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This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.
Nonequilibrium statistical mechanics. --- Phase transformations (Statistical physics). --- Statisitics. --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Physics --- Atomic Physics --- Broken symmetry (Physics) --- Phase transformations (Statistical physics) --- Scaling laws (Statistical physics) --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Symmetry breaking (Physics) --- Physics. --- Probabilities. --- Condensed matter. --- Statistical physics. --- Dynamical systems. --- Theoretical, Mathematical and Computational Physics. --- Condensed Matter Physics. --- Statistical Physics, Dynamical Systems and Complexity. --- Probability Theory and Stochastic Processes. --- Numerical and Computational Physics. --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Symmetry (Physics) --- Phase rule and equilibrium --- Distribution (Probability theory. --- Complex Systems. --- Numerical and Computational Physics, Simulation. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistical methods --- Mathematical physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Physical mathematics --- Nonequilibrium statistical mechanics
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This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.
Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Classical mechanics. Field theory --- Statistical physics --- Solid state physics --- Matter physics --- Physics --- Artificial intelligence. Robotics. Simulation. Graphics --- EMI (electromagnetic interference) --- materie (fysica) --- quantummechanica --- waarschijnlijkheidstheorie --- grafentheorie --- theoretische fysica --- stochastische analyse --- statistiek --- simulaties --- wiskunde --- fysica --- kansrekening --- dynamica
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Understanding cooperative phenomena far from equilibrium is one of fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference for postgraduate students and nonspecialist researchers from related fields, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems. Lecture 1 gives an introduction and overview of the time-dependent behaviour of magnetic spin glasses. Lecture 2 is devoted to an in-depth discussion on the nature of the thermal glass-transition in structural glasses. Lecture 3 examines the glassy behaviour of granular systems. Lecture 4 gives a thorough introduction to the techniques and applications of Monte-Carlo simulations and the analysis of the resulting data through scaling methods. Lecture 5 introduces the zero-range-process concept as simple but subtle model to describe a range of static and dynamic properties of glassy systems. Lecture 6 shows how familiar RG methods for equilibrium systems can be extended to systems far from equilibrium.
Glass transition temperature --- Thermodynamics --- Polymer solutions --- Thermodynamique --- Congresses. --- Congrès --- Glass transition temperature -- Congresses. --- Polymer solutions -- Congresses. --- Thermodynamics -- Congresses. --- Atomic Physics --- Organic Chemistry --- Physics --- Chemistry --- Physical Sciences & Mathematics --- Liquid polymers --- Polymeric liquids --- Glass transformation temperature --- Glass transitions --- Physics. --- Thermodynamics. --- Solid state physics. --- Amorphous substances. --- Complex fluids. --- Phase transitions (Statistical physics). --- Spectroscopy. --- Microscopy. --- Statistical physics. --- Dynamical systems. --- Phase Transitions and Multiphase Systems. --- Statistical Physics, Dynamical Systems and Complexity. --- Solid State Physics. --- Spectroscopy and Microscopy. --- Soft and Granular Matter, Complex Fluids and Microfluidics. --- Polymers --- Solution (Chemistry) --- Materials --- Phase transformations (Statistical physics) --- Transition temperature --- Thermal properties --- Complex Systems. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Heat --- Heat-engines --- Quantum theory --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Solids --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Mathematical statistics --- Complex liquids --- Fluids, Complex --- Amorphous substances --- Liquids --- Soft condensed matter --- Analysis, Microscopic --- Light microscopy --- Micrographic analysis --- Microscope and microscopy --- Microscopic analysis --- Optical microscopy --- Optics --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectrometry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Statistical methods --- Qualitative --- Analytical chemistry
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This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.
Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Probability theory --- Mathematics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- Classical mechanics. Field theory --- Statistical physics --- Solid state physics --- Matter physics --- Physics --- Artificial intelligence. Robotics. Simulation. Graphics --- EMI (electromagnetic interference) --- materie (fysica) --- quantummechanica --- waarschijnlijkheidstheorie --- grafentheorie --- theoretische fysica --- stochastische analyse --- statistiek --- simulaties --- wiskunde --- fysica --- kansrekening --- dynamica --- Phase transformations (Statistical physics) --- Nonequilibrium statistical mechanics
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Statistical physics --- Thermodynamics --- Experimental solid state physics --- Solid state physics --- Chemical technology --- composieten --- metaalkristallen --- thermodynamica --- kristallografie --- spectroscopie --- statistiek --- fysica --- chemische technologie
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Understanding cooperative phenomena far from equilibrium is one of fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference for postgraduate students and nonspecialist researchers from related fields, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems. Lecture 1 gives an introduction and overview of the time-dependent behaviour of magnetic spin glasses. Lecture 2 is devoted to an in-depth discussion on the nature of the thermal glass-transition in structural glasses. Lecture 3 examines the glassy behaviour of granular systems. Lecture 4 gives a thorough introduction to the techniques and applications of Monte-Carlo simulations and the analysis of the resulting data through scaling methods. Lecture 5 introduces the zero-range-process concept as simple but subtle model to describe a range of static and dynamic properties of glassy systems. Lecture 6 shows how familiar RG methods for equilibrium systems can be extended to systems far from equilibrium.
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