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Mean field theory. --- Many-body problem --- Statistical mechanics
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Mean field theory. --- Many-body problem --- Statistical mechanics
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This work is dedicated to the numerically efficient simulation of the material response of polycrystalline aggregates. Therefore, crystal plasticity is combined with a new non-linear homogenization scheme, which is based on piecewise constant stress polarizations with respect to a homogeneous reference medium and corresponds to a generalization of the Hashin-Shtrikman scheme. This mean field approach accounts for the one- and two-point statistics of the microstructure.
mean-field approach --- homogenization --- polycrystalline materials --- inelastic properties
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"Bringing together ideas and techniques from diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling."--Jacket.
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A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
Differential equations, Partial. --- Mathematics. --- Mean field theory. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations. --- Partial differential equations. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Differential Equations. --- Differential equations, partial.
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Dealing with Dynamical Mean-Field Theory (DMFT), this book develops the formalism of many-body Green's functions using the equation of motion approach, which requires an undergraduate solid state physics course and a graduate quantum mechanics course as prerequisites. It also emphasizes how to carry out numerical calculations.
Nanostructures --- Thin films, Multilayered --- Mean field theory. --- Many-body problem. --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Many-body problem --- Statistical mechanics --- Langmuir-Blodgett films --- Multilayered thin films --- Nanoscience --- Physics --- Mathematics.
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In this work, the task of wide-area indoor people detection in a network of depth sensors is examined. In particular, we investigate how the redundant and complementary multi-view information, including the temporal context, can be jointly leveraged to improve the detection performance. We recast the problem of multi-view people detection in overlapping depth images as an inverse problem and present a generative probabilistic framework to jointly exploit the temporal multi-view image evidence.
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Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. .
Mathematics. --- Nonlinear control theory. --- Stochastic control theory. --- System analysis. --- Mean field theory --- Control theory --- Game theory --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Control theory. --- Differential equations, Partial. --- Distribution (Probability theory) --- System theory. --- Systems, Theory of --- Systems science --- Distribution functions --- Frequency distribution --- Partial differential equations --- Partial differential equations. --- Probabilities. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Partial Differential Equations. --- Science --- Characteristic functions --- Probabilities --- Dynamics --- Machine theory --- Philosophy --- Systems theory. --- Distribution (Probability theory. --- Differential equations, partial. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mean field theory. --- Game theory.
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Electronic structure and physical properties of strongly correlated materials containing elements with partially filled 3d, 4d, 4f and 5f electronic shells is analyzed by Dynamical Mean-Field Theory (DMFT). DMFT is the most universal and effective tool used for the theoretical investigation of electronic states with strong correlation effects. In the present book the basics of the method are given and its application to various material classes is shown. The book is aimed at a broad readership: theoretical physicists and experimentalists studying strongly correlated systems. It also serves as a handbook for students and all those who want to be acquainted with fast developing filed of condensed matter physics.
Electron configuration. --- Mean field theory. --- Solid state physics. --- Electron configuration --- Mean field theory --- Solid state physics --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Configuration, Electron --- Electron correlation --- Materials science. --- Condensed matter. --- Microwaves. --- Optical engineering. --- Optical materials. --- Electronic materials. --- Materials Science. --- Optical and Electronic Materials. --- Condensed Matter Physics. --- Microwaves, RF and Optical Engineering. --- Solids --- Many-body problem --- Statistical mechanics --- Atomic orbitals --- Electrons --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Optics --- Materials --- Mechanical engineering --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Electronic materials
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Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Mathematics. --- Game theory. --- System theory. --- Economic theory. --- Game Theory, Economics, Social and Behav. Sciences. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Systems Theory, Control. --- Mean field theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Many-body problem --- Statistical mechanics --- Systems theory. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Math --- Science --- Systems, Theory of --- Systems science --- Philosophy
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