Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Voltage laws for three-dimensional microdomains with cusp-shaped funnels
  derived from Poisson-Nernst-Planck equations   We study the electro-diffusion properties of a domain containing a
cusp-shaped structure in three dimensions when one ionic specie is dominant.
The mathematical problem consists in solving the steady-state
Poisson-Nernst-Planck (PNP) equation with an integral constraint for the number
of charges. A non-homogeneous Neumann boundary condition is imposed on the
boundary. We construct an asymptotic approximation for certain singular limits
that agree with numerical simulations. Finally, we analyse the consequences of
non-homogeneous surface charge density. We conclude that the geometry of
cusp-shaped domains influences the voltage profile, specifically inside the
cusp structure. The main results are summarized in the form of new
three-dimensional electrostatic laws for non-electroneutral electrolytes. We
discuss applications to dendritic spines in neuroscience.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol