Diffusion

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Diffusion

• Mike Sinclair

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Overview

• Diffusion
• Fundamental behavior
• See in biology, chemistry, and physics
• DescriptionThe spontaneous spread of particles
  from region of high concentration to low
  concentration.Equilibrium!

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Set up of the problem

• Equal of particlesin each box
• Random probabilityof moving to other box
• Time-step
• Expectation equal s of particles in each box

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Set up of the problem

• Begin to see mixing
• Random probabilitycontinues
• Time-step remains the same
• Expectation equal s of particles in each box

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Set up of the problem

• Even more mixing
• Approaching equilibrium
• Time-step remains the same
• Expectation equal s of particles in each box

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Set up of the problem

• Mixing complete
• Equilibrium achieved
• Time-step continues
• Expectation equal s of particles in each box
• Results equal s of particles in each box

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Comments

• Each particle follows a random walk
• Previous behavior does not allow prediction of
  next step Markovian
• Equilibrium reached after n time-steps

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Conclusions

• Diffusion is a fundamental behavior in biology,
  chemistry, and physics.
• It can be visualized by a modeling large numbers
  of particles.
• Is Markovian cannot predict previous step or
  next step except end behavior (which is
  equilibrium).