Chemotaxis, Reaction, Network
Mathematics for Self-Organization
Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Physics, Mechanics, Mathematics
| Author: | Takashi Suzuki | ISBN: | 9789813237759 |
| Publisher: | World Scientific Publishing Company | Publication: | July 26, 2018 |
| Imprint: | WSPC | Language: | English |
| Author: | Takashi Suzuki |
| ISBN: | 9789813237759 |
| Publisher: | World Scientific Publishing Company |
| Publication: | July 26, 2018 |
| Imprint: | WSPC |
| Language: | English |
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
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
