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Fractals --- Probabilities --- Statistical mechanics --- Fractales --- Probabilités --- Mécanique statistique --- Congresses --- Congresses --- Congresses --- Congrès --- Congrès --- Congrès --- Lévy, Paul,
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The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface. The substantially revised and enlarged second edition makes in particular the second part of the book more self-contained and tutorial, with many more examples given. Furthermore, two new chapters on Wightman's axioms for quantum field theory and vertex algebras broaden the survey of advanced topics. An outlook making the connection with most recent developments has also been added.
Algebra --- Differential geometry. Global analysis --- Mathematical physics --- Elementary particles --- Physics --- algebra --- elementaire deeltjes --- differentiaal geometrie --- kwantumleer --- wiskunde --- fysica
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The application to Biology of the methodologies developed in Physics is attracting an increasing interest from the scientific community. It has led to the emergence of a new interdisciplinary field, called Physical Biology, with the aim of reaching a better understanding of the biological mechanisms at molecular and cellular levels. Statistical Mechanics in particular plays an important role in the development of this new field. For this reason, the XXth session of the famous Sitges Conference on Statistical Physics was dedicated to "Physical Biology: from Molecular Interactions to Cellular Behavior". As is by now tradition, a number of lectures were subsequently selected, expanded and updated for publication as lecture notes, so as to provide both a state-of-the-art introduction and overview to a number of subjects of broader interest and to favor the interchange and cross-fertilization of ideas between biologists and physicists. The present volume focuses on three main subtopics (biological water, protein solutions as well as transport and replication), presenting for each of the them the on-going debates on recent results. The role of water in biological processes, the mechanisms of protein folding, the phases and cooperative effects in biological solutions, the thermodynamic description of replication, transport and neural activity, all are subjects that are revised in this volume, based on new experiments and new theoretical interpretations.
Fluid mechanics --- Statistical physics --- General biophysics --- materie (fysica) --- biofysica --- statistiek --- fysica --- vloeistoffen
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This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.
Geometry --- Mathematical analysis --- Mathematical physics --- Physics --- analyse (wiskunde) --- wiskunde --- fysica --- geometrie
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Hard spheres and related objects (hard disks and mixtures of hard systems) are paradigmatic systems: indeed, they have served as a basis for the theoretical and numerical development of a number of fields, such as general liquids and fluids, amorphous solids, liquid crystals, colloids and granular matter, to name but a few. The present volume introduces and reviews some important basics and progress in the study of such systems. Their structure, thermodynamic properties, equations of state, as well as kinetic and transport properties are considered from different and complementary points of view. This book addresses graduate students, lecturers as well as researchers in statistical mechanics, physics of liquids, physical chemistry and chemical engineering.
Classical mechanics. Field theory --- Fluid mechanics --- Statistical physics --- Thermodynamics --- Physicochemistry --- Engineering sciences. Technology --- thermodynamica --- materie (fysica) --- toegepaste mechanica --- BIT (biochemische ingenieurstechnieken) --- statistiek --- ingenieurswetenschappen --- fysica --- mechanica --- fysicochemie --- vloeistoffen
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Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics. The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations. This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.
Astrophysics --- Mathematical physics --- Classical mechanics. Field theory --- Plasma physics --- Atomic physics --- astrofysica --- plasmafysica --- wiskunde --- fysica --- mechanica
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This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities. Graduate students and young scientists will benefit from this book by learning how to use the fundamental tools used in computational astrophysical jet research.
Numerical analysis --- Astrophysics --- Computer. Automation --- astrofysica --- algoritmen --- numerieke analyse
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Astrophysics --- Mathematical physics --- Classical mechanics. Field theory --- Plasma physics --- Atomic physics --- astrofysica --- plasmafysica --- wiskunde --- fysica --- mechanica
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Algebra --- Differential geometry. Global analysis --- Mathematical physics --- Elementary particles --- Physics --- algebra --- elementaire deeltjes --- differentiaal geometrie --- kwantumleer --- wiskunde --- fysica
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Numerical analysis --- Astrophysics --- Computer. Automation --- astrofysica --- algoritmen --- numerieke analyse
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