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  3. Collection Alea-Saclay: Monographs and Texts in Statistical Physics

Statistical physics is one of the most active and exciting current areas of research in the physical sciences. Published in collaboration with CEN Saclay, one of the leading European centres of research in this area, this new international series will cover statistical physics in its broadest sense, including condensed matter physics, hydrodynamics, dynamical systems and chaos. Titles published in this series will be at graduate and research level.Aléa is a French word meaning an unpredictable event, and is derived from the Latin word "alea" meaning "dice."

  • General Editors: C. Godrèche

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8 results in Collection Alea-Saclay: Monographs and Texts in Statistical Physics

Introduction to the Replica Theory of Disordered Statistical Systems
  • Viktor Dotsenko
  • Published online:
    08 September 2009
    Print publication:
    02 November 2000
  • This book describes the statistical mechanics of classical spin systems with quenched disorder. The first part of the book covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The technique of replica symmetry breaking is explained in detail, along with a discussion of the underlying physics. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory, which is then used to obtain a new 'random' critical regime in disordered vector ferromagnets and in the two-dimensional Ising model. The third part of the book describes other types of disordered systems, relating to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.

Geometrical Frustration
  • Jean-François Sadoc, Rémy Mosseri
  • Published online:
    06 January 2010
    Print publication:
    12 August 1999
  • This book shows how the concept of geometrical frustration can be used to elucidate the structure and properties of non-periodic materials such as metallic glasses, quasicrystals, amorphous semiconductors and complex liquid crystals. Geometric frustration is introduced through examples and idealized models, leading to a consideration of how the concept can be used to identify ordered and defective regions in real materials. Then it is shown how these principles can also be used to model physical properties of materials, in particular specific volume, melting, the structure factor and the glass transition. Final chapters consider geometric frustration in periodic structures with large cells and quasiperiodic order. Appendices give all necessary background on geometry, symmetry and tilings. The text considers geometrical frustration at different scales in many types of materials and structures, including metals, amorphous solids, liquid crystals, amphiphiles, cholisteric systems, polymers, phospholipid membranes, atomic clusters, and quasicrystals. Of interest to researchers in condensed matter physics, materials science and structural chemistry, as well as mathematics and structural biology.

Nonequilibrium Phase Transitions in Lattice Models
  • Joaquin Marro, Ronald Dickman
  • Published online:
    29 September 2009
    Print publication:
    06 May 1999
  • This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.

Physics of Crystal Growth
  • Alberto Pimpinelli, Jacques Villain
  • Published online:
    07 May 2010
    Print publication:
    10 December 1998
  • This 1998 study introduces the physical principles of how and why crystals grow. The first three chapters recall the fundamental properties of crystal surfaces at equilibrium. The next six chapters describe simple models and basic concepts of crystal growth including diffusion, thermal smoothing of a surface, and applications to semiconductors. Following chapters examine more complex topics such as kinetic roughness, growth instabilities, and elastic effects. A brief closing chapter looks back at the crucial contributions of crystal growth in electronics during the twentieth century. The book focuses on growth using molecular beam epitaxy. Throughout, the emphasis is on the role played by statistical physics. Informative appendices, interesting exercises and an extensive bibliography reinforce the text.

Cellular Automata Modeling of Physical Systems
  • Bastien Chopard, Michel Droz
  • Published online:
    26 October 2009
    Print publication:
    10 December 1998
  • This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemical physics and computer science.

Hydrodynamics and Nonlinear Instabilities
  • Edited by Claude Godrèche, Paul Manneville
  • Published online:
    04 November 2009
    Print publication:
    16 April 1998
  • This book presents five sets of pedagogical lectures by internationally respected researchers on nonlinear instabilities and the transition to turbulence in hydrodynamics. The book begins with a general introduction to hydrodynamics covering fluid properties, flow measurement, dimensional analysis and turbulence. Chapter two reviews the special characteristics of instabilities in open flows. Chapter three presents mathematical tools for multiscale analysis and asymptotic matching applied to the dynamics of fronts and localized nonlinear states. Chapter four gives a detailed review of pattern forming instabilities. The final chapter provides a detailed and comprehensive introduction to the instability of flames, shocks and detonations. Together, these lectures provide a thought-provoking overview of current research in this important area.

Lattice-Gas Cellular Automata
  • Simple Models of Complex Hydrodynamics
  • Daniel H. Rothman, Stiphane Zaleski
  • Published online:
    23 September 2009
    Print publication:
    28 August 1997
  • The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and references are included.

An Introduction to the Modeling of Neural Networks
  • Pierre Peretto
  • Published online:
    30 November 2009
    Print publication:
    29 October 1992
  • This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual neuronal supercomputers, with the potential for one-hundred-fold increase in speed over contemporary serial machines.