User:TheLarry/Notebook/Larrys Notebook/2010/08/15

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Smulochowski Equation

last post i said that i found an expectation value for k of about 300/s. That was wrong. I forgot i was took only every 100 time points so that value should have been about 3/s. Which is way worse and horrible.

So i've been thinking about what is wrong. and hoping that this whole processes wasn't a waste of time. And i realized my diffusion constant was wrong. my unites were in pN and nm but my viscosity was in N/m^2. So when i changed my viscosity, my diffusion constant increased by a factor of 10^7. Now with this my expectation value for k is around 10^7 which again is fantastic. However, i don't know how to deal with the probability. You see that is the rate constant to reach the binding point about 4.5 nm away, but to reach -8 nm away it has about the same except it's probability doesn't peak above 10^-10 or so. So it is extremely unlikely to reach there. So i need to think of how to deal with the overall probability. Maybe multiply it by the expected time it takes to reach the point.

this is the graphs of smulochowski equation at the time shown (about 1E-7 seconds). THe lower right graph is the probability of reaching 4.5 nm as it evolves in time. The two graphs to the left are the dirac delta function (initial conditions). I used them when i was initially programming to make sure it was working.