TY - JOUR
T1 - Mapping of diffusion in a channel with soft walls
AU - Kalinay, Pavol
AU - Percus, Jerome K.
PY - 2011/3/10
Y1 - 2011/3/10
N2 - We study diffusion of pointlike particles biased toward the x axis by a quadratic potential U(x,y)=κ(x)y2. This system mimics a channel with soft walls of some varying (effective) cross section A(x), depending on the stiffness κ(x). We show that diffusion in this geometry can also be mapped rigorously onto the longitudinal coordinate x by a procedure known for channels with hard walls; i.e., we arrive at a one-dimensional evolution equation of the Fick-Jacobs type. On the other hand, the calculation presented serves as a prototype for mapping of the Smoluchowski equation with a wide class of potentials U(x,y) varying in both the longitudinal as well as the transverse directions, which is necessary for understanding, e.g., stochastic resonance.
AB - We study diffusion of pointlike particles biased toward the x axis by a quadratic potential U(x,y)=κ(x)y2. This system mimics a channel with soft walls of some varying (effective) cross section A(x), depending on the stiffness κ(x). We show that diffusion in this geometry can also be mapped rigorously onto the longitudinal coordinate x by a procedure known for channels with hard walls; i.e., we arrive at a one-dimensional evolution equation of the Fick-Jacobs type. On the other hand, the calculation presented serves as a prototype for mapping of the Smoluchowski equation with a wide class of potentials U(x,y) varying in both the longitudinal as well as the transverse directions, which is necessary for understanding, e.g., stochastic resonance.
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U2 - 10.1103/PhysRevE.83.031109
DO - 10.1103/PhysRevE.83.031109
M3 - Article
AN - SCOPUS:79953152847
VL - 83
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 3
M1 - 031109
ER -