Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closure method for spatially averaged dynamics of particle chains   We study the closure problem for continuum balance equations that model
mesoscale dynamics of large ODE systems. The underlying microscale model
consists of classical Newton equations of particle dynamics. As a mesoscale
model we use the balance equations for spatial averages obtained earlier by a
number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum
balance equation contains a flux (stress), which is given by an exact function
of particle positions and velocities. We propose a method for approximating
this function by a sequence of operators applied to average density and
momentum. The resulting approximate mesoscopic models are systems in closed
form. The closed from property allows one to work directly with the mesoscale
equaitons without the need to calculate underlying particle trajectories, which
is useful for modeling and simulation of large particle systems. The proposed
closure method utilizes the theory of ill-posed problems, in particular
iterative regularization methods for solving first order linear integral
equations. The closed from approximations are obtained in two steps. First, we
use Landweber regularization to (approximately) reconstruct the interpolants of
relevant microscale quantitites from the average density and momentum. Second,
these reconstructions are substituted into the exact formulas for stress. The
developed general theory is then applied to non-linear oscillator chains. We
conduct a detailed study of the simplest zero-order approximation, and show
numerically that it works well as long as fluctuations of velocity are nearly
constant.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: eess
37
The categories of this paper are: supr-con