Chemotaxis, Reaction, Network (ePub)

-->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-organizationMathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniquesFusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network--> -->Sample Chapter(s)Preface -->Contents:Chemotaxis:Keller–Segel SystemsBlowup in Finite TimeScaling LimitResidual VanishingBounded DomainsSimple Blowup PointsBlowup in Infinite TimeA Recursive HierarchyInitial Mass QuantizationBounded Free Energy Notes2D Turbulence:Point VorticesMean Field LimitPatch ModelPoint Vortex LimitKinetic ModelBoltzmann-Poisson Equation — Classical TheoryGeometric Structuresup + inf InequalityRadial SolutionsLaplace-Beltrami OperatorsMean Value TheoremsRecursive Control of the HamiltonianConvex Domains NotesFluid Motion:Self-Gravitating FluidsPlasma ConfinementsMaximum Entropy ProductionDegenerate Parabolic EquationsStructure of the Blowup SetStationary States NotesReaction:Mathematical Modeling of ReactionThermodynamics of Reaction DiffusionCritical Dimension of Lotka-Volterra SystemsVirus DynamicsDissipative Systems with Quadratic GrowthL1-Compactness of the OrbitClassical Solutions for 2D CaseSpatial Homogenization NotesNetwork:Chemical Reaction NetworkMulti-Component ReactionEntropy DissipationLogarithmic Sobolev InequalityPathway GroupingNested Periodic OrbitsDynamical Equilibrium and Its Break DownTransient Oscillation Notes --> -->Readership: Researchers in partial differential equations, mathematical modeling, mathematical physics. -->Nonlinear PDE;Chemotaxis;Turbulence;Fluid Motion;Reaction;Network0Key Features:New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organizationMathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniquesFusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network