✍ Scribed by Augusto Visintin
No coin nor oath required. For personal study only.
.. "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/: " "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple .... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in- tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Front Matter....Pages i-ix
Introduction....Pages 1-5
Models and P.D.E.s....Pages 6-30
A Class of Quasilinear Parabolic P.D.E.s....Pages 31-67
Doubly Nonlinear Parabolic P.D.E.s....Pages 68-89
The Stefan Problem....Pages 90-122
Generalizations of the Stefan Problem....Pages 123-154
The Gibbs-Thomson Law....Pages 155-177
Nucleation and Growth....Pages 178-202
The Stefan-Gibbs-Thomson Problem with Nucleation....Pages 203-228
Two-Scale Models of Phase Transitions....Pages 229-247
Compactness by Strict Convexity....Pages 248-259
Toolbox....Pages 260-294
Back Matter....Pages 295-325
Phase transformations (Statistical physics) -- Mathematical models;Transport theory -- Mathematical models;Differential equations, Partial -- Numerical solutions;Transitions de phases -- Modèles mathématiques;Transport, Théorie du -- Modèles mathématiques;Equations aux dérivés partielles -- Solutions numériques;Partielle Differentialgleichung;Phasenumwandlung
📜 SIMILAR VOLUMES
<p><P>"The book is well organized, concise and clearly written with a strict interplay between physics and mathematics... Largely self-contained ... highly recommended to all graduate students and reserachers in applied mathematics."</P><P><STRONG>--ZAA</STRONG></P></p>
This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena, examining simulation results in detail. Later cha
<p><P> Foreword by Walter J. Freeman.</P><P></P><P>The induction of unconsciousness using anesthetic drugs demonstrates that the cerebral cortex can operate in two very different modes: alert and responsive versus unaware and quiescent. But the states of wakefulness and sleep are not single-neuron p
<p><P> Foreword by Walter J. Freeman.</P><P></P><P>The induction of unconsciousness using anesthetic drugs demonstrates that the cerebral cortex can operate in two very different modes: alert and responsive versus unaware and quiescent. But the states of wakefulness and sleep are not single-neuron p