DOCSLIB.ORG

Table of Contents (Online)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Table of Contents (Online) PERIODICALS PHYSICAL REVIEW E Postmaster send address changes to: For editorial and subscription correspondence, APS Subscription Services please see inside front cover Suite 1NO1 „ISSN: 1539-3755… 2 Huntington Quadrangle Melville, NY 11747-4502 THIRD SERIES, VOLUME 80, NUMBER 5 CONTENTS NOVEMBER 2009 PART 1: STATISTICAL, SOFT MATTER, AND BIOLOGICAL PHYSICS RAPID COMMUNICATIONS Statistical physics Avalanche dynamics in fluid imbibition near the depinning transition (4 pages) ......................... 050101͑R͒ Marc Pradas, Juan M. López, and A. Hernández-Machado Loewner driving functions for off-critical percolation clusters (4 pages) ............................... 050102͑R͒ Yoichiro Kondo, Namiko Mitarai, and Hiizu Nakanishi Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles (4 pages) .......................................................................... 050103͑R͒ Gabriel Baglietto and Ezequiel V. Albano Experimental investigation of a Brownian ratchet effect in ferrofluids (4 pages) ......................... 050104͑R͒ Thomas John and Ralf Stannarius Films, interfaces, and crystal growth Size-dependent nucleation kinetics at nonplanar nanowire growth interfaces (4 pages) ................... 050601͑R͒ T. Haxhimali, D. Buta, M. Asta, P. W. Voorhees, and J. J. Hoyt Liquid crystals Micropatterning of light-sensitive liquid-crystal elastomers (4 pages) ................................. 050701͑R͒ Miha Devetak, Blaž Zupančič, Andrija Lebar, Polona Umek, Boštjan Zalar, Valentina Domenici, Gabriela Ambrožič, Majda Žigon, Martin Čopič, and Irena Drevenšek-Olenik ARTICLES Statistical physics Finite-size analysis of a two-dimensional Ising model within a nonextensive approach (8 pages) ........... 051101 N. Crokidakis, D. O. Soares-Pinto, M. S. Reis, A. M. Souza, R. S. Sarthour, and I. S. Oliveira Phase-space networks of geometrically frustrated systems (5 pages) .................................. 051102 Yilong Han (韩一龙͒ Copyright 2009 by The American Physical Society (Continued) Selected for a Viewpoint in Physics. Please visit http://physics.aps.org/. CONTENTS - Continued PHYSICAL REVIEW E THIRD SERIES, VOLUME 80, NUMBER 5 NOVEMBER 2009 Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics (16 pages) ................................................................................. 051103 L. Lizana and T. Ambjörnsson Social tolerance allows cooperation to prevail in an adaptive environment (7 pages) ..................... 051104 Xiaojie Chen, Feng Fu, and Long Wang Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat (13 pages) . 051105 L. A. Fernandez, A. Gordillo-Guerrero, V. Martin-Mayor, and J. J. Ruiz-Lorenzo Semiclassical treatment of a Brownian ratchet using the quantum Smoluchowski equation (14 pages) ....... 051106 Liam Cleary, William T. Coffey, Yuri P. Kalmykov, and Serguey V. Titov Fluctuation relations for diffusion that is thermally driven by a nonstationary bath (9 pages) .............. 051107 Raphaël Chetrite Avalanche dynamics of fiber bundle models (8 pages) ............................................. 051108 R. C. Hidalgo, F. Kun, K. Kovács, and I. Pagonabarraga Escape dynamics of coupled particles in nonlinear, disordered lattices (12 pages) ....................... 051109 K. Manski and D. Hennig Diffusion in the special theory of relativity (9 pages) .............................................. 051110 Joachim Herrmann Ab initio method for locating characteristic potential-energy minima of liquids (7 pages) ................. 051111 E. Holmström, N. Bock, Travis B. Peery, R. Lizárraga, G. De Lorenzi-Venneri, Eric D. Chisolm, and Duane C. Wallace Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension (15 pages) .... 051112 S. J. Manzi, V. J. Huespe, R. E. Belardinelli, and V. D. Pereyra Multiplicative Lévy processes: Itô versus Stratonovich interpretation (8 pages) ......................... 051113 Tomasz Srokowski Coagulation reactions in low dimensions: Revisiting subdiffusive A+A reactions in one dimension (11 pages) ................................................................................. 051114 S. B. Yuste, J. J. Ruiz-Lorenzo, and Katja Lindenberg Velocity and cluster distributions in a bottleneck system (9 pages) ................................... 