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Mean-Square Displacement HELP
Can anyone (preferably expert) please help. How do you calculate the mean squared distance of a single particle moving randomly in a given period of time (in 2D)? I have the formula in front of me and I've spent alot of time on this but keep confusing myself, so I thought some of you guys can help.
The formula is < s^2(t) > = < (s(t)-s(t+tau))^2 >. Basically, the particle is left to move around from t=0 to t=600 and I want to end up with a figure with discrete times on the x-axis (t=100,200,300,400,500,600) and <s^2> on the y-axis -- the aim is to get a straight line relationship.
The way I'm doing it is as follows:
1.Run the program from t=0 to t=100
2.Calculate (s(t)-s(t+tau)) at each timestep (ie. at t=1,2,3,...100)
3.Square the answer to number 2
4.Sum the result of number 3
Then repeat the same procedure for t=200,..600
The question is, do you divide the sum of (s(t)-s(t+tau))^2 by the number of timesteps? If you do, then I get a very small number (which is incorrect!). Also, do you "sum" in the first place? Please shed some light on this, I have spent alot of time on it.
Thanks for any hints,
PS: I have read alot of theory on MSD but I just need a "person" to walk me through it step by step.
|displacement , meansquare|
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