Baus, M. & Tejero, C. F.
Equilibrium Statistical Physics
Phases of Matter and Phase Transitions
Springer-Verlag 2008.1.3
364 pp.(H)
ISBN 3-540-74631-5
13,500円
Contents
Part I. Basics: Mechanics: 1.Thermodynamics/ 2.Statistical Physics/ Part II. Ideal Systems: 3.Microcanonical Ensemble/ 4.Canonical Ensemble/ 5.Grand Canonical Ensemble/ Part III. Non-Ideal Systems: 6.Classical Systems with Interactions/ 7.Phases of Matter/ 8.Phase Transitions/ Part IV. More Advanced Topics: 9.Critical Phenomena/ 10.Interfaces/ 11.Topological Defects/ 12. Phase Transformation Kinetics/ Part V Appendices: 13.Legendre Transformations/ 14.Random Variables/ 15.Functional and Functional Derivative/ 16.A Quasicrystalline Lattice/ Index/
* 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. *
Onuki, A.
Phase Transition Dynamics
Cambridge University Press 2007.8
724 pp.(P)
ISBN 0-521-03905-3
16,400円
Contents
Part 1: Statics: 1. Spin systems and fluids/ 2. Critical phenomena and scaling/ 3. Mean field theories/ 4. Advanced theories in statics/ Part 2: Dynamic models and dynamics in fluids and polymers: 5. Dynamic models/ 6. Dynamics in fluids/ 7. Dynamics in polymers and gels/ Part 3: Dynamics of phase changes: 8. Phase ordering and defect dynamics/ 9. Nucleation/ 10. Phase transition dynamics in solids/ 11. Phase transitions of fluids in shear flow/ References/ Index/
* This book treats a wide variety of topics systematically by constructing time-dependent Ginzburg-Landau models for various systems in physics, metallurgy, and polymer science. Beginning with a summary of advanced statistical-mechanical theories including the renormalization group theory, the book reviews dynamical theories, and covers the kinetics of phase ordering, spinodal decomposition, and nucleation in depth.
* The phase transition dynamics of real systems are discussed, treating interdisciplinary problems in a unified manner. New topics include supercritical fluid dynamics, stress-diffusion coupling in polymers, and mesoscopic dynamics at structural phase transitions in solids. *
Smirnov, B. M. & Berry, R. S.
Phase Transitions of Simple Systems
Springer-Verlag 2008.
247 pp.(H) 【在庫有り】
ISBN 3-540-71513-4
19,400円
Contents
Part I Thermodynamics of Ensembles of Classical Particles: 1 Excitations in Simple Atomic Ensembles/ 2 Structures of Ensembles of Interacting Particles/ 3 Thermodynamics of Dense Gases and Liquids/ 4 Clusters with Short-Range Interaction/ 5 Ensembles of Classical Particles with Repulsion/ Part II Configurational Excitations and Aggregate States of Ensembles of Classical Particles: 6 Configurational Excitation and Voids in Ensembles of Bound Classical Atoms/ 7 Configurational Cluster Excitation with Pairwise Interactions/ 8 Phase Transitions in Macroscopic Systems of Atoms/ 9 Melting of Clusters and Bulk Atomic Ensembles/ Part III Dynamics of Configurational Excitations in Ensembles of Classical Particles: 10 Coexistence of Cluster Phases/ 11 Glassy States of an Ensemble of Bound Atoms/ 12 Transport of Voids in Nucleation Processes/ References/ Index/
* This monograph develops a unified microscopic basis for phases and phase changes of bulk matter and small systems in terms of classical physics. The origins of such phase changes are derived from simple but physically relevant models of how transitions between rigid crystalline, glassy and fluid states occur, how phase equilibria arise, and how bulk properties evolve from those of small systems. *
Keller, A. et al. ed.
Monte Carlo and Quasi-Monte Carlo Methods 2006
Springer-Verlag 2008.
