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This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems.
Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout.
This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.
List of contents
Introduction.- Convection in Cylindrical Cavities.- Convection in Liquid Layers.- Convection in Binary Liquids. Amplitude Equations for Stationary and Oscillatory Patterns.- Instabilities of Parallel Flows.- Instabilities of Fronts.- Longwave Modulations of Shortwave Patterns.- Control of Longwave Instabilities.- Outlook.- A. Solvability Conditions for an Inhomogenous Linear Boundary Value Problem.- B. Types of Bifurcations.- C. Stationary Pattern Selection.- D. Regular Wave Patterns.- E. Resonant Perturbations.
Summary
This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems.
Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout.
This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.
Additional text
“This book represents an important and interesting contribution to the theory of longwave instabilities and patterns in fluids. The hypotheses are clearly stated and the governing parameters are correctly selected, and the governing equations are solved both analytically and numerically. … The book will be of interest for researchers and graduate students in applied mathematics, physics, and engineering. The authors are to be lauded for presenting an excellent book.” (Ioan Pop, zbMATH 1384.76001, 2018)
Report
"This book represents an important and interesting contribution to the theory of longwave instabilities and patterns in fluids. The hypotheses are clearly stated and the governing parameters are correctly selected, and the governing equations are solved both analytically and numerically. ... The book will be of interest for researchers and graduate students in applied mathematics, physics, and engineering. The authors are to be lauded for presenting an excellent book." (Ioan Pop, zbMATH 1384.76001, 2018)
