Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stochastic approximation scheme and convergence theorem for particle
  interactions with perfectly reflecting boundaries   We prove the existence of a solution to an equation governing the number
density within a compact domain of a discrete particle system for a prescribed
class of particle interactions taking into account the effects of the diffusion
and drift of the set of particles. Each particle carries a number of internal
coordinates which may evolve continuously in time, determined by what we will
refer to as the internal drift, or discretely via the interaction kernels.
Perfectly reflecting boundary conditions are imposed on the system and all the
processes may be spatially and temporally inhomogeneous. We use a relative
compactness argument to construct a sequence of measures that converge weakly
to a solution of the governing equation. Since the proof of existence is a
constructive one, it provides a stochastic approximation scheme that can be
used for the numerical study of molecular dynamics.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci