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A Fokker–Planck equation for a piecewise entropy functional defined in different space domains. An application to solute partitioning at the membrane–water interface

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  • Grassi, Antonio
  • Raudino, Antonio

Abstract

A nonlinear Fokker–Planck equation is proposed for a system subject to different statistics (in the present study, the Gibbs–Boltzmann and Fermi–Dirac statistics) defined in different contiguous regions of space. We solved the time-dependent mono-dimensional equation numerically, and solved the time-independent mono-dimensional equation analytically under the effect of a generic external potential equation. These zones are connected by a sharp but continuous transition region. Accurate numerical procedures ensure the convergence of the Fokker–Planck equation in the transition layer. We applied our general procedure to investigate both the stationary and the time-dependent kinetics of solute partitioning between aqueous and membrane phases. Because of the relative volumes of solute, water, and lipid (Vsolute≈Vwater<

Suggested Citation

  • Grassi, Antonio & Raudino, Antonio, 2014. "A Fokker–Planck equation for a piecewise entropy functional defined in different space domains. An application to solute partitioning at the membrane–water interface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 171-182.
    • Handle: RePEc:eee:phsmap:v:395:y:2014:i:c:p:171-182
    DOI: 10.1016/j.physa.2013.09.029
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