1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Diffusion Length

  1. Aug 9, 2010 #1
    I am trying to do simulations of a random walk, I get out a normal distribution in 1D how do I get the "diffusion length" from the gaussian fit?
     
  2. jcsd
  3. Aug 9, 2010 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    From wikipedia

    Gaussian random walk

    A random walk having a step size that varies according to a normal distribution is used as a model for real-world time series data such as financial markets. The Black-Scholes formula for modeling equity option prices, for example, uses a gaussian random walk as an underlying assumption.

    Here, the step size is the inverse cumulative normal distribution Φ − 1(z,μ,σ) where 0 ≤ z ≤ 1 is a uniformly distributed random number, and μ and σ are the mean and standard deviations of the normal distribution, respectively.

    For steps distributed according to any distribution with a finite variance (not necessarily just a normal distribution), the root mean squared expected translation distance after n steps is

    E|S_n| = σ√n.
     
  4. Aug 9, 2010 #3
    So, if I am looking for the diffusion length of an exciton with lifetime [tex] \tau [/tex], where [tex] l_{D}=\sqrt{D_{X}\tau} [/tex], and I want to find out what the equivalent diffusion length in my simulation is where I am using random steps of length dx, I can fit the gaussian and find the E mentioned above?
     
  5. Aug 10, 2010 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Your original question and your comment are confusing me. Are you talking about a random walk with steps of fixed length (random direction) or are the step lengths distributed normally? Also, how many dimensions is your walk? I am not familiar with the physics notion (exciton) and the diffusion length (?) formula.
     
  6. Aug 18, 2010 #5
    I think I figured it out.
    In general (1D) you can solve for:

    [itex] \frac{\partial n_{x}}{\partial t} = D_{x}\frac{\partial^{2} n_{x}}{\partial x}-\frac{n_{x}}{\tau} + I(x,t) [/itex]

    This can be solved with a Gaussian and [itex]\sigma^{2} = 4D_{x}t[/itex]. What I was trying to do was using a random step matlab simulation with a time step, lifetime, and spatial step figure out what the equivalent diffusion length was.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Diffusion Length
  1. Diffusion of CO2 (Replies: 1)

  2. Diffusion rate (Replies: 0)

  3. Diffusion interpetation (Replies: 10)

  4. Diffusion on liquid (Replies: 1)

Loading...