Discontinuous (first-order) phase transitions constitute the most fundamental and widespread type of structural transitions existing in Nature, forming a large majority of the transitions found in elemental crystals, alloys, inorganic compounds, minerals and complex fluids. Nevertheless, only a small part of them, namely, weakly discontinuous transformations, were considered by phenomenological theories, leaving aside the most interesting from a theoretical point of view and the most important for application cases. Discontinuous Phase Transitions in Condensed Matter introduces a density-wave approach to phase transitions which results in a unified, symmetry-based, model-free theory of the weak crystallization of molecular mixtures to liquid-crystalline mesophases, strongly discontinuous crystallization from molten metals and alloys to conventional, fully segregated crystals, to aperiodic, quasi-crystalline structures. Assembly of aperiodic closed virus capsids with non-crystallographic symmetry also falls into the domain of applicability of the density-wave approach.The book also considers the applicability domains of the symmetry-based approach in physics of low-dimensional systems. It includes comparisons of stability of different surface superstructures and metal monoatomic coverage structures on the surface of single-crystalline substrates. The example of the twisted graphene bilayer demonstrates how parametrization in the spirit of an advanced phenomenological approach can establish symmetry-controlled, and therefore model-free, links between geometrical parameters of the twisted bilayer structure and reconstruction of its Brillouin zone and energy bands.

Magnetism and Structure in Functional Materials addresses three distinct but related topics: (i) magnetoelastic materials such as magnetic martensites and magnetic shape memory alloys, (ii) the magnetocaloric effect related to magnetostructural transitions, and (iii) colossal magnetoresistance (CMR) and related manganites. The goal is to identify common underlying principles in these classes of materials that are relevant for optimizing various functionalities. The emergence of apparently different magnetic/structural phenomena in disparate classes of materials clearly points to a need for common concepts in order to achieve a broader understanding of the interplay between magnetism and structure in this general class of new functional materials exhibiting ever more complex microstructure and function. The topic is interdisciplinary in nature and the contributors correspondingly include physicists, materials scientists and engineers. Likewise the book will appeal to scientists from all these areas.

This book brings together an emerging consensus on our understanding of the complex functional materials including ferroics, perovskites, multiferroics, CMR and high-temperature superconductors. The common theme is the existence of many competing ground states and frustration as a collusion of spin, charge, orbital and lattice degrees of freedom in the presence of disorder and (both dipolar and elastic) long-range forces. An important consequence of the complex unit cell and the competing interactions is that the emergent materials properties are very sensitive to external fields thus rendering these materials with highly desirable, technologically important applications enabled by cross-response.

Elements of Rapid Solidification: Fundamentals and Applications is the product of many years of concentrated work in the field of rapid solidification and processing. This quasi-monograph is unique in two ways. It brings together the talent of many international scientists in an effort to focus attention on all aspects of a new scientific field and it concentrates on fundamentals and practical applications. Simply stated, this book has been written by the senior students in the field of rapid solidification technology for the new generation of solid-state physicists, materials scientists, materials engineers, metallurgists and ceramicists.

In the fall of 1998, Prof. Sergey Firstov invited me to the Frantcevych Institute for Problems of Materials Science (IPMS) in Kyiv, Ukraine to discuss possible collaborations in the area of advanced metals research. During this visit, a strong mutual interest was evident in a broad range of structural metals technologies, and a quick friendship was established. Countless subsequent emails and a reciprocal visit to the U. S Air Force Research Laboratory by Prof. Firstov and a team of scientists from IPMS ensued to discuss and detail a broad collaboration in the area of structural metals. Two years after the initial visit, a major investment by the U. S. Air Force Office of Scientific Research (AFOSR) was established to pursue the technologies defined by these interactions. The annual reviews of the AFOSR Ukrainian Metals Initiative were held in late May, a most beautiful time in Kyiv when the lilacs are in bright display and the air is scented with the smell of falling blossoms from the chestnut trees that line the major streets and many parks. The sunny days and mild evenings provide a welcome break from winter, and on weekend evenings festive crowds spill onto the Khreshchatyk, Kyiv’s downtown boulevard, to listen to street musicians, watch jugglers and comedians, or simply to celebrate with friends. The annual reviews featured long days of intensive discussion of technical progress, followed in the evenings by the warm hospitality of the Ukrainian hosts.

Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.