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This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.
The volumes present investigations on grain growth phenomena and their observation in various materials: metals and alloys, ceramics, sintered materials, thin films, etc.; normal and abnormal grain growth including twinning, texture, particle and other drag effects as well as analysis of topological aspects and grain size and grain orientation correlations; grain boundary structure, mobility and interaction with particles and impurity atoms. Experimental methods applicable to measurements of grain size, orientation of individual grains, etc.
This volume contains about 180 papers including seven keynotes presented at the 7th NUMIFORM Conference. It reflects the state-of-the-art of simulation of industrial forming processes such as rolling, forging, sheet metal forming, injection moulding and casting.
This issue of the Ceramic Transactions compiles 41 papers covering a rich diversity of the sintering science and technology topics. These papers were presented at the International Conference on Sintering, November 16-20, 2008 in La Jolla, California. The Ceramic Transactions series contains a collection of papers dealing with issues in both traditional ceramics (i.e., glass, whitewares, refractories, and porcelain enamel) and advanced ceramics. Topics covered in the area of advanced ceramic include bioceramics, nanomaterials, composites, solid oxide fuel cells, mechanical properties and structural design, advanced ceramic coatings, ceramic armor, porous ceramics, and more.
It is about fifteen years since we started hearing about Computational Ma terials Science and Materials Modelling and Design. Fifteen years is a long time and all of us realise that the use of computational methods in the design of materials has not been rapid enough. We also know the reasons for this. Mate rials properties are not dependent on a single phenomenon. The properties of materials cover a wide range from electronic, thermal, mechanical to chemical and electro-chemical. Each of these class of properties depend on specific phe nomenon that takes place at different scales or levels of length from sub atomic to visible length levels. The energies controlling the phenomena also varies widely from a fraction of an electron volt to many joules. The complexity of materials are such that while models and methods for treating individual phenomenon have been perfected, incorporating them into a single programme taking into account the synergism is a formidable task. Two specific areas where the progress has been very rapid and substantive are prediction of phase stability and phase diagrams and embrittlement of steels by metalloids. The first three sections of the book contain papers which review the theoreti cal principles underlying materials modeling and simulations and show how they can be applied to the problems just mentioned. There is now a strong interest in designing new materials starting from nanoparticles and clusters.
The Ceramic Engineering and Science Proceeding has been published by The American Ceramic Society since 1980. This series contains a collection of papers dealing with issues in both traditional ceramics (i.e., glass, whitewares, refractories, and porcelain enamel) and advanced ceramics. Topics covered in the area of advanced ceramic include bioceramics, nanomaterials, composites, solid oxide fuel cells, mechanical properties and structural design, advanced ceramic coatings, ceramic armor, porous ceramics, and more.
The TMS 2015 Annual Meeting Supplemental Proceedings is a collection of papers from the TMS 2015 Annual Meeting & Exhibition, held March 15-19 in Orlando, Florida, USA. The papers in this volume represent 33 symposia from the meeting. This volume, along with the other proceedings volumes published for the meeting, and archival journals, such as Metallurgical and Materials Transactions and Journal of Electronic Materials, represents the available written record of the 73 symposia held at TMS2015. This proceedings volume contains both edited and unedited papers; the unedited papers have not necessarily been reviewed by the symposium organizers and are presented "as is." The opinions and statements expressed within the papers are those of the individual authors only, and no confirmations or endorsements are intended or implied.