One Dimensional Turbulence And The Stochastic Burgers Equation
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One Dimensional Turbulence And The Stochastic Burgers Equation
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Author : Alexandre Boritchev
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-01
One Dimensional Turbulence And The Stochastic Burgers Equation written by Alexandre Boritchev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Education categories.
This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3 2/3-law, and the Kolmogorov–Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L 1 L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.
Non Perturbative Methods In Statistical Descriptions Of Turbulence
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Author : Jan Friedrich
language : en
Publisher: Springer Nature
Release Date : 2020-09-25
Non Perturbative Methods In Statistical Descriptions Of Turbulence written by Jan Friedrich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-25 with Technology & Engineering categories.
This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier–Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier–Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.
Seminar On Stochastic Analysis Random Fields And Applications V
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Author : Robert Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-12
Seminar On Stochastic Analysis Random Fields And Applications V written by Robert Dalang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-12 with Mathematics categories.
This volume contains refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 29 to June 3, 2004. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering.
New Trends In Stochastic Analysis And Related Topics
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Author : Huaizhong Zhao
language : en
Publisher: World Scientific
Release Date : 2012
New Trends In Stochastic Analysis And Related Topics written by Huaizhong Zhao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Analysis And Stochastics Of Growth Processes And Interface Models
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Author : Peter Mörters
language : en
Publisher: OUP Oxford
Release Date : 2008-07-24
Analysis And Stochastics Of Growth Processes And Interface Models written by Peter Mörters and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-24 with Mathematics categories.
This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.
Stochastic Partial Differential Equations In Fluid Mechanics
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Author : Franco Flandoli
language : en
Publisher: Springer Nature
Release Date : 2023-06-11
Stochastic Partial Differential Equations In Fluid Mechanics written by Franco Flandoli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-11 with Mathematics categories.
This book is devoted to stochastic Navier–Stokes equations and more generally to stochasticity in fluid mechanics. The two opening chapters describe basic material about the existence and uniqueness of solutions: first in the case of additive noise treated pathwise and then in the case of state-dependent noise. The main mathematical techniques of these two chapters are known and given in detail for using the book as a reference for advanced courses. By contrast, the third and fourth chapters describe new material that has been developed in very recent years or in works now in preparation. The new material deals with transport-type noise, its origin, and its consequences on dissipation and well-posedness properties. Finally, the last chapter is devoted to the physical intuition behind the stochastic modeling presented in the book, giving great attention to the question of the origin of noise in connection with small-scale turbulence, its mathematical form, and its consequences on large-scale properties of a fluid.
Probabilistic Methods In Fluids
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Author : Ian Malcolm Davies
language : en
Publisher: World Scientific
Release Date : 2003
Probabilistic Methods In Fluids written by Ian Malcolm Davies and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This volume contains recent research papers presented at the international workshop on ?Probabilistic Methods in Fluids? held in Swansea. The central problems considered were turbulence and the Navier-Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.
Probabilistic Methods In Fluids Proceedings Of The Swansea 2002 Workshop
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Author : Ian M Davies
language : en
Publisher: World Scientific
Release Date : 2003-06-13
Probabilistic Methods In Fluids Proceedings Of The Swansea 2002 Workshop written by Ian M Davies and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-13 with Mathematics categories.
This volume contains recent research papers presented at the international workshop on “Probabilistic Methods in Fluids” held in Swansea. The central problems considered were turbulence and the Navier-Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.
Stochastic Optimal Control In Infinite Dimension
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Author : Giorgio Fabbri
language : en
Publisher: Springer
Release Date : 2017-06-22
Stochastic Optimal Control In Infinite Dimension written by Giorgio Fabbri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Mathematics categories.
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Iwasawa Theory And Its Perspective Volume 1
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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-03
Iwasawa Theory And Its Perspective Volume 1 written by Tadashi Ochiai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-03 with Mathematics categories.
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory. The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects. The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.
