Heike Emmerich Bücher

The book explores inhomogeneous systems characterized by distinct phases separated by interfaces, particularly focusing on how these phases behave when driven out of equilibrium. It delves into phenomena such as phase separation and dendritic solidification, emphasizing the sharp interface approach used in both analytical and numerical studies. This method involves defining boundary conditions that dictate the movement of the interface, rooted in symmetry arguments and intuitive reasoning. The text provides a comprehensive examination of these complex physical processes.

. . . Eat not up your property among yourselves unjustly except it be a trade amongst you, by mutual consent . . . and help you one another in righteousness and piety. . . (Al-Hadid 4:29; Al-Ma’idah 5:2) There cannot be any doubt that the current ?nancial crisis, which began in the US, has gone global. This realization has fuelled the ?re of debate over globalization. Today’s globalization is no longer the globalization that Theodore Levitt, a former professor at the Harvard Business School, described in 1983 in his world famous article ‘‘The Globalization of Markets. ’’ Although, in old days, Levitt and his successors had not seen globalization as an utopian state free of problems, no- days globalization has been reshaped completely. Therefore, in the perception of the editors it is justi?ed to use the phrase ‘‘Globalisation 2. 0’’ for the range of effects interpenetrating global economic arrangements. Globalisation 1. 0 will never be restored again. Since the subprime crisis made its way to the global arena in the year 2008, companies and managers are confronted with the breathtaking speed of global, regional, and local changes. It is more than a provocation to divide dev- opments into cause and effects. Forecasts in strategic management are no longer valid even for the moment they are published. Uncertainty occupies the driving seats in global, regional, and local oriented companies.

The workshop on "computational physics of transport and interfacial dynamics" took place in Dresden, Germany, from February 25 to March 8, 2002, sponsored by the Max Planck Institute for the Physics of Complex Systems. It focused on recent advancements in computational physics and materials science, particularly in modeling traffic flow phenomena and complex multi-scale solidification. These areas connect diverse disciplines, including physics, mathematical and computational modeling, nonlinear dynamics, materials sciences, statistical mechanics, and foundry techniques. The international gathering aimed to foster knowledge exchange, assess common interests, and promote collaboration among researchers from various fields. It sought to create a comprehensive understanding of the current research landscape and outline potential future joint activities. Special emphasis was placed on sharing experiences with numerical tools and bridging scales relevant to various scientific and engineering applications. A notable aspect discussed was the coupling of different computational methods for hybrid simulations. The workshop specifically addressed researchers using a range of numerical schemes, including cellular automata, coupled maps, and finite difference and finite element algorithms for partial differential equations, such as phase-field computations.

The book is devoted to the application of phase-field (diffuse interface) models in materials science. Phase-field modeling emerged only recently as a theoretical approach to tackle questions concerning the evolution of materials microstructure, the relation between microstructure and materials properties and the transformation and evolution of different phases. This volume brings together the essential thermodynamic ideas as well as the essential mathematical tools to derive phase-field model equations. Starting from an elementary level such that any graduate student familiar with the basic concepts of partial differential equations can follow, it shows how advances in the field of phase-field modeling will come from a combination of thermodynamic, mathematical and computational tools. Also included are two extensive examples of the application of phase-field models in materials science.