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Diffusion is the net movement (spreading out) of molecules or atoms down a concentration gradient: from a region of high concentration to a region of low concentration.
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probability density distribution: From free diffusion to presence of a barrier
We have the solution for "absence of a barrier" = free diffusion (1st case). We have the solution in presence of a barrier (2nd case). …
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Properties of random-walk in infinite and finite two-dimensional space: probability of two p...
$G(z, t | p)$ is expressed as a free diffusion process:
$$G(z, t | p) = \frac{1}{4\pi Dt} \exp[-(p-z)^2/4Dt]$$
In few words, it seems that one of the property of a random walk is that the probability density …
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Random walk in finite VERSUS infinite space: Probability density functions and their interpr...
particle move from $x_0$ to $x$ in time $t$, and $\tau = (\frac{L}{2})^2\frac{1}{D}$ , which represents the characteristic time-scale; $L$ is the length of the box (equal for each direction); $D$ is the diffusion …