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Torre Rodríguez, Jaime Arturo de la

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0000-0002-1657-0820
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Torre Rodríguez
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Jaime Arturo de la
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20101
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Tipo: master thesis ×

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    Coarse-graining Brownian motion : from particles to a discrete diffusion equation
    (Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2010-10-13) Torre Rodríguez, Jaime Arturo de la
    We consider a recently obtained coarse-grained discrete equation for the diffusion of Brownian particles. The detailed level of description is governed by a Brownian dynamics of non-interacting particles. The coarse-level is described by discrete concentration variables defined in terms of the Delaunay cell. These coarse variables obey a stochastic differential equation that can be understood as a discrete version of a diffusion equation. The diffusion equation contains two basic building blocks which are the entropy function and the friction matrix. The entropy function is shown to be non-additive due to the overlapping of cells in the Delaunay construction. The friction matrix is state dependent in principle, but for near-equilibrium situations it is shown that it may safely evaluated at the equilibrium value of the density field