051115 Vidar Frette and Per C. Hemmer Experimental realization of directed percolation criticality in turbulent liquid crystals (12 pages) ........... 051116 Kazumasa A. Takeuchi, Masafumi Kuroda, Hugues Chaté, and Masaki Sano Phase diagram and critical behavior of the square-lattice Ising model with competing nearest-neighbor and next-nearest-neighbor interactions (8 pages) ...................................................... 051117 Junqi Yin and D. P. Landau Asymptotic shape of the region visited by an Eulerian walker (7 pages) ............................... 051118 Rajeev Kapri and Deepak Dhar Queueing process with excluded-volume effect (10 pages) .......................................... 051119 Chikashi Arita Trapping in scale-free networks with hierarchical organization of modularity (8 pages) ................... 051120 Zhongzhi Zhang, Yuan Lin, Shuyang Gao, Shuigeng Zhou, Jihong Guan, and Mo Li (Continued) Selected for a Viewpoint in Physics. Please visit http://physics.aps.org/. CONTENTS - Continued PHYSICAL REVIEW E THIRD SERIES, VOLUME 80, NUMBER 5 NOVEMBER 2009 Negative mobility induced by colored thermal fluctuations (7 pages) .................................. 051121 M. Kostur, J. Łuczka, and P. Hänggi Analytical expressions for the fourth virial coefficient of a hard-sphere mixture (8 pages) ................ 051122 Stanislav Labík and Jiří Kolafa Proposal and applications of a method for the study of irreversible phase transitions (5 pages) ............ 051123 Ernesto S. Loscar, Nara Guisoni, and Ezequiel V. Albano Dual structures of chaos and turbulence, and their dynamic scaling laws (7 pages) ...................... 051124 Hazime Mori and Makoto Okamura Generalized Fisher information matrix in nonextensive systems with spatial correlation (8 pages) .......... 051125 Hideo Hasegawa Monte Carlo study of the phase transition in the critical behavior of the Ising model with shear (10 pages) . 051126 G. P. Saracco and G. Gonnella Critical behavior of the Ising model in annealed scale-free networks (10 pages) ........................ 051127 Sang Hoon Lee, Meesoon Ha, Hawoong Jeong, Jae Dong Noh, and Hyunggyu Park Estimating causal dependencies in networks of nonlinear stochastic dynamical systems (9 pages) .......... 051128 Linda Sommerlade, Michael Eichler, Michael Jachan, Kathrin Henschel, Jens Timmer, and Björn Schelter Condensate density of interacting bosons: A functional renormalization group approach (8 pages) .......... 051129 Christopher Eichler, Nils Hasselmann, and Peter Kopietz Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates (19 pages) ................................................................................. 051130 Boris V. Fine Equilibrium and linear transport properties of fluids Asymptotic current-voltage relations for currents exceeding the diffusion limit (7 pages) ................. 051201 Ehud Yariv Boltzmann equation and hydrodynamic fluctuations (12 pages) ...................................... 051202 Matteo Colangeli, Martin Kröger, and Hans Christian Öttinger Improved implementation of Kirkwood-Buff solution theory in periodic molecular simulations (10 pages) . 051203 Joseph W. Nichols, Stan G. Moore, and Dean R. Wheeler Granular materials Self-organized patterns in collections of chains (4 pages) ........................................... 051301 T. Sykes and T. Mullin Pulse propagation in decorated granular chains: An analytical approach (9 pages) ....................... 051302 Upendra Harbola, Alexandre Rosas, Aldo H. Romero, Massimiliano Esposito, and Katja Lindenberg Boolean reconstructions of complex materials: Integral geometric approach (17 pages) ................... 051303 C. H. Arns, M. A. Knackstedt, and K. R. Mecke Dynamic effective mass of granular media and the attenuation of structure-borne sound (20 pages) ......... 051304 John Valenza, Chaur-Jian Hsu, Rohit Ingale, Nicolas Gland, Hernán A. Makse, and David Linton Johnson (Continued) Selected for a Viewpoint in Physics. Please visit http://physics.aps.org/. CONTENTS - Continued PHYSICAL REVIEW E THIRD SERIES, VOLUME 80, NUMBER 5 NOVEMBER 2009 Random close packing of disks and spheres in confined geometries (11 pages) ......................... 051305 Kenneth W. Desmond and Eric R. Weeks Colloidal dispersions, suspensions, and aggregates Dynamics of colloids in a narrow channel driven by a nonuniform force (10 pages) ..................... 051401 D. V. Tkachenko, V. R. Misko, and F. M. Peeters Beyond diffusion-limited aggregation kinetics in microparticle suspensions (7 pages) .................... 051402 Randall M. Erb, Melissa D. Krebs, Eben Alsberg, Bappaditya Samanta, Vincent M. Rotello, and Benjamin B. Yellen Structure and rheology of SiO2 nanoparticle suspensions under very high shear rates (7 pages) ............ 051403 J. Chevalier, O. Tillement, and F. Ayela Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids (8 pages) .................................................................................. 051404 Alessio Zaccone, Hua Wu, Daniele
