Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Modified Poisson--Nernst--Planck Model with Excluded Volume Effect:
  Theory and Numerical Implementation   The Poisson--Nernst--Planck (PNP) equations have been widely applied to
describe ionic transport in ion channels, nanofluidic devices, and many
electrochemical systems. Despite their wide applications, the PNP equations
fail in predicting dynamics and equilibrium states of ionic concentrations in
confined environments, due to the ignorance of the excluded volume effect. In
this work, a simple but effective modified PNP (MPNP) model with the excluded
volume effect is derived, based on a modification of diffusion coefficients of
ions. At the steady state, a modified Poisson--Boltzmann (MPB) equation is
obtained with the help of the Lambert-W special function. The existence and
uniqueness of a weak solution to the MPB equation are established. Further
analysis on the limit of weak and strong electrostatic potential leads to two
modified Debye screening lengths, respectively. A numerical scheme that
conserves total ionic concentration and satisfies energy dissipation is
developed for the MPNP model. Numerical analysis is performed to prove that our
scheme respects ionic mass conservation and satisfies a corresponding discrete
free energy dissipation law. Positivity of numerical solutions is also
discussed and numerically investigated. Numerical tests are conducted to
demonstrate that the scheme is of second-order accurate in spatial
discretization and has expected properties. Extensive numerical simulations
reveal that the excluded volume effect has pronounced impacts on the dynamics
of ionic concentration and flux. In addition, the effect of volume exclusion on
the timescales of charge diffusion is systematically investigated by studying
the evolution of free energies and diffuse charges.

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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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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: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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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: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph