Interfacial Wave Theory Of Pattern Formation Selection Of Dendritic Growth And Viscous Fingering In Heleshaw Flow

Jian-Jun Xu

The stabiltiy mechanisms of a curved front and the pattern formation in dendrite growth and viscous fingering have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for about half a century. This book studies interfacial instability and pattern formation in dynamic systems away from the equilibrium state. In particular, it deals with the two prominent prototype systems: dendrite growth in solidification and viscous fingering in Hele--Shaw flow. It elucidates the key problems step by step and systematically derives their mathematical solutions, on the basis of the newly established interfacial wave theory. Finally, it carefully examines these results by comparisons with the available experimental results. The unified, asymptotic approach described in this book will be useful for investigation of pattern formation...