The modelling and the study of phase transition phenomena are capital issues as they have essential applications in material sciences and in biological and industrial processes. We can mention, e.g., phase separation in alloys, ageing of materials, microstructure evolution, crystal growth, solidification in complex alloys, surface diffusion in the presence of stress, evolution of the surface of a thin flow in heteroepitaxial growth, motion of voids in interconnects in integrated circuits, treatment of airway closure disease by surfactant injection, fuel injection, fire extinguishers etc., This book consists of 11 contributions from specialists in the mathematical modelling and analysis of phase transitions. The content of these contributions ranges from the modelling to the mathematical and numerical analysis. Furthermore, many numerical simulations are presented. Finally, the contributors have tried to give comprehensive and accurate reference lists. This book should thus serve as a reference book for researchers interested in phase transition phenomena.
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.
Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics.
Wilson, D.G., Solomon, A.D. & Boggs, P.T. (eds.) – Moving boundary problems, Academic Press, New York, London, 1978. - Yi Fahuai – An evolutionary continuous casting problem of two-phase and its periodic behaviour (to appear in Journal ...
This book contains the papers presented at the conference on “Mathematical Models and Methods for Smart Materials”, held in Italy in 2001.
The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems.
This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
Non-Fourier melting of a semi-infinite solid. ... transfer in rapidly solidifying supercooled pure melt during final transient. Phys A 2012;391:5935–5947. [560] Herlach DM, Galenko P, Miritz DH. Metastable solids from undercooled melts.
E. Bonetti, P. Colli, M. Fr ́emond, 2003, A phase field model with thermal memory governed by the entropy balance, Math. Models and Methods in Appl. Sci., 13, 231–256. E. Bonetti, M. Fr ́emond, 2003, A phase transition model with the ...
This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids.
89–100 (2013) Favini, A., Yagi, A.: Multivalued linear operators and degenerate evolution equations. Annali di Matematica Pura ed Applicata 163(1), 353–384 (1993) Favini, A., Yagi, A.: Degenerate Differential Equations in Banach Spaces.