Load more

Recommended publications
  • CURRICULUM VITA Edward Ott Distinguished University Professor of Electrical Engineering and of Physics
    CURRICULUM VITA Edward Ott Distinguished University Professor of Electrical Engineering and of Physics I. Personal Data: Date and Place of Birth: Dec. 22, 1941, New York City, NY Home Address: 12421 Borges Ave., Silver Spring, MD 20904 Work Address: Institute for Plasma Research University of Maryland College Park, MD 20472 Work Telephone: (301)405-5033 II. Education: B.S. (1963), Electrical Engineering, The Cooper Union. M.S. (1965), Electrophysics, Polytechnic University. Ph.D. (1967), Electrophysics, Polytechnic University. III. Experience: 1967-1968 NSF Postdoctoral Fellow, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, U.K. 1968-1979 Faculty of the Department of Electrical Engineering, Cornell University, Ithaca, NY. 1976 and Plasma Physics Division, Naval Research 1971-1972 Laboratory, Washington, D.C. 1985 Institute for Theoretical Physics, University of California, Santa Barbara, CA. 1979-Present Department of Physics and Department of Electrical Engineering, University of Maryland, College Park, MD. (Ott–2) IV. Professional Activities: Fellow, American Physical Society. Fellow, IEEE. Fellow, World Innovation Foundation. Listed in the Highly Cited Researchers Database of the ISI. Associate Editor, Physics of Fluids (1977–1979). Correspondent, Comments on Plasma Physics (1983–1993). Board of Editors, Physical Review A (1986–1988). Divisional Associate Editor, Physical Review Letters (1989–1993). Editor of Special Issue of Chaos on Chaotic Scattering (1993). Advisory Board, Chaos: An Interdisciplinary Journal of Nonlinear Science (1991–2000). Editorial Board, Chaos: An Interdisciplinary Journal of Nonlinear Science (2000–2003). Editorial Board, Dynamics and Stability of Systems (1995–2000). Editorial Board, Central European Journal of Physics (2002–present). Editor, Physica D: Nonlinear Phenomena (1999–2002).
    [Show full text]
  • Chaos Theory: the Essential for Military Applications
    U.S. Naval War College U.S. Naval War College Digital Commons Newport Papers Special Collections 10-1996 Chaos Theory: The Essential for Military Applications James E. Glenn Follow this and additional works at: https://digital-commons.usnwc.edu/usnwc-newport-papers Recommended Citation Glenn, James E., "Chaos Theory: The Essential for Military Applications" (1996). Newport Papers. 10. https://digital-commons.usnwc.edu/usnwc-newport-papers/10 This Book is brought to you for free and open access by the Special Collections at U.S. Naval War College Digital Commons. It has been accepted for inclusion in Newport Papers by an authorized administrator of U.S. Naval War College Digital Commons. For more information, please contact [email protected]. The Newport Papers Tenth in the Series CHAOS ,J '.' 'l.I!I\'lt!' J.. ,\t, ,,1>.., Glenn E. James Major, U.S. Air Force NAVAL WAR COLLEGE Chaos Theory Naval War College Newport, Rhode Island Center for Naval Warfare Studies Newport Paper Number Ten October 1996 The Newport Papers are extended research projects that the editor, the Dean of Naval Warfare Studies, and the President of the Naval War CoJIege consider of particular in terest to policy makers, scholars, and analysts. Papers are drawn generally from manuscripts not scheduled for publication either as articles in the Naval War CollegeReview or as books from the Naval War College Press but that nonetheless merit extensive distribution. Candidates are considered by an edito­ rial board under the auspices of the Dean of Naval Warfare Studies. The views expressed in The Newport Papers are those of the authors and not necessarily those of the Naval War College or the Department of the Navy.
