Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion |
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Authors: | Pavol Kalinay Jerome K. Percus |
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Affiliation: | (1) Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA;(2) Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 84511 Bratislava, Slovak Republic;(3) Department of Physics, New York University, New York, NY 10003, USA |
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Abstract: | In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics. |
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Keywords: | diffusion Fick-Jacobs equation dimensional reduction mapping |
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