0
votes
0answers
60 views

First passage time of diffusing particle with partially absorbing boundary

Given the solution to the spatiotemporal evolution of a single particle on a 1-D surface $P(x,t)$ a nice result (that I gleaned elsewhere on physics.SE) is that for a boundary at $x=0$ where ...
1
vote
1answer
40 views

Can you equate the diffusivity constant in random walks with the one in Brownian motion (Einstein relation)?

In an unbiased random walk in one dimension, the coefficient of diffusion is $D = l^2/2\tau$, where $l$ is the size of the jump and $\tau$ is time taken for that jump. In simple Brownian motion, ...
0
votes
2answers
64 views

Simulating diffusion from bulk to individual particles

I have a 2 compartment simulation. The first compartment simulates reactions using ODEs. The second compartment uses Brownian motion. I want to be able to have molecules from the ODE compartment ...
5
votes
2answers
113 views

Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
2
votes
1answer
96 views

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 ...
3
votes
1answer
281 views

What is the return probability for Brownian motion in three dimensions?

I would like to know the probability of return to the initial point in three dimensional Brownian motion. Does someone know an expression for the diffusion constant? (Suggestions of books on this ...
2
votes
1answer
74 views

What interpretive difference is there between defining a function with or without a differential as a postfactor?

I have thought about this and looked for answers for a long time now, but I do not have any name or label for this problem, which is the reason for the long title of this question. I have come across ...