    [Show full text]
  • CURRICULUM VITAE Edward Ott Distinguished University Professor
    Ott-1 CURRICULUM VITAE Edward Ott Distinguished University Professor of Electrical Engineering and of Physics Work Address: Institute for Research in Electronics and Applied Physics University of Maryland 8279 Paint Branch Drive College Park, MD 20742-3511 Work Telephone: 301-405-5033 I. Education: B.S. 1963 Electrical Engineering, The Cooper Union M.S. 1965 Electrophysics, Polytechnic University Ph.D. 1967 Electrophysics, Polytechnic University II. Experience 1967-1968 NSF Postdoctoral Fellow Department of Applied Mathematics and Theoretical Physics Cambridge University, Cambridge, U.K. 1968-1979 Faculty of the Department of Electrical Engineering Cornell University, Ithaca, NY 1976 and Plasma Physics Division 1971-1972 Naval Research Laboratory, Washington, D.C. 1985 Institute for Theoretical Physics University of California Santa Barbara, CA 1979-Present Department of Electrical and Computer Engineering, and Department of Physics University of Maryland, College Park, MD III. Publications Ott-2 Professor Ott is an author of over 450 papers in refereed scientific journals. He is the author of the book Chaos in Dynamical Systems (Cambridge University Press), a graduate level textbook also widely used by researchers in the field (over 6000 Google Scholar citations) and an editor of the book Coping with Chaos (John Wiley). According to Google Scholar, Prof. Ott has received over 58,600 citations and has an h- index of 109. According to the ISI Web of Science, Prof. Ott’s journal articles have received over 33,800 citations with a corrosponding h-index of 91. (Note: For these citation and h- index data, papers have been filtered out if they list E.Ott as an author, but the E.
    [Show full text]
  • Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos
    Physica 7D (1983) 181-200 North-Holland Publishing Company CRISES, SUDDEN CHANGES IN CHAOTIC ATTRACTORS, AND TRANSIENT CHAOS Celso GREBOGI and Edward OTT Laboratory for Plasma and Fusion Energy Studies, Unit'ersity of Maryland, College Park, Md. 20742, USA and James A. YORKE Institute for Physical Science and Technology and Department of Mathematics, Unit ersi O, of Mao'land, College Park, Md. 20742, USA The occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated. It is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor. We call such collisions crises. Phenomena associated with crises include sudden changes in the size of chaotic attractors, sudden appearances of chaotic attractors (a possible route to chaos), and sudden destructions of chaotic attractors and their basins. This paper presents examples illustrating that crisis events are prevalent in many circumstances and systems, and that, just past a crisis, certain characteristic statistical behavior (whose type depends on the type of crisis) occurs. In particular the phenomenon of chaotic transients is investigated. The examples discussed illustrate crises in progressively higher dimension and include the one-dimensional quadratic map, the (two-dimensional) H~non map, systems of ordinary differential equations in three dimensions and a three-dimensional map. In the case of our study of the three-dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four, respectively. Based on the examples presented the following conjecture is proposed: almost all sudden changes in the size of chaotic attractors and almost all sudden destructions or creations of chaotic attractors and their basins are due to crises.
