This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.

Geometric Theory of Incompressible Flows With Applications to Fluid Dynamics (Mathematical Surveys and Monographs, 119)

Science & Math

Wang, Shouhong

Ma, Tian

Mathematics

Amer Mathematical Society

This book introduces a general principle of dynamic transitions for dissipative systems, establishes a systematic dynamic transition theory, and explores the physical implications of applications of the theory to a range of problems in the nonlinear sciences.

Phase Transition Dynamics

Reference

Springer

This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. 
This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). 
Reviews of first edition: 
“The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. … The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) 
“This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. … The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)\nFrom the Back Cover\nThis book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. 
This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity).\nReviews of first edition: 
“The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. … The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) 
“This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. … The book is a very u

Contesting Crimmigration in Post-hukou China (Springer Series on Asian Criminology and Criminal Justice Research)

Health, Fitness & Dieting

Psychology & Counseling

1/7 Surviving Game (Chinese Edition)

Ma Tian

This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.

BIFURCATION THEORY AND APPLICATIONS (World Scientific Nonlinear Science Series a)

World Scientific Publishing Company

This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.

Chemistry

See the best price to sell, buy, or rent books by Ma, Tian. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ma, Tian

See the best price to sell, buy, or rent books by Ma, Tian. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Geometric Theory of Incompressible Flows With Applications to Fluid Dynamics (Mathematical Surveys and Monographs, 119)

Phase Transition Dynamics

Phase Transition Dynamics

Phase Transition Dynamics

Contesting Crimmigration in Post-hukou China (Springer Series on Asian Criminology and Criminal Justice Research)

1/7 Surviving Game (Chinese Edition)

BIFURCATION THEORY AND APPLICATIONS (World Scientific Nonlinear Science Series a)

BIFURCATION THEORY AND APPLICATIONS (World Scientific Nonlinear Science Series a)