Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walk approximation for irreversible drift-diffusion process on
  manifold: ergodicity, unconditional stability and convergence   Irreversible drift-diffusion processes are very common in biochemical
reactions. They have a non-equilibrium stationary state (invariant measure)
which does not satisfy detailed balance. For the corresponding Fokker-Planck
equation on a closed manifold, via Voronoi tessellation, we propose two upwind
finite volume schemes with or without the information of the invariant measure.
Both two schemes enjoy stochastic $Q$-matrix structures and can be decomposed
as a gradient flow part and a Hamiltonian flow part, which enable us to prove
unconditional stability, ergodicity and error estimates. Based on two upwind
schemes, several numerical examples - including sampling accelerated by a
mixture flow, image transformations and simulations for stochastic model of
chaotic system - are conducted. These two structure-preserving schemes also
give a natural random walk approximation for a generic irreversible
drift-diffusion process on a manifold. Thus they can be adapted to
manifold-related computations induced from high dimensional molecular dynamics.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