    [Show full text]
  • Fourth SIAM Conference on Applications of Dynamical Systems
    Utah State University DigitalCommons@USU All U.S. Government Documents (Utah Regional U.S. Government Documents (Utah Regional Depository) Depository) 5-1997 Fourth SIAM Conference on Applications of Dynamical Systems SIAM Activity Group on Dynamical Systems Follow this and additional works at: https://digitalcommons.usu.edu/govdocs Part of the Physical Sciences and Mathematics Commons Recommended Citation Final program and abstracts, May 18-22, 1997 This Other is brought to you for free and open access by the U.S. Government Documents (Utah Regional Depository) at DigitalCommons@USU. It has been accepted for inclusion in All U.S. Government Documents (Utah Regional Depository) by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. tI...~ Confers ~'t' '"' \ 1I~c9 ~ 1'-" ~ J' .. c "'. to APPLICAliONS cJ May 18-22, 1997 Snowbird Ski and Summer Resort • Snowbird, Utah Sponsored by SIAM Activity Group on Dynamical Systems Conference Themes The themes of the 1997 conference will include the following topics. Principal Themes: • Dynamics in undergraduate education • Experimental studies of nonlinear phenomena • Hamiltonian systems and transport • Mathematical biology • Noise in dynamical systems • Patterns and spatio-temporal chaos Applications in • Synchronization • Aerospace engineering • Biology • Condensed matter physics • Control • Fluids • Manufacturing • Me;h~~~~nograPhY 19970915 120 • Lasers and o~ • Quantum UldU) • 51a m.@ Society for Industrial and Applied Mathematics http://www.siam.org/meetingslds97/ds97home.htm 2 " DYNAMICAL SYSTEMS Conference Prl Contents A Message from the Conference Chairs ... Get-Togethers 2 Dear Colleagues: Welcoming Message 2 Welcome to Snowbird for the Fourth SIAM Conference on Applications of Dynamica Systems. Organizing Committee 2 This highly interdisciplinary meeting brings together a diverse group of mathematicians Audiovisual Notice 2 scientists, and engineers, all working on dynamical systems and their applications.
    [Show full text]
  • Machine Learning for Analysis of High-Dimensional Chaotic Spatiotemporal Dynamical Systems
    MACHINE LEARNING FOR ANALYSIS OF HIGH-DIMENSIONAL CHAOTIC SPATIOTEMPORAL DYNAMICAL SYSTEMS 6th December 2018 Princeton Plasma Physics Laboratory Theory Seminar Jaideep Pathak Zhixin Lu, Alex Wikner, Rebeckah Fussell, Brian Hunt, Michelle Girvan, Edward Ott University of Maryland, College Park Given some data from a dynamical system, what can we say about the dynamical process that generated this data? !2 OUTLINE Short-term forecasting Prediction Given a limited time series of past measurements can we predict the future state of the dynamical system, at least in the short term? Reconstructing the attractor Long-term Can we learn something about the long-term dynamics of the dynamics system? Specifically, can we use our setup to understand the ergodic properties of a high-dimensional dynamical system? Scalability Can we use our setup for very high-dimensional attractors? Large systems !3 INTRODUCTION Operationally, we say a x1(t) − x2(t) = δx(t) dynamical system is chaotic if, in a ∥δx(t)∥ ∼ ∥δx(0)∥ exp(Λt) bounded phase space, two nearby trajectories diverge exponentially. !4 INTRODUCTION In a chaotic system, a perturbation to the trajectory may be stable (contracting) in some directions, unstable (expanding) in some directions. !5 INTRODUCTION This leads to the concept of a spectrum of ‘Lyapunov exponents’. The exponential rates of growth (or contraction) of perturbations in different directions are characterized by corresponding Lyapunov exponents. !6 INTRODUCTION The Lyapunov exponents of a dynamical system are an important characteristic and provide us with a lot of useful information. What is the ‘complexity’? Is a system chaotic? of the system What is the effective dimension of the chaotic What is the possible attractor of the system prediction horizon? (via the ‘Kaplan-Yorke conjecture’)? !7 INTRODUCTION In general, in the past it has proven difficult (and sometimes not possible) to estimate the spectrum of Lyapunov exponents of a dynamical system purely from limited time series data.
