Diffusion-Limited Growth: Pattern Formation

The following sections are included:

• Diffusion Equation

• Flat Interface

• Spherical Crystal

• Parabolic Crystal

• Stability of a Flat Interface

• Fractal Dendrite

  • Diffusion-limited Aggregation (DLA)

  • Fractal-to-Compact Crossover of an Aggregate in a Finite Gas Density

• Capillary Effect and Regular Dendrite

  • Velocity Selection by Microscopic Solvability

  • Tip Stability and Sidebranches

  • Dendrite in a Channel

  • Morphology Diagram

• Unidirectional Solidification from the Solution

  • Fundamental Equations

  • Stability of a Flat Interface

  • Eckhaus Instability

  • Fully Nonlinear Behavior

• Eutectic Growth

  • Lamellar Structure

  • Parity Breaking and Oscillation

• Diffusion Effect on Polyhedral Crystal: Berg Effect