One Dimensional Turbulence And The Stochastic Burgers Equation

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One-Dimensional Turbulence and the Stochastic Burgers Equation

Author : Alexandre Boritchev
Publisher : American Mathematical Soc.
ISBN 13 : 1470464365
Total Pages : 192 pages
Book Rating : 4.4/5 (74 download)

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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 and published by American Mathematical Soc.. This book was released on 2021-07-01 with total page 192 pages. 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

Author : Robert Dalang
Publisher : Springer Science & Business Media
ISBN 13 : 3764384581
Total Pages : 518 pages
Book Rating : 4.7/5 (643 download)

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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 and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 518 pages. 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.

New Trends in Stochastic Analysis and Related Topics

Author : Huaizhong Zhao
Publisher : World Scientific
ISBN 13 : 9814360910
Total Pages : 458 pages
Book Rating : 4.8/5 (143 download)

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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 and published by World Scientific. This book was released on 2012 with total page 458 pages. 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.

Non-perturbative Methods in Statistical Descriptions of Turbulence

Author : Jan Friedrich
Publisher : Springer Nature
ISBN 13 : 3030519775
Total Pages : 173 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Non-perturbative Methods in Statistical Descriptions of Turbulence by : Jan Friedrich

Download or read book Non-perturbative Methods in Statistical Descriptions of Turbulence written by Jan Friedrich and published by Springer Nature. This book was released on 2020-09-25 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probabilistic Methods in Fluids

Author : Ian Malcolm Davies
Publisher : World Scientific
ISBN 13 : 9812382267
Total Pages : 383 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Probabilistic Methods in Fluids by : Ian Malcolm Davies

Download or read book Probabilistic Methods in Fluids written by Ian Malcolm Davies and published by World Scientific. This book was released on 2003 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : I M Davies
Publisher : World Scientific
ISBN 13 : 9814487058
Total Pages : 380 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Probabilistic Methods in Fluids by : I M Davies

Download or read book Probabilistic Methods in Fluids written by I M Davies and published by World Scientific. This book was released on 2003-06-13 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Probabilistic Approach to Hydrodynamic Equations (S Albeverio & Y Belopolskaya)A Mean Field Result for 3D Vortex Filaments (H Bessaih & F Flandoli)Semilinear Stochastic Wave Equations (P-L Chow)Some Remarks on a Statistical Theory of Turbulent Flows (F Flandoli)On the Dispersion of Sets Under the Action of an Isotropic Brownian Flow (H Lisei & M Scheutzow)A Version of the Law of Large Numbers and Applications (A Shirikyan)A Comparison Theorem for Solutions of Backward Stochastic Differential Equations with Two Reflecting Barriers and Its Applications (T-S Zhang)and other papers Readership: Research mathematicians with an interest in stochastic analysis, turbulence, fluid mechanics and stochastic partial differential equations. Keywords:Stochastic Analysis;Turbulence;Fluid Mechanics

Stochastic Partial Differential Equations in Fluid Mechanics

Author : Franco Flandoli
Publisher : Springer Nature
ISBN 13 : 9819903858
Total Pages : 206 pages
Book Rating : 4.8/5 (199 download)

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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 and published by Springer Nature. This book was released on 2023-06-11 with total page 206 pages. 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.

Analysis and Stochastics of Growth Processes and Interface Models

Author : Peter Mörters
Publisher : Oxford University Press
ISBN 13 : 0199239258
Total Pages : 347 pages
Book Rating : 4.1/5 (992 download)

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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 and published by Oxford University Press. This book was released on 2008-07-24 with total page 347 pages. 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.

Mathematics of Two-Dimensional Turbulence

Author : Sergei Kuksin
Publisher : Cambridge University Press
ISBN 13 : 113957695X
Total Pages : 337 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Mathematics of Two-Dimensional Turbulence by : Sergei Kuksin

Download or read book Mathematics of Two-Dimensional Turbulence written by Sergei Kuksin and published by Cambridge University Press. This book was released on 2012-09-20 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

Burgers-KPZ Turbulence

Author : Wojbor A. Woyczynski
Publisher : Springer
ISBN 13 : 3540494804
Total Pages : 326 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Burgers-KPZ Turbulence by : Wojbor A. Woyczynski

Download or read book Burgers-KPZ Turbulence written by Wojbor A. Woyczynski and published by Springer. This book was released on 2006-11-13 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Iwasawa Theory and Its Perspective, Volume 2

Author : Tadashi Ochiai
Publisher : American Mathematical Society
ISBN 13 : 1470456737
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.

SPDE in Hydrodynamics: Recent Progress and Prospects

Author : Sergio Albeverio
Publisher : Springer
ISBN 13 : 3540784934
Total Pages : 174 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis SPDE in Hydrodynamics: Recent Progress and Prospects by : Sergio Albeverio

Download or read book SPDE in Hydrodynamics: Recent Progress and Prospects written by Sergio Albeverio and published by Springer. This book was released on 2008-04-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

Perverse Sheaves and Applications to Representation Theory

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
ISBN 13 : 1470455978
Total Pages : 562 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar

Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

Maximal Function Methods for Sobolev Spaces

Author : Juha Kinnunen
Publisher : American Mathematical Soc.
ISBN 13 : 1470465752
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Maximal Function Methods for Sobolev Spaces by : Juha Kinnunen

Download or read book Maximal Function Methods for Sobolev Spaces written by Juha Kinnunen and published by American Mathematical Soc.. This book was released on 2021-08-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Hopf Algebras and Galois Module Theory

Author : Lindsay N. Childs
Publisher : American Mathematical Soc.
ISBN 13 : 1470465167
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hopf Algebras and Galois Module Theory by : Lindsay N. Childs

Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Maximal Cohen–Macaulay Modules and Tate Cohomology

Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Society
ISBN 13 : 1470453401
Total Pages : 175 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Maximal Cohen–Macaulay Modules and Tate Cohomology by : Ragnar-Olaf Buchweitz

Download or read book Maximal Cohen–Macaulay Modules and Tate Cohomology written by Ragnar-Olaf Buchweitz and published by American Mathematical Society. This book was released on 2021-12-16 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Diagrammatic Algebra

Author : J. Scott Carter
Publisher : American Mathematical Society
ISBN 13 : 1470466716
Total Pages : 365 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Diagrammatic Algebra by : J. Scott Carter

Download or read book Diagrammatic Algebra written by J. Scott Carter and published by American Mathematical Society. This book was released on 2021-12-15 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.