Statistical mechanics derivation of hydrodynamic boundary conditions : the diffusion equation
Statistical mechanics derivation of hydrodynamic boundary conditions : the diffusion equation
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2002
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Kroy, Klaus
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Journal of Physics: Condensed Matter ; 14 (2002). - pp. 9223-9235
Abstract
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic structure in a microscopic relaxation kernel connected to the frequency-dependent penetration length familiar for diffusive processes, and leads to a microscopic definition of the position where the hydrodynamic boundary condition has to be applied. Corrections to the hydrodynamic limit are obtained andwe derive general amplitudes of spatially and temporally longranged fluctuations in the diffusive system considered.
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530 Physics
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FUCHS, Matthias, Klaus KROY, 2002. Statistical mechanics derivation of hydrodynamic boundary conditions : the diffusion equation. In: Journal of Physics: Condensed Matter. 14, pp. 9223-9235. Available under: doi: 10.1088/0953-8984/14/40/313BibTex
@article{Fuchs2002Stati-8975, year={2002}, doi={10.1088/0953-8984/14/40/313}, title={Statistical mechanics derivation of hydrodynamic boundary conditions : the diffusion equation}, volume={14}, journal={Journal of Physics: Condensed Matter}, pages={9223--9235}, author={Fuchs, Matthias and Kroy, Klaus} }
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