Berry's Phase and Quantized Hall Effect
Franz Wegner (1988)
Recherche Coopérative sur Programme n°25
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Franz Wegner (1988)
Recherche Coopérative sur Programme n°25
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Guo-Wei Wei (2017)
Molecular Based Mathematical Biology
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Fife, Paul C. (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Stephan Luckhaus, Augusto Visintin (1983)
Manuscripta mathematica
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Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)
Banach Center Publications
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A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase. ...
J. Slawny (1975)
Publications mathématiques et informatique de Rennes
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Erik von Schwerin, Anders Szepessy (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...
A. Visintin (1998)
Bollettino dell'Unione Matematica Italiana
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Le transizioni di fase si presentano in svariati processi fisici: un esempio tipico è la transizione solido-liquido. Il classico modello matematico, noto come , tiene conto solo dello scambio del calore latente e della diffusione termica nelle fasi. Si tratta di un problema di frontiera libera, poiché l'evoluzione dell'interfaccia solido liquido è una delle incognite. In questo articolo si rivedono le formulazioni forte e debole di tale problema, e quindi si considerano alcune generalizzazioni...
Eduard Feireisl, Hana Petzeltová (2008)
Banach Center Publications
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This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.
Geoffrey Sewell (1998)
Banach Center Publications
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We present a scheme for the theory of phase transitions in open dissipative systems, and show that its demands are fulfilled by quantum stochastic models of open systems, such as the laser.
Miroslav Laitoch (1993)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Beneš, M. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Zenon Kosowski (2007)
Applicationes Mathematicae
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We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified...