Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Generalized Debye-H\"uckel Equation from Poisson-Fermi
  Theory   The Debye-H\"uckel equation is a fundamental physical model in chemical
thermodynamics that describes the free energy (chemical potential, activity) of
an ion in electrolyte solutions at variable salt concentration, temperature,
and pressure. It is based on the linear Poisson-Boltzmann equation that ignores
the steric (finite size), correlation, and polarization effects of ions and
water (or solvent molecules). The Poisson-Fermi theory developed in recent
years takes these effects into account. A generalized Debye-H\"uckel equation
is derived from the Poisson-Fermi theory and is shown to consistently reduce to
the classical equation when these effects vanish in limiting cases. As a
result, a linear fourth-order Poisson-Fermi equation is presented for which
unique solutions are shown to exist for spherically symmetric systems.
Moreover, a generalized Debye length is proposed to include the size effects of
ions and water.

11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc