Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Hard-Sphere Poisson-Nernst-Planck Models for Ionic Channels with
  Permanent Charges   The main goal of this work is to examine the qualitative effect of ion sizes
via a steady-state boundary value problem. We study a one-dimensional version
of a Poisson-Nernst-Planck system with a local hard-sphere potential model for
ionic flow through a membrane channel with fixed boundary ion concentrations
and electric potentials. A complete set of integrals for the inner system is
illustrated that delivers information for boundary and internal layers. In
addition, a group of simultaneous equations appears in the construction of
singular orbits. The research aims to set up a simple formation defined by the
profile of permanent charges with two mobile ion species, one positively
charged, cation, and one negatively charged, anion. A local hard-sphere
potential that depends pointwise on ion concentrations is included in the model
to estimate ion-size impacts on the ionic flow. The analysis is built on the
geometric singular perturbation theory, particularly on specific structures of
this concrete model. For 1:1 ionic mixtures, we first conduct precise
mathematical analysis and derive a matching system of nonlinear algebraic
equations. We then extend the results by directing on a critical case where the
current is zero. Treating the ion sizes as small parameters, we derive an
approximation of zero-current fluxes for general values of permanent charge. We
then focus on small values of permanent charge to obtain more concrete outputs.
We will also examine ion size effects on the flow rate of matter for the
zero-current case.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga