First slide

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Pictures obtained with the free software POVray on a Linux PC. Available at http://www.dmf.bs.unicatt.it/~paolini/research/PhTIEE/

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• Definition of the anisotropy
  1. Wulff shape
  2. Frank diagram
  3. Both
• Ex. 1. Evolution of the Wulff shape
  1. Initial surface and Cahn-Hoffmann field
  2. Exact evolution (ode approach)
  3. Allen-Cahn computation at time t=0.05
  4. Allen-Cahn evolution at intervals dt=0.05
  5. Comparison at times 0.05 and 0.10
• Ex. 2. Evolution of the unit sphere
  1. Initial surface
  2. Sketch of expected exact evolution at later time
  3. Allen-Cahn evolution at t=0.021
  4. Allen-Cahn time steps at intervals 0.02
• Ex. 3. Bending example
  1. Wulff shape
  2. Initial surface
  3. Exact evolution (ode approach)
  4. Allen-Cahn computation at time=0.0042
  5. Comparison at time=0.0042