TY - JOUR
T1 - Exact dimensional reduction of linear dynamics
T2 - Application to confined diffusion
AU - Kalinay, Pavol
AU - Percus, Jerome K.
N1 - Funding Information:
K. K. Mon has been instrumental in motivating the research reported here, and R. Bowles has contributed as well. Support from DOE Grant No. DE-FG02-02ER15292 is gratefully acknowledged, and P. Kalinay thanks the Courant Institute for its hospitality, as well as VEGA grant No. 2/3107/24 for additional support.
PY - 2006/6
Y1 - 2006/6
N2 - 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.
AB - 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.
KW - Diffusion
KW - Dimensional reduction
KW - Fick-Jacobs equation
KW - Mapping
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U2 - 10.1007/s10955-006-9081-3
DO - 10.1007/s10955-006-9081-3
M3 - Article
AN - SCOPUS:33746931214
SN - 0022-4715
VL - 123
SP - 1059
EP - 1069
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5
ER -