Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
Author: Viorel Barbu
Publisher: Springer Nature
Published:
Total Pages: 219
ISBN-13: 3031617347
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Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
Author: Viorel Barbu
Publisher: Springer
Published: 2024-08-05
Total Pages: 0
ISBN-13: 9783031617331
DOWNLOAD EBOOK →This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions. The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.
Gradient Flows
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
Published: 2008-10-29
Total Pages: 334
ISBN-13: 376438722X
DOWNLOAD EBOOK →The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Advances in Nonlinear Geosciences
Author: Anastasios A. Tsonis
Publisher: Springer
Published: 2017-10-13
Total Pages: 707
ISBN-13: 3319588958
DOWNLOAD EBOOK →Advances in Nonlinear Geosciences is a set of contributions from the participants of “30 Years of Nonlinear Dynamics” held July 3-8, 2016 in Rhodes, Greece as part of the Aegean Conferences, as well as from several other experts in the field who could not attend the meeting. The volume brings together up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences and presents the new advances made in the last 10 years. Topics include chaos synchronization, topological data analysis, new insights on fractals, multifractals and stochasticity, climate dynamics, extreme events, complexity, and causality, among other topics.
The Fokker-Planck Equation
Author: Hannes Risken
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 486
ISBN-13: 3642615449
DOWNLOAD EBOOK →This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.
Topological Optimization and Optimal Transport
Author: Maïtine Bergounioux
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2017-08-07
Total Pages: 432
ISBN-13: 311043041X
DOWNLOAD EBOOK →By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance
Applied Stochastic Differential Equations
Author: Simo Särkkä
Publisher: Cambridge University Press
Published: 2019-05-02
Total Pages: 327
ISBN-13: 1316510085
DOWNLOAD EBOOK →With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Numerical Methods for Non-Newtonian Fluids
Author:
Publisher: Elsevier
Published: 2010-12-20
Total Pages: 824
ISBN-13: 0080932029
DOWNLOAD EBOOK →Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume’s articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics. New review of well-known computational methods for the simulation viscoelastic and viscoplastic types.; Discusses new numerical methods that have proven to be more efficient and more accurate than traditional methods.; Articles that discuss the numerical simulation of particulate flow for viscoelastic fluids.;
Fokker-Planck-Kolmogorov Equations
Author: Vladimir I. Bogachev
Publisher: American Mathematical Soc.
Published: 2015-12-17
Total Pages: 482
ISBN-13: 1470425580
DOWNLOAD EBOOK →This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Numerical Methods for Non-Newtonian Fluids
Author: Philippe G. Ciarlet
Publisher: Elsevier
Published: 1990
Total Pages: 827
ISBN-13: 0444530479
DOWNLOAD EBOOK →Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.
