Overview

This comprehensive work explores interfacial instability and pattern formation in dynamic systems away from the equilibrium state in solidification and crystal growth. Further, this significantly expanded 2nd edition introduces and reviews the progress made during the last two decades. In particular, it describes the most prominent pattern formation phenomena commonly observed in material processing and crystal growth in the framework of the previously established interfacial wave theory, including free dendritic growth from undercooled melt, cellular growth and eutectic growth in directional solidification, as well as viscous fingering in Hele-Shaw flow. It elucidates the key problems, systematically derives their mathematical solutions by pursuing a unified, asymptotic approach, and finally carefully examines these results by comparing them with the available experimental results. The asymptotic approach described here will be useful for the investigation of pattern formation phenomena occurring in a much broader class of inhomogeneous dynamical systems. In addition, the results on global stability and selection mechanisms of pattern formation will be of particular interest to researchers working on material processing and crystal growth. The stability mechanisms of a curved front and the pattern formation have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for some time now. This book offers a stimulating and insightful introduction for all physicists, engineers and applied mathematicians working in the fields of soft condensed-matter physics, materials science, mechanical and chemical engineering, fluid dynamics, and nonlinear sciences.

Full Product Details

Author:   Jian-Jun Xu
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 2nd ed. 2017
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   0.926kg
ISBN:  

9783319849560

ISBN 10:   3319849565
Pages:   591
Publication Date:   08 May 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Introduction.- Unidirectional Solidification and the Mullins-sekkerka instability.- Mathematical formulation of free dendrite growth from a pure melt.- Basic steady state of axi-symmetric free dendritic growth.- The steady state for dendritic growth with nonzero surface tension.- Global interfacial wave instability of dendrite growth from a pure melt.- Two dimensional dendritic growth.- Three dimensional dendritic growth from undercooled binary mixture.- Viscous fingering in a hele-shaw cell.- Spatially-periodic deep-cellular growth in hele-shaw cell.- Steady lamellar eutectic growth.

Reviews

I was particularly pleased with Xu's coverage of material that is often missing from conventional texts on pattern growth and nonequilibrium phenomena in condensed matter. ... such an ambitious, advanced text will surely be of great interest to mathematical physicists and researchers in chemical physics, engineering, and materials science. (Domenico Truzzolillo, Physics Today, March, 2018)

“I was particularly pleased with Xu’s coverage of material that is often missing from conventional texts on pattern growth and nonequilibrium phenomena in condensed matter. … such an ambitious, advanced text will surely be of great interest to mathematical physicists and researchers in chemical physics, engineering, and materials science.” (Domenico Truzzolillo, Physics Today, March, 2018)

Author Information

Dr Jian-Jun Xu is a professor in the Department of Mathematics and Statistics at McGill University, Canada. He is an outstanding applied mathematician, working in the interdisciplinary area of applied mathematics, condensed matter physics, material science and fluid dynamics. He has published four monographs and about one hundred research papers. His expertise includes but is not limited to: asymptotics and numerical analysis, dynamical systems of non-Linear PDE with particular emphasis in the areas of solidification physics,  interfacial wave theory, pattern formation and crystal growth.  

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