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Phase Field Theory in Materials Physics
This book deals with the use of the hodograph equation in phase transformations in condensed matter, especially, for crystallization and solidification processes. The main focus of the book is the interpretation of the phase-field equations for isotropic and anisotropic interfaces based on the advanced Gibbs–Thomson and Herring conditions, respectively. Beginning with the basic ideas behind the extended irreversible thermodynamics, the kinetic phase-field model for slow and arbitrarily fast phase transformations is derived where the unified hodograph equation follows from: • the sharp interface limit of the diffuse interface or • the traveling wave solution of the propagating phase field. Under the example of solute trapping and disorder trapping effects, comparing theoretical results with molecular dynamics simulations, and with the analysis of experimental data, the concrete workability of the developed hodograph equation is demonstrated for widest range of driving force in phase transformations.
Metastable Solids from Undercooled Melts
This book presents the physical concepts and tools to characterize and describe the formation of metastable solids from undercooled melts. Its aim is to facilitate understanding of the development of the science and technology of solidification of melts and to introduce new concepts within this exciting research field in order to fulfil the challenges of the future in the field of undercooled melts. A comprehensive description of the science and applications of the undercooling phenomenon is given. It is composed of several main parts: experimental techniques for undercooling; characterization of the undercooled melt as the first step in rapid solidification; introducing the concepts of modern theories of rapid dendrite and eutectic growth and their comparison with experimental results, and a survey of metastable materials formed from the non-equilibrium state of an undercooled melt.* Showing clear links to possible application of results obtained from basic research * The subject matter is multidisciplinary and will be of interest to material scientists, physicists, physical chemists, mechanical and electrical engineers
Interface and Transport Dynamics
An overview of the recent progress of research in computational physics and materials science. Particular topics are modelling of traffic flow and complex multi-scale solidification phenomena. The sections introduce novel research results of experts from a considerable diversity of disciplines such as physics, mathematical and computational modelling, nonlinear dynamics, materials sciences, statistical mechanics and foundry technique. The book intends to create a comprehensive and coherent image of the current research status and illustrates new simulation results of transport and interface dynamics by high resolution graphics. Various possible perspectives are formulated for future activities. Special emphasis is laid on exchanging experiences concerning numerical tools and on the bridging of the scales as is necessary in a variety of scientific and engineering applications. An interesting possibility along this line was the coupling of different computational approaches leading to hybrid simulations.
Physics of Dendrites
This volume presents the growth of macrostructures in first-order nonequilibrium phase transitions in physical, chemical and biological multicomponent systems. Nonequilibrium thermodynamics and modern problems of crystallization synergetics are discussed. An introduction to computer physics of dendrites is also given. Wonderful variety in growth structures appears to be the consequence of different nonequilibrium alloy crystallization conditions and concerns problems of crystallization synergetics. This book has computer simulation results of the origin and development of the observed variety of primary macroscopic growth structures ? cells, dendrites and grains should be regarded as one of the fundamental problems of alloy crystallization. Special attention is paid to the physical nature of phenomena of dendrite formation in alloys.
Complexus Mundi
The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavor. Do nonlinear interact...
Phase-Field Crystals
The Phase Field Crystal (PFC) model incorporates microscopic structural details into a mesoscopic continuum theory. Methods for fast propagation of PFC interfaces are discussed in this book. They can handle a wide range of thermal gradients, supersaturations and supercoolings, including applications such as selective laser melting. The reader will find theoretical treatment in the first half, while the latter half discusses numerical models.
Solidification of Containerless Undercooled Melts
All metallic materials are prepared from the liquid state as their parent phase. Solidification is therefore one of the most important phase transformation in daily human life. Solidification is the transition from liquid to solid state of matter. The conditions under which material is transformed determines the physical and chemical properties of the as-solidified body. The processes involved, like nucleation and crystal growth, are governed by heat and mass transport. Convection and undercooling provide additional processing parameters to tune the solidification process and to control solid material performance from the very beginning of the production chain. To develop a predictive capabi...
Rigid Body Dynamics
This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of ...
Mathematical Models of Convection
The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.
