الصفحة 1
الصفحة 1
Nonlinear Fokker-Planck Equations : Fundamentals and Applications
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, population dynamics, and computational physics.
Non-Linear Dynamics Near and Far from Equilibrium
This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling.
Non-Linear Dynamics and Fundamental Interactions
This volume contains the papers presented at the NATO Advanced Research Institute on "Non-Linear Dynamics and Fundamental Interactions" held in Tashkent, Uzbekistan, from Oct.10-16,2004. The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions.
Non-Equilibrium Phase Transitions ; Vol. I : Absorbing Phase Transitions
This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed.
Nano- and Micromaterials
The future focus of nanotechnology will be on realizing new functions over greater scales. This book describes the creation of nano- and microscale structures and functions by controlling temperature, light, pressure, or carrier injections. It covers novel nano-integration technologies such as quantum-well devices possilbe by utilizing, for example, the self-organization of surface nanostructures and optically or pressure-induced phase transitions, micro machines using microstereolithography, as well as new techniques of laser spectroscopy and new computational methods for estimating atomic and electronic structures and their functions on the nano- and microscales.
Modern Hematology : Biology and Clinical Management
The first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter.
High Tc superconductors and related transition metal oxides : Special Contributions in Honor of K. Alex Müller on the Occasion of his 80th Birthday
This book containing 30 articles the contributions reflect the major research areas of K. Alex Müller which he activated in high temperature superconductivity and phase transitions. They are theoretical as well as experimental ones and focus mainly on high temperature superconductivity. A smaller part deals with ferroelectricity and their applications.
From microphysics to macrophysics : Methods and applications of statistical physics; Vol.1
Volume 1 discusses in detail the probabilistic description of quantum or classical systems, the Boltzmann-Gibbs distributions, the conservation laws, and the interpretation of entropy as missing information. Thermodynamics and electromagnetism in matter are dealt with, as well as applications to gases, both dilute and condensed, and to phase transitions.
Equilibrium statistical physics : Phases of matter and phase transitions
This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The latter include the renormalisation group approach to critical phenomena, the density functional theory of interfaces, the topological defects of nematic liquid crystals and the kinematic aspects of the phase transformation process. This textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. References include suggestions for more detailed treatments and four appendices supply overviews of the mathematical tools employed in the text.
Eigenvalues, Inequalities, and Ergodic Theory
A problem of broad interest – the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) – is covered in this book. The area has a wide range of applications, and provides a tool to describe the phase transitions and the effectiveness of random algorithms. In particular, the book studies a subset of the general problem, taking some approaches that have, up till now, only appeared largely in the Chinese literature.Eigenvalues, Inequalities and Ergodic Theory serves as an introduction to this developing field, and provides an overview of the methods used, in an accessible and concise manner.
Crystallography and the World of Symmetry
Symmetry exists in realms from crystals to patterns, in external shapes of living or non-living objects, as well as in the fundamental particles and the physical laws that govern them. In fact, the search for this symmetry is the driving force for the discovery of many fundamental particles and the formulation of many physical laws. While one can not imagine a world which is absolutely symmetrical nor can one a world which is absolutely asymmetrical. These two aspects of nature are intermingled with each other inseparably. This is the basis of the existence of aperiodicity manifested in the liquid crystals and also quasi-crystals also discussed in Crystallography and the World of Symmetry.
Consciousness : A Mathematical Treatment of the Global Neuronal Workspace Model
This book brings together the fundamental ideas of information theory and the statistical mechanics of phase transitions within the context of the neurosciences, culture, immunology and socio-psychological studies. Outlined is a program pertaining to a dynamic and semantic extension of current models for the global neuronal workspace as were previously introduced by Baars, Dretske and others.
Computer simulation studies in condensed-matter physics XVIII ; Proceedings of the Eighteenth Workshop, Athens, GA, USA, March 7-11, 2005
This volume represents a "status report" emanating from presentations made during the 18th Annual Workshop on Computer Simulations Studies in Condensed Matter Physics at the Center for Simulational Physics at the University of Georgia in March 2005. It provides a broad overview of the most recent advances in the field, spanning the range from statistical physics to soft condensed matter and biological systems. Results on nanostructures and materials are included as are several descriptions of advances in quantum simulations and quantum computing as well as.methodological advances.
Computer simulation studies in condensed-matter physics XVI ; Proceedings of the Seventeenth Workshop, Athens, GA, USA, February 16-20, 2004
This status report features the most recent developments in the field, spanning a wide range of topical areas in the computer simulation of condensed matter/materials physics. Both established and new topics are included, ranging from the statistical mechanics of classical magnetic spin models to electronic structure calculations, quantum simulations, and simulations of soft condensed matter. The book presents new physical results as well as novel methods of simulation and data analysis. Highlights of this volume include various aspects of non-equilibrium statistical mechanics, studies of properties of real materials using both classical model simulations and electronic structure calculations, and the use of computer simulations in teaching.
Collective Dynamics of Nonlinear and Disordered Systems
Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.
Mathematical Modelling of Biosystems
This volume is an interdisciplinary book, which introduces, in a very readable way, state of the art research in the fundamental topics of mathematical modelling of Biosystems. These topics include: the study of Biological Growth and its mechanisms, the coupling of pattern to form via theorems of Differential Geometry, the human immunodeficiency virus dynamics, the inverse folding problem and the possibility of analysing true protein backbone flexibility, the Biclustering techniques for the organization of microarray data, the analytical approach to the modelling of biomolecular structure via Steiner trees, the action of biocides on resistance mechanisms of mutated and phenotypic bacteria strains, a description of the fundamental processes for the distribution and abundances of species towards a unified theory of Ecology, and a special introduction to Protein Physics aiming to explain the all-or-none first order phase transitions from native to denatured states.
Complex Nonlinearity : Chaos, Phase Transitions, Topology Change and Path Integrals
The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism.
Classical Nucleation Theory in Multicomponent Systems
Nucleation is the initial step of every first-order phase transition, and most phase transitions encountered both in everyday life and industrial processes are of the first-order. Using an elegant classical theory based on thermodynamics and kinetics, this book provides a fully detailed picture of multi-component nucleation. As many of the issues concerning multi-component nucleation theory have been solved during the last 10-15 years, it also thoroughly integrates both fundamental theory with recent advances presented in the literature. It covered are: the basic relevant thermodynamics and statistical physics; modelling a molecular cluster as a spherical liquid droplet; predicting the size and composition of the nucleating critical clusters; kinetic models for cluster growth and decay; calculating nucleation rates; and a full derivation and application of nucleation theorems that can be used to extract microscopic cluster properties from nucleation rate measurements.
Analysis and Simulation of Fluid Dynamics
This volume collects the contributions of a Conference held in June 2005, at the laboratoire Paul Painlev́ e (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in ?uid dynamics.
