Patterns and Interfaces in Dissipative Dynamics: Revised and Extended, Now also Covering Patterns of Active Matter

✍ Scribed by Len Pismen

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 402
• Series: Springer Series in Synergetics
• Edition: 2
• Category: Library

✦ Synopsis

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

✦ Table of Contents

Foreword
Preface to the First Edition
Preface to the Second Edition
Contents
Introduction
Quest for Complexity
Field Variables
Conservative Systems
Dissipative Systems
Historical and Bibliographical Notes
1 Genesis of Patterns
1.1 Basic Models
1.1.1 Representative Models of Open Systems
1.1.2 Spectral Decompositions
1.1.3 Linear Analysis
1.1.4 Evolution of Perturbations
1.1.5 Multiscale Expansion
1.2 Reaction–Diffusion Systems
1.2.1 General Structure of RDS
1.2.2 Examples of RDS
1.2.3 Bifurcation of Stationary States
1.2.4 Global Bifurcations
1.3 Space-Dependent Amplitude Equations
1.3.1 Turing Instability
1.3.2 Wave Instability
1.3.3 Derivation of Amplitude Equations
1.3.4 Anisotropy of Long-Scale Spatial Dependence
1.4 Convective Systems
1.4.1 Convection Driven by Heat or Mass Transfer
1.4.2 Convection Driven by Buoyancy
1.4.3 Convection Driven by Marangoni Flow
1.5 Dynamics of Planforms
1.5.1 Interaction of Degenerate Modes
1.5.2 Resonant Interactions
1.5.3 Stripes–Hexagons Competition
1.5.4 Wave–Turing Resonance
1.5.5 Resonant StandingWaves
1.6 Conserved Systems
1.6.1 Nonlocal and Local Description
1.6.2 Phase Separation
1.6.3 Symmetry Breaking in Conserved Systems
1.6.4 Partially Conserved Systems
2 Fronts between Uniform States
2.1 Planar Fronts
2.1.1 Advance into a Metastable State
2.1.2 Computation of the Propagation Speed
2.1.3 Nonmonotonic Solutions
2.1.4 Propagation into an Unstable State
2.1.5 Stability of the Leading Edge
2.1.6 Pulled and Pushed Fronts
2.2 Weakly Curved Fronts
2.2.1 Aligned Coordinate Frame
2.2.2 Expansion Near the Maxwell Construction
2.2.3 Burgers Equation
2.2.4 Ripening under Global Control
2.3 Fronts in Conserved Systems
2.3.1 Inner and Outer Equations
2.3.2 Solvability Condition and Matching
2.3.3 Propagation and Coarsening in 1D
2.3.4 Ostwald Ripening
2.3.5 Phase Field Model
2.4 Instabilities of Interphase Boundaries
2.4.1 Instabilities due to Coupling to Control Field
2.4.2 Mullins–Sekerka Instability
2.4.3 Instability of a Curved Interface
2.4.4 Directional Solidification
2.4.5 Long-Scale Instability
3 Structures with Sharp Interfaces
3.1 Rectilinear Structures
3.1.1 Basic Model and Scaling
3.1.2 Stationary Fronts
3.1.3 Propagating Fronts
3.1.4 Stationary Bands
3.1.5 Migration-Enhanced Structures
3.1.6 Propagating Bands
3.2 Curvilinear Structures
3.2.1 Solitary Disk and Sphere
3.2.2 Splitting and Bending Instabilities
3.2.3 Traveling and Oscillatory Instabilities
3.2.4 Quasistationary Dynamics
3.2.5 Phenomenological Velocity–Curvature Relation
3.2.6 Long-Scale Evolution Equations
3.3 Locally Induced Motion
3.3.1 Intrinsic Equations of Motion
3.3.2 Steadily Rotating Spiral
3.3.3 Propagation into a Quiescent State
3.3.4 Spiral Band near Traveling Bifurcation
3.4 Advective Limit
3.4.1 Inertial Scaling
3.4.2 Dispersion Relation for Wave Trains
