé, Inria, F-59000 Lille, France 2Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France 3Institut de Mathématiques de Bourgogne (IMB), CNRS, UMR 5584, Université Bourgogne Franche Comté, F-21000 Dijon, France 4Department of Engineering, University of Ferrara, I-44122 Ferrara, Italy (Received 3 March 2021; accepted 7 May 2021; published 24 May 2021) We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. -
Bifurcations, Mode Locking, and Chaos in a Dissipative System
The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System David K. Arrowsmith, School of Mathematical Sciences Queen Mary and Westfield College University of London Mile End Road London E1 4NS, UK Julyan H. E. Cartwright, Departament de F´ısica Universitat de les Illes Balears 07071 Palma de Mallorca, Spain Alexis N. Lansbury, Department of Physics Brunel, The University of West London Uxbridge, Middlesex UB8 3PH, UK &ColinM.Place.∗ Int. J. Bifurcation and Chaos, 3,803–842,1993 We investigate the bifurcations and basins of attraction in the Bog- danov map, a planar quadratic map which is conjugate to the Henon´ area-preserving map in its conservative limit. It undergoesaHopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homoclinic tangency of the manifolds of aremotesaddlepoint.TheBogdanovmapistheEulermapofatwo- dimensional system of ordinary differential equations firstconsidered by Bogdanov and Arnold in their study of the versal unfolding of the double-zero-eigenvalue singularity, and equivalently of avectorfield invariant under rotation of the plane by an angle 2π.Itisauseful system in which to observe the effect of dissipative perturbations on Hamiltonian structure. In addition, we argue that the Bogdanov map provides a good approximation to the dynamics of the Poincaremaps´ of periodically forced oscillators. ∗Formerly: Department of Mathematics, Westfield College, University of London, UK. 1 1. Introduction Tisnowwellknownthatthestudyofsystemsofordinarydifferential equations, which commonly arise in dynamical systems investigated in I many fields of science, can be aided by utilizing the surface-of-section technique of Poincaremaps.The´ Poincar´e or return map of a system of or- dinary differential equations reduces the dimension of the problem, replac- ing an n-dimensional set of ordinary differential equations with an (n 1)- dimensional set of difference equations. -
Mini-Review on Particle Acceleration in Solar Flares
Combining MHD and kinetic modelling of solar flares Mykola Gordovskyy∗, Philippa Browning Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK Rui F. Pinto Institut de Recherche en Astrophysique et Plan´etologie, Universit´ede Toulouse, OMP/CNRS, 31028 Toulouse Cedex 4, France Abstract Solar flares are explosive events in the solar corona, representing fast conver- sion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely diffi- cult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging the gap between fluid and kinetic modelling of solar flares. Two types of approaches are discussed: combined MHD/test-particle (MHDTP) models, which can be used for modelling the flaring corona with relatively small numbers of energetic particles, and hybrid fluid-kinetic methods, which can be used for modelling stronger events with higher numbers of energetic particles. Two specific examples are discussed in more detail: MHDTP models of magnetic reconnection and particle acceleration in kink-unstable twisted coronal loops, and a novel reduced-kinetic model of particle transport. arXiv:1809.05751v2 [astro-ph.SR] 26 Sep 2018 Keywords: Solar flares, Magnetic reconnection, Particle acceleration, Computational modelling ∗Corresponding author Email address: [email protected] (Mykola Gordovskyy) 1. Introduction Solar flares are the most powerful non-stationary phenomena in the Solar System, releasing up to 1025 J within 10-100 s. -
Autoassociative Memory and Pattern Recognition in Micromechanical
www.nature.com/scientificreports OPEN Autoassociative Memory and Pattern Recognition in Micromechanical Oscillator Received: 30 August 2016 Accepted: 28 February 2017 Network Published: xx xx xxxx Ankit Kumar1 & Pritiraj Mohanty2 Towards practical realization of brain-inspired computing in a scalable physical system, we investigate a network of coupled micromechanical oscillators. We numerically simulate this array of all-to-all coupled nonlinear oscillators in the presence of stochasticity and demonstrate its ability to synchronize and store information in the relative phase differences at synchronization. Sensitivity of behavior to coupling strength, frequency distribution, nonlinearity strength, and noise amplitude is investigated. Our results demonstrate that neurocomputing in a physically realistic network of micromechanical oscillators with silicon-based fabrication process can be robust against noise sources and fabrication process variations. This opens up tantalizing prospects for hardware realization of a low-power brain- inspired computing architecture that captures complexity on a scalable manufacturing platform. Inspired by studies that have indicated that subsystems of the brain involved in associative learning exhibit syn- chronization dynamics by which pattern recognition emerges from the frequency entrainment of the constituent oscillating neurons1, significant recent interest has developed around the prospect of constructing analogous systems using artificial, physical oscillators. Such systems of coupled physical oscillators are capable of autoasso- ciative memory operation and other forms of parallel, non-Boolean and neuromorphic computing, and suitably engineered, offer the advantages of far higher operating frequencies than their biological counterparts, and far lower power requirements than attempts to simulate neural networks on traditional hardware. The dynamics of a system of coupled oscillators can exhibit attractive limit cycles that represent synchronized states. -
Flare Particle Acceleration in the Interaction of Twisted Coronal Flux Ropes
Astronomy & Astrophysics manuscript no. AA31915 c ESO 2018 January 10, 2018 Flare particle acceleration in the interaction of twisted coronal flux ropes J. Threlfall1, A. W. Hood1, and P. K. Browning2 1 School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, U.K. e-mail: {jwt9;awh}@st-andrews.ac.uk 2 School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, U.K. e-mail: [email protected] ABSTRACT Aims. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohy- drodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods. We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results. The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.