Free Energy and Self-Interacting Particles

This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary format...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Suzuki, Takashi (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2005.
Edición:1st ed. 2005.
Colección:Progress in Nonlinear Differential Equations and Their Applications, 62
Temas:
Mathematics.
Differential equations.
Mathematical analysis.
Mathematical physics.
Biomathematics.
Engineering mathematics.
Engineering-Data processing.
Applications of Mathematics.
Differential Equations.
Analysis.
Mathematical Methods in Physics.
Mathematical and Computational Biology.
Mathematical and Computational Engineering Applications.
Acceso en línea:Texto Completo
Descripción
Sumario:This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean ?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, Fokker-Planck, Liouville-Gel'fand, and the gradient ?ow. All of the equations are subject to the second law of thermodynamics - the decrease of free energy. The mat- matical principle of this hierarchy, on the other hand, is referred to as the qu- tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass.
Descripción Física:XIII, 370 p. online resource.
ISBN:9780817644369
ISSN:2374-0280 ;

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