3.4.3 ChaoticWave Trains
3.5 Rotating SpiralWaves
3.5.1 Advective Limit for a Rotating Spiral
3.5.2 Propagating Finger
3.5.3 Slender Spiral Band
3.5.4 Tip Meandering
3.5.5 Phenomenology of Complex Spiral Motion
3.5.6 ScrollWaves
4 Irregular Stationary Patterns
4.1 Striped Patterns
4.1.1 Stationary Solutions of Amplitude Equations
4.1.2 Stability of Stationary Solutions
4.1.3 Universal Form of Phase Equations
4.1.4 Variational Formulation
4.1.5 Phase Dynamics of a Nongradient System
4.1.6 Covariant Phase-Amplitude Equation
4.2 Defects in Striped Patterns
4.2.1 Natural Patterns
4.2.2 Phase Field of a Dislocation
4.2.3 Dislocations in NWS Equation
4.2.4 Dislocation Core
4.2.5 Disclinations
4.2.6 DomainWalls
4.3 Motion of Dislocations
4.3.1 Phase Field of a Moving Defect
4.3.2 Dissipation Integral and Peach–Köhler Force
4.3.3 Matched Asymptotic Expansions
4.3.4 Interaction of Dislocations
4.3.5 Motion in a Supercriticality Ramp
4.4 Propagation of Pattern and Pinning
4.4.1 Wavelength Selection in a Propagating Pattern
4.4.2 Self-Induced Pinning
4.4.3 Crystallization Kinetics
4.4.4 Pinning of Defects
4.5 Hexagonal Patterns
4.5.1 Triplet Amplitude Equations
4.5.2 Skewed Triplets
4.5.3 Penta–Hepta Defects
4.5.4 Domain Boundaries
4.5.5 Propagation of the Hexagonal Pattern
5 IrregularWave Patterns
5.1 Plane Waves
5.1.1 Complex Ginzburg–Landau Equation
5.1.2 Perturbations of PlaneWaves
5.1.3 Phase Equations
5.1.4 Propagation of Wave Pattern
5.2 One-Dimensional Structures
5.2.1 Converting CGL Equation into an ODE
5.2.2 Holes and Wavenumber Kinks
5.2.3 ModulatedWaves and Phase Turbulence
5.2.4 Transition to Defect Chaos
5.2.5 Coupled CGL Equations
5.3 Waves in Two Dimensions
5.3.1 Symmetric Spiral
5.3.2 Asymptotic Relations
5.3.3 Nondissipative Limit
5.3.4 Acceleration Instability
5.3.5 Broken Phase Symmetry
5.4 Interaction of Spiral Vortices
5.4.1 Nonradiative Limit
5.4.2 Weakly Radiative Vortices
5.4.3 Advective Correction
5.4.4 Strong Radiation and Shocks
5.4.5 Multispiral Patterns
5.4.6 Period Doubling in Spirals
5.5 Line Vortices and Scroll Waves
5.5.1 Curvature-Driven Motion
5.5.2 Nondissipative Motion
5.5.3 Dissipative Nonradiative Line Vortex
5.5.4 Instability of Line Vortices
6 Patterns of Active Matter
6.1 Dry Active Matter
6.1.1 Scalar Active Particles
6.1.2 Continuum and Statistical Description
6.1.3 Rod-like Particles
6.1.4 Broken Chiral Symmetry
6.1.5 Active Phase Separation
6.1.6 Surface Tension and Pseudotension
6.2 Active Nematic Fluids
6.2.1 Dynamics of Nematic Director
6.2.2 Instabilities in the Director-based Description
6.2.3 Nematodynamics with Variable Modulus
6.2.4 Instability of Flow and Nematic Alignment
6.2.5 Topological Defects
6.2.6 Interactions of Half-Charged Defects
6.3 Nematic Elastomers
6.3.1 Nematoelastic Interactions
6.3.2 Doped Elastomers
6.3.3 Phase Separation and Patterns
6.3.4 Bending Elastomer Sheets
6.3.5 Inhomogeneous Actuation
6.3.6 Janus Filaments
6.4 Active Polar Media
6.4.1 Dynamics of Polar Order Parameter
6.4.2 Dynamic Selection of the Structure of Defects
6.4.3 Instabilities Due to Variable Concentration
6.4.4 Chemo-elastic Interactions
6.4.5 Crawling Cells
References
Index