Chemotaxis, Reaction, Network

Mathematics for Self-Organization

This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:

• New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organization
• Mathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniques
• Fusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network

Sample Chapter(s)
Preface

Contents:

• Chemotaxis:

  • Keller–Segel Systems
  • Blowup in Finite Time
  • Scaling Limit
  • Residual Vanishing
  • Bounded Domains
  • Simple Blowup Points
  • Blowup in Infinite Time
  • A Recursive Hierarchy
  • Initial Mass Quantization
  • Bounded Free Energy
  • Notes

• 2D Turbulence:

  • Point Vortices
  • Mean Field Limit
  • Patch Model
  • Point Vortex Limit
  • Kinetic Model
  • Boltzmann-Poisson Equation — Classical Theory
  • Geometric Structure
  • sup + inf Inequality
  • Radial Solutions
  • Laplace-Beltrami Operators
  • Mean Value Theorems
  • Recursive Control of the Hamiltonian
  • Convex Domains
  • Notes

• Fluid Motion:

  • Self-Gravitating Fluids
  • Plasma Confinements
  • Maximum Entropy Production
  • Degenerate Parabolic Equations
  • Structure of the Blowup Set
  • Stationary States
  • Notes

• Reaction:

  • Mathematical Modeling of Reaction
  • Thermodynamics of Reaction Diffusion
  • Critical Dimension of Lotka-Volterra Systems
  • Virus Dynamics
  • Dissipative Systems with Quadratic Growth
  • L1-Compactness of the Orbit
  • Classical Solutions for 2D Case
  • Spatial Homogenization
  • Notes

• Network:

  • Chemical Reaction Network
  • Multi-Component Reaction
  • Entropy Dissipation
  • Logarithmic Sobolev Inequality
  • Pathway Grouping
  • Nested Periodic Orbits
  • Dynamical Equilibrium and Its Break Down
  • Transient Oscillation
  • Notes

Readership: Researchers in partial differential equations, mathematical modeling, mathematical physics.
Key Features:

• New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organization
• Mathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniques
• Fusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network