Download or read book The Wulff Crystal in Ising and Percolation Models written by Raphaël Cerf and published by Springer. This book was released on 2006-08-29 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.
Download or read book The Wulff Crystal in Ising and Percolation Models written by Raphaël Cerf and published by . This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Wulff Crystal in Ising and Percolation Models written by Raphaël Cerf and published by . This book was released on 2004 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Wulff Crystal in Ising and Percolation Models written by Raphaël Cerf and published by Springer Science & Business Media. This book was released on 2006-05-12 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.
Download or read book The Wulff Crystal in Ising and Percolation Models written by Raphaël Cerf and published by Springer. This book was released on 2009-09-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.
Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Download or read book Gibbs Measures and Phase Transitions written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2011-05-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Download or read book Handbook of Crystal Growth written by Tatau Nishinaga and published by Elsevier. This book was released on 2014-11-04 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume IAHandbook of Crystal Growth, 2nd Edition (Fundamentals: Thermodynamics and Kinetics) Volume IA addresses the present status of crystal growth science, and provides scientific tools for the following volumes: Volume II (Bulk Crystal Growth) and III (Thin Film Growth and Epitaxy). Volume IA highlights thermodynamics and kinetics. After historical introduction of the crystal growth, phase equilibria, defect thermodynamics, stoichiometry, and shape of crystal and structure of melt are described. Then, the most fundamental and basic aspects of crystal growth are presented, along with the theories of nucleation and growth kinetics. In addition, the simulations of crystal growth by Monte Carlo, ab initio-based approach and colloidal assembly are thoroughly investigated. Volume IBHandbook of Crystal Growth, 2nd Edition (Fundamentals: Transport and Stability) Volume IB discusses pattern formation, a typical problem in crystal growth. In addition, an introduction to morphological stability is given and the phase-field model is explained with comparison to experiments. The field of nanocrystal growth is rapidly expanding and here the growth from vapor is presented as an example. For the advancement of life science, the crystal growth of protein and other biological molecules is indispensable and biological crystallization in nature gives many hints for their crystal growth. Another subject discussed is pharmaceutical crystal growth. To understand the crystal growth, in situ observation is extremely powerful. The observation techniques are demonstrated. Volume IA - Explores phase equilibria, defect thermodynamics of Si, stoichiometry of oxides and atomistic structure of melt and alloys - Explains basic ideas to understand crystal growth, equilibrium shape of crystal, rough-smooth transition of step and surface, nucleation and growth mechanisms - Focuses on simulation of crystal growth by classical Monte Carlo, ab-initio based quantum mechanical approach, kinetic Monte Carlo and phase field model. Controlled colloidal assembly is presented as an experimental model for crystal growth. Volume IIB - Describes morphological stability theory and phase-field model and comparison to experiments of dendritic growth - Presents nanocrystal growth in vapor as well as protein crystal growth and biological crystallization - Interprets mass production of pharmaceutical crystals to be understood as ordinary crystal growth and explains crystallization of chiral molecules - Demonstrates in situ observation of crystal growth in vapor, solution and melt on the ground and in space
Download or read book Progress in High Dimensional Percolation and Random Graphs written by Markus Heydenreich and published by Springer. This book was released on 2017-11-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.
Download or read book Probability on Discrete Structures written by Harry Kesten and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Download or read book Physics of Wetting written by Edward Yu. Bormashenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by a plethora of phenomena from nature, this textbook introduces into the physics of wetting of surfaces. After a brief discussion of the foundations of surface tension, its implementation for floating objects, capillary waves, bouncing droplets, walking of water striders, etc. is discussed. Furthermore, Marangoni flows, surface tension inspired instabilities, condensation and evaporation of droplets, liquid marbles, superhydrophobicity and superoleophobicity (lotus effect) are introduced. All relevant concepts are illustrated by the numerous qualitative and quantitative exercises. Contents What is surface tension? Wetting of surfaces: the contact angle Surface tension-assisted floating of heavy and light objects and walking of water striders Capillary interactions between particles. Particles placed on liquid surfaces. Elasticity of liquid surfaces, covered by colloidal particles Capillary waves Oscillation of droplets Marangoni flow and surface instabilities Evaporation of droplets. The Kelvin and the coffee-stain effects Condensation, growth and coalescence of droplets and the breath-figure self-assembly Dynamics of wetting: bouncing, spreading and rolling of droplets (water hammer effect – water entry and drag-out problems)Superhydrophobicity and superoleophobicity: the Wenzel and Cassie wetting regimes The Leidenfrost effect. Liquid marbles: self-propulsion Physics, geometry, life and death of soap films and bubbles
Download or read book 2018 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2020-04-07 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Download or read book In and Out of Equilibrium written by Vladas Sidoravicius and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom were personally responsible for advances in the various subfields of probability. Graduate students and researchers in probability theory and math physics will find this book a useful reference.
Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Download or read book The Low temperature Expansion of the Wulff Crystal in the 3D Ising Model written by Raphaël Cerf and published by . This book was released on 2001 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Variational Problems with Interfaces written by Roberto Alicandro and published by Cambridge University Press. This book was released on 2023-12-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
