Share

One-Dimensional Turbulence and the Stochastic Burgers Equation

2021-07-01 Education
Download One-Dimensional Turbulence and the Stochastic Burgers Equation PDF Online Free

Author :
Release : 2021-07-01
Genre : Education
Kind : eBook
Book Rating : 365/5 ( reviews)

GET EBOOK


Book Synopsis One-Dimensional Turbulence and the Stochastic Burgers Equation by : Alexandre Boritchev

Download or read book One-Dimensional Turbulence and the Stochastic Burgers Equation written by Alexandre Boritchev. This book was released on 2021-07-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Seminar on Stochastic Analysis, Random Fields and Applications V

2008-03-12 Mathematics
Download Seminar on Stochastic Analysis, Random Fields and Applications V PDF Online Free

Author :
Release : 2008-03-12
Genre : Mathematics
Kind : eBook
Book Rating : 581/5 ( reviews)

GET EBOOK


Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications V by : Robert Dalang

Download or read book Seminar on Stochastic Analysis, Random Fields and Applications V written by Robert Dalang. This book was released on 2008-03-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis and Stochastics of Growth Processes and Interface Models

2008-07-24 Mathematics
Download Analysis and Stochastics of Growth Processes and Interface Models PDF Online Free

Author :
Release : 2008-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 258/5 ( reviews)

GET EBOOK


Book Synopsis Analysis and Stochastics of Growth Processes and Interface Models by : Peter Mörters

Download or read book Analysis and Stochastics of Growth Processes and Interface Models written by Peter Mörters. This book was released on 2008-07-24. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of topical survey articles by researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is given to the interplay of the usually separate fields of applied analysis and probability theory.

Stochastic Partial Differential Equations in Fluid Mechanics

2023-06-11 Mathematics
Download Stochastic Partial Differential Equations in Fluid Mechanics PDF Online Free

Author :
Release : 2023-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 858/5 ( reviews)

GET EBOOK


Book Synopsis Stochastic Partial Differential Equations in Fluid Mechanics by : Franco Flandoli

Download or read book Stochastic Partial Differential Equations in Fluid Mechanics written by Franco Flandoli. This book was released on 2023-06-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Stochastic Analysis and Related Topics

2012 Mathematics
Download New Trends in Stochastic Analysis and Related Topics PDF Online Free

Author :
Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 910/5 ( reviews)

GET EBOOK


Book Synopsis New Trends in Stochastic Analysis and Related Topics by : Huaizhong Zhao

Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...