[Diffusion with Ratchets] - A New Kind of Science: The NKS Forum

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Diffusion with Ratchets

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Posted by: Jason Cawley

An interesting empirical bio paper examining ion transport issues got me thinking about minimal additions to typical random-walk diffusion that might capture ratchet effects. A thread about the paper that prompted the thought is here -

http://forum.wolframscience.com/sho...s=&threadid=822

Attached is a simple Mathematica notebook that evolves idealized 1D systems incorporating standard random-walk style diffusion on the one hand (with a bias "field" allowed), and ratchet-like behavior for one particle at a time, at some portion of the array locations, on the other hand. A wide range of transport characteristics would seem to be possible for different values of its natural parameters.

I hope this is interesting.


Posted by: Jason Cawley

Sure, you can get much nicer plots easily with e.g. -

SetOptions[ArrayPlot, ColorFunction -> (If[# == 0, GrayLevel[1], Hue[#]] &), ColorFunctionScaling -> True, Mesh -> True];


Then you can make tables of plots for different values of prob, different widths, different numbers of steps, different numbers of starting particles on the left or in the center or distributed randomly, different periodic or random placements of ratchet locations, etc. It forms a whole little NKS system.

Lots of ratchets tend to "sort" everything to the right, ending in a one per location ordered stack or a cloud sloshed up on the right edge depending on the field value and number of particles involved. Few leave diffusion, which can be turned into a current by tuning the probability. You can dial in anything in between diffusion, current like flow, and one by one deterministic "sorting", for some set of parameter values.




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