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# Kinetic Monte Carlo - PowerPoint PPT Presentation

Kinetic Monte Carlo. Triangular lattice. Diffusion. Thermodynamic factor. Self Diffusion Coefficient. Diffusion. Standard Monte Carlo to study diffusion. Pick an atom at random. Standard Monte Carlo to study diffusion. Pick an atom at random Pick a hop direction.

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## PowerPoint Slideshow about 'Kinetic Monte Carlo' - aliya

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Presentation Transcript

### Kinetic Monte Carlo

Triangular lattice

Thermodynamic

factor

Self Diffusion

Coefficient

• Pick an atom at random

• Pick an atom at random

• Pick a hop direction

• Pick an atom at random

• Pick a hop direction

• Calculate

• Pick an atom at random

• Pick a hop direction

• Calculate

• If ( > random number) do the hop

Consider all hops simultaneously

A. B. Bortz, M. H. Kalos, J. L. Lebowitz, J. Comput Phys, 17, 10 (1975).

F. M. Bulnes, V. D. Pereyra, J. L. Riccardo, Phys. Rev. E, 58, 86 (1998).

calculate the hop rate

calculate the hop rate

Then randomly choose a hop k, with probability

calculate the hop rate

Then randomly choose a hop k, with probability

= random number

calculate the hop rate

Then randomly choose a hop k, with probability

= random number

Then randomly choose a hop k, with probability

= random number

After hop k we need to update the time

= random number

Two independent stochastic variables: the hop k and the waiting time

• Hop every time

• Consider all possible hops simultaneously

• Pick hop according its relative probability

• Update the time such that on average equals the time that we would have waited in standard Monte Carlo

A. B. Bortz, M. H. Kalos, J. L. Lebowitz, J. Comput Phys, 17, 10 (1975).

F. M. Bulnes, V. D. Pereyra, J. L. Riccardo, Phys. Rev. E, 58, 86 (1998).