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.
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
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.
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