Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Introduction -- References -- 2 Pure substances -- 2.1 Planar Interfaces -- 2.1.1 Mathematical Model -- 2.1.2 One-Dimensional Freezing from a Cold Boundary -- Notes -- 2.1.3 One-Dimensional Freezing from a Cold Boundary: Small Undercooling -- 2.1.4 One-Dimensional Freezing into an Undercooled Melt -- 2.1.5 One-Dimensional Freezing into an Undercooled Melt: Effect of Kinetic Undercooling -- 2.2 Curved Interfaces -- 2.2.1 Boundary Conditions -- 2.2.2 Growth of a Nucleus in an Undercooled Melt -- 2.2.3 Linearized Instability of Growing Nucleus -- 2.2.4 Linearized Instability of a Plane Front Growing into an Undercooled Melt -- 2.2.5 Remarks -- References -- 3 Binary substances -- 3.1 Mathematical Model -- 3.2 Directional Solidification -- 3.3 Basic State and Approximate Models -- 3.4 Linearized Instability of a Moving Front in Directional Solidification -- 3.5 Mechanism of Morphological Instability -- 3.6 More General Models -- 3.7 Remarks -- References -- 4 Nonlinear theory for directional solidification -- 4.1 Bifurcation Theory -- 4.1.1 Two-Dimensional Theory -- 4.1.2 Two-Dimensional Theory for Wave Number Selection -- 4.1.3 Three-Dimensional Theory -- 4.2 Long-Scale Theories -- 4.2.1 Small Segregation Coefficient -- 4.2.2 Small Segregation Coefficient and Large Surface Energy -- 4.2.3 Near Absolute Stability -- 4.3 Remarks -- References -- 5 Anisotropy -- 5.1 Surface Energy and Kinetics -- 5.2 Directional Solidification with "Small" Anisotropy -- 5.3 Directional Solidification with "Small" Anisotropy: Stepwise Growth -- 5.4 Unconstrained Growth with "Small" Anisotropy -- 5.4.1 Two-Dimensional Crystal and One-Dimensional Front -- 5.4.2 Three-Dimensional Crystal and Two-Dimensional Front.

5.5 Unconstrained Growth with "Large" Anisotropy - One-Dimensional Interfaces -- 5.6 Unconstrained Growth with "Large" Anisotropy - Two-Dimensional Interfaces -- 5.7 Faceting with Constant Driving Force -- 5.8 Coarsening -- 5.9 Remarks -- References -- 6 Disequilibrium -- 6.1 Model of Rapid Solidification -- 6.2 Basic State and Linear Stability Theory -- 6.3 Thermal Effects -- 6.4 Linear-Stability Theory with Thermal Effects -- 6.4.1 Steady Mode -- 6.4.2 Oscillatory Mode -- 6.4.3 The Two Modes -- 6.5 Cellular Modes in the FTA: Two-Dimensional Bifurcation Theory -- 6.6 Oscillatory Modes in the FTA: Two-Dimensional Bifurcation Theory -- 6.7 Strongly Nonlinear Pulsations -- 6.7.1 Small beta -- 6.7.2 Large beta -- 6.7.3 Numerical Simulation -- 6.8 Mode Coupling -- 6.8.1 Pulsatile-Cellular Interactions -- 6.8.2 Oscillatory-Cellular Interactions -- 6.8.3 Oscillatory-pulsatile interactions -- 6.9 Phenomenological Models -- 6.10 Remarks -- References -- 7 Dendrites -- 7.1 Isolated Needle Crystals -- 7.2 Approximate Selection Arguments -- 7.3 Selection Theories -- 7.4 Arrays of Needles -- 7.5 Remarks -- References -- 8 Eutectics -- 8.1 Formulation -- 8.2 Approximate Theories for Steady Growth and Selection -- 8.3 Instabilities -- 8.4 Remarks -- References -- 9 Microscale fluid flow -- 9.1 Formulation -- 9.2 Prototype Flows -- 9.2.1 Free Convection -- 9.2.2 Bénard Convection -- 9.3 Directional Solidification and Volume-Change Convection -- 9.4 Directional Solidification and Buoyancy-Driven Convection -- 9.5 Directional Solidification and Forced Flows -- 9.6 Directional Solidification with Imposed Cellular Convection -- 9.7 Flows over Ivantsov Needles -- 9.8 Remarks -- References -- 10 Mesoscale fluid flow -- 10.1 Formulation -- 10.2 Planar Solidification between Horizontal Planes -- 10.3 Mushy-Zone Models -- 10.4 Mushy Zones with Volume-Change Convection.

10.5 Mushy Zones with Buoyancy-Driven Convective Instability -- 10.6 An Oscillatory Mode of Convective Instability -- 10.7 Weakly Nonlinear Convection -- 10.8 Chimneys -- 10.9 Remarks -- References -- 11 Phase-field models -- 11.1 Pure Materials - A Model System -- 11.2 Pure Materials - A Deduced System -- 11.3 Pure Materials - Computations -- 11.4 Remarks -- References -- Index.