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Nonlinear Dynamics of Surface-Tension-Driven Instabilities: With a Foreword by I. Prigogine

Nonlinear Dynamics of Surface-Tension-Driven Instabilities: With a Foreword by I. Prigogine

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Description

A century after Henri Bénard discovered cellular convective structures, thermal convection in fluid layers still remains a central subject in nonlinear physics. Within this framework, surface-tension-driven instabilities have increasingly been the subject of attention over the last few years, owing to the even greater variety of pattern and wave-forming phenomena observed in this situation. This book provides readers with a progressive and complete insight into this vast field, describing as it does a number of "first principle" analyses of realistic set-ups, including several physicochemical processes at interfaces. Nonetheless, much emphasis is placed on the generality of the results and methods used, by way of the detailed derivation and analysis of a number of generic nonlinear equations known to hold in many physical systems, even outside the realm of fluid mechanics.

The first introductory chapter describes nonlinear dissipative structures at a general level, with several examples of hydrodynamic instabilities in systems with interfaces. Chapter 2 contains a summary of the derivation of thermo-hydrodynamic equations, including boundary conditions prevailing at interfaces, while the third chapter is devoted to linear stability analyzes and identification of basic instability modes. The following two chapters deal with weakly nonlinear theories, both monotonic and oscillatory. Chapter 6 presents experimental and theoretical results on solitonic and shock-like surface waves, while Chapter 7 explores examples of multiple bifurcations. Finally, Chapter 8 presents recent results on strongly nonlinear surface-tension-driven convection and chaotic interfacial dynamics.
Introduction
Balance Equations and Boundary Conditions
Instability Modes in Benard Systems
Weakly Nonlinear Pattern Dynamics
Weakly Nonlinear Waves
Codimension-Two Bifurcations
Strongly Nonlinear and Turbulent Regimes
"... clearly written ...can be used by graduate students as a textbook and by mature experts in the fileds of applied mathematics and engineering science as an up-to-date review of the probem. It may also be useful for a wide circle of experts working in diefferent fields of nonliniar science." Mathematical Reviews

"The authors have compiled an authoritative exhaustive monograph of this theory, of the kind that few today can find the time to embark upon." Contemporary Physics

"...it can be e firm foundation stone for generations of graduate students..." Contemporary Physics