698 pp.(P)
ISBN 3-540-74495-9
18,700円
Contents
Part I: Invited Articles: 1.A Belgian View on Lattice Rules/ 2.MCQMC Algorithms for Solving some Classes of Equations/ 3.MCQMC Methods for Multivariate Statistical Distributions/ 4.Minimal Errors for Strong and Weak Approximation of Stochastic Differential Equations/ 5.Nets, (t, s)-Sequences, and Codes/ 6.Quadratic Optimal Functional Quantization of Stochastic Processes and Numerical Applications/ 7.Random Field Simulation and Applications/ 8.Monte Carlo and Quasi-Monte Carlo Methods for Computer Graphics/ Part II: Contributed Articles: 9.Random Walk Algorithm for Estimating the Derivatives of Solution to the Elliptic BVP/ 10.Free-Knot Spline Approximation of Fractional Brownian Motion/ 11.Simulation on Rank-1 Lattices/ 12.Image Synthesis by Rank-1 Lattices/ 13.Continuous Runge-Kutta Methods for Stratonovich Stochastic Differential Equations/ 14.Issues on Computer Search for Large Order Multiple Recursive Generators/ 15.Design and Implementation of Efficient and Portable Multiple Recursive Generators with Few Zero Coefficients/ 16.Approximation of Functions Using Digital Nets/ 17.Construction of Low-Discrepancy Point Sets of Small Size by Bracketing Covers and Dependent Randomized Rounding/ 18.A Coding Theoretic Approach to Building Nets with Well-Equidistributed Projections/ 19.Improvements on Low Discrepancy One-Dimensional Sequences and Two-Dimensional Point Sets/ 20.Improved Multilevel Monte Carlo Convergence using the Milstein Scheme/ 21.Generalized Tractability for Linear Functionals/ 22.An Improved Implementation of Stochastic Particle Methods and Applications to 23.Coagulation Equations/ (t, m, s)-Nets and Maximized Minimum Distance/ 24.Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces/ 25.Computational Engine for a Virtual Tissue Simulator/ 26.Randomized Approximation of Sobolev Embeddings/ 27.Tractability of Linear Multivariate Problems in the Average Case Setting/ 28.Zinterhof Sequences in GRID-Based Numerical Integration/ 29.A Pragmatic View on Numerical Integration of Unbounded Functions/ 30.Assessment of Genetic Association using Haplotypes Inferred with Uncertainty via Markov Chain Monte Carlo/ 31.The Generalized Gibbs Sampler and the Neighborhood Sampler/ 32.The Weighted Dyadic Diaphony of Digital Sequences/ 33.A New Criterion for Finiteness of Weight Estimator Variance in Statistical Simulation/ 34.Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise/ 35.Unbiased Global Illumination with Participating Media/ 36.SIMD-Oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator/ 37.A New Lower Bound on the t-Parameter of (t, s)-Sequences/ 38.Walk-on-Spheres Algorithm for Solving Boundary-Value Problems with Continuity Flux Conditions/ 39.Good Lattice Rules with a Composite Number of Points Based on the Product Weighted Star Discrepancy/ 40.Ergodic Simulations for Diffusion in Random Velocity Fields/ 41.Efficient Simultaneous Simulation of Markov Chains/ Part III: Appendix: 42.Conference Participants/ Author Index/
* This book represents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm (Germany) in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications, as well as providing information on current research in these very active areas. Besides covering theory, the book is an excellent resource work for practitioners as well. *
Zinn-Justin, J.
Phase Transitions and Renormalisation Group
Oxford U.P. 2007.8
464 pp. (H)
ISBN 0-19-922719-5
11,100円
Contents
1. Quantum Field Theory and Renormalization Group / 2. Gaussian Expectation Values. Steepest Descent Method / 3. Universality and Continuum Limit / 4. Classical Statistical Physics: One Dimension / 5. Continuum Limit and Path Integral / 6. Ferromagnetic Systems. Correlations / 7. Phase transitions: Generalities and Examples / 8. Quasi-Gaussian Approximation: Universality, Critical Dimension / 9. Renormalization Group: General Formulation / 10. Perturbative Renormalization Group: Explicit Calculations / 11. Renormalization group: N-component fields / 12. Statistical Field Theory: Perturbative Expansion / 13. The sigma4 Field Theory near Dimension 4 / 14. The O(N) Symmetric (phi2)2 Field Theory: Large N Limit / 15. The Non-Linear sigma-Model / 16. Functional Renormalization Group / Appendix / *
* This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. *
Oystaeyen, F. V.
Virtual Topology and Functor Geometry
CRC Press 2007.11
168 pp.(P)
ISBN 1-4200-6056-2
13,100円
Contents
Part.1:A Taste of Category Theory: 1.Basic Notions/ 2.Grothendieck Categories/ 3.Separable Functors/ Part.2:Noncommtative Spaces: 4.Small Categories, Posets, and Noncommutative Topologies/ 5.The Topology of Virtual Opens and Its Commutative Shadow/ 6.Points and the Point Spectrum: Points in a Pointless World/ 7.Presheaves and Sheaves over Noncommutative Topologies/ 8.Noncommutative Grothendieck Topologies/ 9.The Fundamental Examples I: Torsion Theories/ 10.The Fundamental Examples II: L(H)/ 11.Ore Sets in Schematic Algebras/ Part.3:Grothendieck Categorical Reoresentations: 12.Spectral Representations/ 13.Affine Elements/ 14.Quotient Representations/ 15.Noncommutative Projective Space/ part.4:Sheaves and Dynamical Topology: 16.Introducing Structure Sheaves/ 17.Dynamical Presheaves and Temporal Points/ 18.The Spaced-Time Model/ Bibliography/ Index/
* Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra. *
Schweitzer, F.
Brownian Agents and Active Particles
Collective Dynamics in the Natural and Social Sciences
ブラウン運動をする構成要素と活性粒子 自然科学と社会科学における集団力学
Springer-Verlag 2007.9
420 pp. (P)
ISBN 3-540-73844-4
8,200円
Contents
1.Complex Systems and Agent Models.- 2.Active Particles.- 3.Aggregation and Physico-Chemical Structure Formation.- 4.Self-Organization of Networks.- 5.Tracks and Trail Formation in Biological Systems.- 6.Movement and Trail Formation of Pedestrians.- 7.Evolutionary Optimization Using Brownian Searchers.- 8.Analysis and Simulation of Urban Aggregation.- 9.Economic Agglomeration.- 10.Spatial Opinion Sructures in Social Systems/ *
* "This book lays out a vision for a coherent framework for understanding complex systems'' (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from physicochemical pattern formation, to active motion and swarming in biological systems, to self-assembling of networks, evolutionary optimization, urban growth, economic agglomeration and even social systems. *
170-52 登録日 08.03.17
