Book Details

Free Energy and Self-Interacting Particles

Publication year: 2005

: 978-0-8176-4436-9

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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 field of many particles, interacting under the gravitational inner force or the chemical reaction


: Mathematics and Statistics, Applied Mathematics, Green's function, Mathematical Biology, Mathematical Physics, Partial Differential Equations, STATISTICA, calculus, differential equation, mechanics, modeling, partial differential equation, quantum mechanics, thermodynamics