Instabilities and Nonequilibrium Structures IV

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.

Inhalt

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.- The Role 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.