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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Άλλοι συγγραφείς: Suzuki, Takashi (Επιμελητής έκδοσης)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston, MA : Birkhäuser Boston, 2005.
Σειρά:Progress in Nonlinear Differential Equations and Their Applications ; 62
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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245 1 0 |a Free Energy and Self-Interacting Particles  |h [electronic resource] /  |c edited by Takashi Suzuki. 
264 1 |a Boston, MA :  |b Birkhäuser Boston,  |c 2005. 
300 |a XIII, 370 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Progress in Nonlinear Differential Equations and Their Applications ;  |v 62 
505 0 |a Summary -- Background -- Fundamental Theorem -- Trudinger-Moser Inequality -- The Green’s Function -- Equilibrium States -- Blowup Analysis for Stationary Solutions -- Multiple Existence -- Dynamical Equivalence -- Formation of Collapses -- Finiteness of Blowup Points -- Concentration Lemma -- Weak Solution -- Hyperparabolicity -- Quantized Blowup Mechanism -- Theory of Dual Variation. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Mathematical analysis. 
650 0 |a Analysis (Mathematics). 
650 0 |a Partial differential equations. 
650 0 |a Applied mathematics. 
650 0 |a Engineering mathematics. 
650 0 |a Biomathematics. 
650 0 |a Physics. 
650 1 4 |a Mathematics. 
650 2 4 |a Applications of Mathematics. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Analysis. 
650 2 4 |a Mathematical Methods in Physics. 
650 2 4 |a Mathematical and Computational Biology. 
650 2 4 |a Appl.Mathematics/Computational Methods of Engineering. 
700 1 |a Suzuki, Takashi.  |e editor. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9780817643027 
830 0 |a Progress in Nonlinear Differential Equations and Their Applications ;  |v 62 
856 4 0 |u http://dx.doi.org/10.1007/0-8176-4436-9  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)