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Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
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Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
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Concentration of Proteins

You release a billion protein molecules at position $x = 0$ in the middle of a narrow capillary test tube. The molecules’ diffusion constant is $10^{−6} \ cm^2 s^{−1}$. An electric field pulls ...
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Mechanical effects of convective flow in steady-state stagnant film diffusion

When analysing diffusion problems in the context of the simplified film model, two limiting cases are ussually introduced during the solution of the differential chemical species mass balance ...
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Ask for help: the Reaction-Diffusion related problem

In container there are two kinds of molecules A and B which are distributed uniformly. Initially the quantities of A and B are $N_A$ and $N_B$ respectively A and B are distributed uniform, i.e., in ...