    [Show full text]
  • Introduction to Focus Issue: When Machine Learning Meets Complex Systems: Networks, Chaos, and Nonlinear Dynamics
    Introduction to Focus Issue: When machine learning meets complex systems: Networks, chaos, and nonlinear dynamics Cite as: Chaos 30, 063151 (2020); https://doi.org/10.1063/5.0016505 Submitted: 04 June 2020 . Accepted: 05 June 2020 . Published Online: 26 June 2020 Yang Tang , Jürgen Kurths , Wei Lin , Edward Ott, and Ljupco Kocarev COLLECTIONS Paper published as part of the special topic on When Machine Learning Meets Complex Systems: Networks, Chaos and Nonlinear Dynamics Note: This paper is part of the Focus Issue, “When Machine Learning Meets Complex Systems: Networks, Chaos and Nonlinear Dynamics.” ARTICLES YOU MAY BE INTERESTED IN Recurrence analysis of slow–fast systems Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063152 (2020); https:// doi.org/10.1063/1.5144630 Reducing network size and improving prediction stability of reservoir computing Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063136 (2020); https:// doi.org/10.1063/5.0006869 Detecting causality from time series in a machine learning framework Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063116 (2020); https:// doi.org/10.1063/5.0007670 Chaos 30, 063151 (2020); https://doi.org/10.1063/5.0016505 30, 063151 © 2020 Author(s). Chaos ARTICLE scitation.org/journal/cha Introduction to Focus Issue: When machine learning meets complex systems: Networks, chaos, and nonlinear dynamics Cite as: Chaos 30, 063151 (2020); doi: 10.1063/5.0016505 Submitted: 4 June 2020 · Accepted: 5 June 2020 · Published Online: 26 June 2020 View Online Export
    [Show full text]
  • Pynamical: Model and Visualize Discrete Nonlinear Dynamical Systems, Chaos, and Fractals
    UC Berkeley UC Berkeley Previously Published Works Title Pynamical: Model and visualize discrete nonlinear dynamical systems, chaos, and fractals Permalink https://escholarship.org/uc/item/8j79j92z Journal Journal of Open Source Education, 1(1) ISSN 2577-3569 Author Boeing, Geoff Publication Date 2018-06-21 DOI 10.21105/jose.00015 Data Availability The data associated with this publication are available at: https://github.com/gboeing/pynamical Peer reviewed eScholarship.org Powered by the California Digital Library University of California Pynamical: Model and visualize discrete nonlinear dynamical systems, chaos, and fractals Geoff Boeing1 DOI: 10.21105/jose.00015 1 University of California, Berkeley Software • Review Summary • Repository • Archive Pynamical is an educational Python package for introducing the modeling, simulation, Submitted: 15 May 2018 and visualization of discrete nonlinear dynamical systems and chaos, focusing on one- Published: 21 June 2018 dimensional maps (such as the logistic map and the cubic map). Pynamical facilitates defining discrete one-dimensional nonlinear models as Python functions with just-in-time License Authors of papers retain copyright compilation for fast simulation. It comes packaged with the logistic map, the Singer map, and release the work under a Cre- and the cubic map predefined. The models may be run with a range of parameter val- ative Commons Attribution 4.0 In- ues over a set of time steps, and the resulting numerical output is returned as a pandas ternational License (CC-BY). DataFrame. Pynamical can then visualize this output in various ways, including with bifurcation diagrams (May 1976), two-dimensional phase diagrams (Packard et al. 1980), three-dimensional phase diagrams, and cobweb plots (Hofstadter 1985).
    [Show full text]
  • Chaotic Dynamics in Hybrid Systems
    Chaotic Dynamics in Hybrid Systems Pieter Collins∗ Centrum voor Wiskunde en Informatica, Postbus 94079 1090 GB Amsterdam, The Netherlands Abstract In this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological dynamics and ergodic theory may be used to study hybrid sys- tems, and review existing bifurcation theory for one-dimensional non-smooth maps, including the spontaneous formation of robust chaotic attractors. We present case studies of chaotic dynamics in a switched arrival system and in a system with periodic forcing. Keywords: chaotic dynamics; hybrid systems; symbolic dynamics; nonsmooth bifurcations. Mathematics Subject Classification (2000): 34A37; 37B10; 37A40; 34A36; 37G35. 1 Introduction A hybrid system is a dynamic system which comprises different types of behaviour. Classic examples of hybrid dynamical systems in the literature are impacting mechanical systems, for which the behaviour consists of continuous evolution interspersed by instantaneous jumps in the velocity, and dc-dc power converters, in which the behaviour depends on the state of a diode and a switch. Hybrid control systems occur when a continuous system is controlled using discrete sensors and actuators, such as thermostats and switched heating/cooling devices. Hybrid dynamics may also occur due to saturation effects on components of a system, and in idealised models of hysteresis. Finally, we mention that hybrid systems can be derived as singular limits of systems operating in multiple time-scales; indeed we may consider almost all hybrid systems to arise in this way.
