Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subdiffusion in a system with a partially permeable partially absorbing
  wall   We consider subdiffusion of a particle in a one-dimensional system with a
thin partially permeable wall. Passing through the wall, the particle can be
absorbed with a certain probability. We call such a wall partially permeable
partially absorbing wall (PPAW). Using the diffusion model in a system with
discrete time and spatial variable, probability densities (Green's functions)
describing subdiffusion in the system have been derived. Knowing the Green's
functions we derive boundary conditions at the wall. The boundary conditions
take a specific form in which time derivatives of the fractional order
controlled by the subdiffusion parameter are involved. We assume that the
absorption of a particle can occur only when the particle jumps through the
wall. It is not possible to temporarily retain a particle inside a thin wall.
The wall can represent a thin membrane. If a system with a thick membrane
inside which particles may diffuse is considered, it can be treated as a
three-part with a thick membrane as the middle part. The boundary conditions at
membrane surfaces can be assumed as for PPAW. The system with PPAW can be used
to filter diffusing particles. The temporal evolution of the probability that
the diffusing molecule has not been absorbed is considered. This function shows
the efficiency of the filtering process. The impact of subdiffusion and wall
parameters on this function is discussed.

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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math