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1. Present a finite-difference scheme to solve the Allen-Cahn equation in a one-dimensional phase-field calculation. You may use a free energy function of your own

1. Present a finite-difference scheme to solve the Allen-Cahn equation in a one-dimensional phase-field calculation. You may use a free energy function of your own choice.

2. Show by analytical derivations how one can rationalize the choice of the waiting time distribution in the Kinetic Monte Carlo method.

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