Interfacial Wave Theory of Pattern Formation in Solidification

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This comprehensive work delves into interfacial instability and pattern formation in dynamic systems away from equilibrium, focusing on solidification and crystal growth. The significantly expanded 2nd edition reviews progress made over the last two decades, detailing prominent pattern formation phenomena observed in material processing and crystal growth through the lens of interfacial wave theory. Key topics include free dendritic growth from undercooled melt, cellular growth, eutectic growth in directional solidification, and viscous fingering in Hele-Shaw flow. The text systematically derives mathematical solutions using a unified, asymptotic approach and examines these results against available experimental data. This approach is applicable to a broader range of inhomogeneous dynamical systems. Additionally, findings on global stability and selection mechanisms of pattern formation will interest researchers in material processing and crystal growth. The stability mechanisms of curved fronts and pattern formation are fundamental in condensed-matter physics, materials science, crystal growth, and fluid mechanics. This work serves as a stimulating introduction for physicists, engineers, and applied mathematicians in soft condensed-matter physics, materials science, mechanical and chemical engineering, fluid dynamics, and nonlinear sciences.