We have classified the articles presented here in two Sections according to their general content. In Part I we have included papers which deal with statistical mechanics, math ematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject. Most recent developments in this fascinating and rapidly growing area are discussed. PART I STATISTICAL MECHANICS AND RELATED TOPICS NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen 1 Germany ABSTRACT. In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2. In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian noise, (b) for more general non Gaussian noise, and (c) for the case of a strange repeller. Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given. 1.
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ISBN-13
978-94-011-1906-1 (9789401119061)
DOI
10.1007/978-94-011-1906-1
Schweitzer Klassifikation
I Statistical Mechanics And Related Topics.- Nonequilibrium Potentials For Period Doubling.- On Soliton Instabilities In 1 + 1 Dimensional Integrable Systems.- A Catastrophic View Of Quasi And Pseudospin Physics.- An Approach To Quantum Dissipation.- Arnold Tongues In A Periodically Perturbed Logistic Oscillator.- Axisymmetric Coherent Vortex States In AC Driven Josephson Junctions Arrays.- Comments On The Topological Organization Of 3D-Flows And 2D-Maps.- Phase Bistability And Squeezing In A Two-Photon Micromaser.- Phase Space Fluctuations In Neutral Fermi Liquids.- Polar Decomposition And Dense Similarity To Unitary Operators.- Site-Exchange Cellular Automata.- Steady State Segregation In Diffusion-Limited Bimolecular Reactions: Effect Of Strong Space Disorder And A Galanin Approach.- Schrödinger's Cat And Squeezing.- Sequential Iteration For Extremal Automata.- A Stochastic Approach Towards The Study Of The One-Dimensional Landau Ginzgurg Distribution.- Effective Potential For Stochastic Processes.- II Instabilities In Nonequilibrium Systems.- Some Asymptotic Time Behavior For The Real Ginzburg Landau Equations.- Anomalous Transport In Heterogeneous Materials.- Subcritical Traveling Pulses And Pattern Formation In A Film Dragging Experiment.- Empirical Determination Of The Onset Of Convection For A Hard Disk System.- 1D And 2D Nonlinear Evolution Equations For Bénard-Marangoni Convection.- A Generalized Swift-Hohenberg Model For Several Convective Problems.- Two Dimensional Patterns In A Model For The Electrohydrodynamic Instability Of Nematic Liquid Crystals.- Turing Structures In The Presence Of Gradients.- Stability Limits Of Defects And Spatio-Temporal Chaos In Nonequilibrium Media.- The Fragmentation Of A Drop Falling In A Fluid: Geometry And Velocity.- TheRole Of Dispersion In The Generalized Kuramoto Sivashinsky Equation.- Three-Modes Nonlinear Statistical Description For A Global Drift Wave Turbulence.- Spreading Of A Droplet On A Solid Surface And The Hoffman-Tanner Law.- Coriolis Force And Centrifugal Force Induced Flow Instabilities.- Amplitude Equations For Viscoelastic Convective Fluids.- Instabilities Mediated By Line Defects In Three Dimensions Without Unbinding.- Generation Of Side Jets In Forced Axisymmetric Jets.- Parametric Forcing Of Coupled Pendula.- Tracer Dispersion In The Taylor-Couette Instability With Axial Flow.- Critical Velocities And Nucleation Of Vortices In A Model Of Superflow.
