Diffusion

For a particle that can either move left or right and makes $n$ steps each of size $\delta$

Topics

• Fick’s Equations
• Diffusion Equation
• Advection Diffusion Equation

$⟨x(n)⟩=0$

• Average position of a particle after $n$ steps is $0$ due to random chance

$⟨x^2(n)⟩=n{\delta }^2=2Dt$

• Average of square of particle position after $n$ steps
• $D$ is the diffusive constant
• $t$ is the total time for $n$ steps

$⟨r^2⟩=6Dt$

• Statistical independence in 3D