    [Show full text]
  • Notices of the American Mathematical Society
    Norman Program (March 18-19)- Page 180 Notices of the American Mathematical Society February 1983, Issue 224 Volume 30, Number 2, Pages 137- 248 Providence, Rhode Island USA JSSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to whi·ch no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to tout of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.
    [Show full text]
  • Machine Learning's
    Quanta Magazine Machine Learning’s ‘Amazing’ Ability to Predict Chaos In new computer experiments, artificial-intelligence algorithms can tell the future of chaotic systems. By Natalie Wolchover Half a century ago, the pioneers of chaos theory discovered that the “butterfly effect” makes long- term prediction impossible. Even the smallest perturbation to a complex system (like the weather, the economy or just about anything else) can touch off a concatenation of events that leads to a dramatically divergent future. Unable to pin down the state of these systems precisely enough to predict how they’ll play out, we live under a veil of uncertainty. But now the robots are here to help. In a series of results reported in the journals Physical Review Letters and Chaos, scientists have used machine learning — the same computational technique behind recent successes in artificial intelligence — to predict the future evolution of chaotic systems out to stunningly distant horizons. The approach is being lauded by outside experts as groundbreaking and likely to find wide application. “I find it really amazing how far into the future they predict” a system’s chaotic evolution, said Herbert Jaeger, a professor of computational science at Jacobs University in Bremen, Germany. The findings come from veteran chaos theorist Edward Ott and four collaborators at the University of Maryland. They employed a machine-learning algorithm called reservoir computing to “learn” the dynamics of an archetypal chaotic system called the Kuramoto-Sivashinsky equation. The evolving solution to this equation behaves like a flame front, flickering as it advances through a combustible medium. The equation also describes drift waves in plasmas and other phenomena, and serves as “a test bed for studying turbulence and spatiotemporal chaos,” said Jaideep Pathak, Ott’s graduate student and the lead author of the new papers.
    [Show full text]
  • Differentiable Generalized Synchronization of Chaos
    PHYSICAL REVIEW E VOLUME 55, NUMBER 4 APRIL 1997 Differentiable generalized synchronization of chaos Brian R. Hunt,* Edward Ott,† and James A. Yorke*,‡ University of Maryland, College Park, Maryland 20742 ~Received 13 September 1996! We consider simple Lyapunov-exponent-based conditions under which the response of a system to a chaotic drive is a smooth function of the drive state. We call this differentiable generalized synchronization ~DGS!. When DGS does not hold, we quantify the degree of nondifferentiability using the Ho¨lder exponent. We also discuss the consequences of DGS and give an illustrative numerical example. @S1063-651X~97!02704-9# PACS number~s!: 05.45.1b I. INTRODUCTION stable if there is a region of y space B such that, for any two ~1! ~2! ~1! initial y vectors y0 ,y0 PB, we have limt `iy~t,x0 ,y0 ! ~2! ~1! →~2! Recently, the concept of generalized synchronization has 2y~t,x0 ,y0 !i50, and y~t,x0 ,y ! and y~t,x0 ,y ! are in the been introduced @1# to characterize the dynamics of a re- interior of B for t sufficiently large. In the remainder of this sponse system that is driven by the output of a chaotic driv- paper we assume the response system is asymptotically ing system. Generalized synchronization ~GS! is said to oc- stable. cur if, ignoring transients, the response y is uniquely There are various situations motivating consideration of determined by the current drive state x. That is, y5f~x!, GS. The most natural such situation occurs in the one-way where f is a function of x for x on the chaotic attractor of synchronization of two oscillators.
    [Show full text]