Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Size Effects in Thermal Conduction by Phonons   Heat transport in nanoscale systems is both hard to measure microscopically,
and hard to interpret. Ballistic and diffusive heat flow coexist, adding
confusion. This paper looks at a very simple case: a nanoscale crystal repeated
periodically. This is a popular model for simulation of bulk heat transport
using classical molecular dynamics (MD), and is related to transient thermal
grating experiments. Nanoscale effects are seen in perhaps their simplest form.
The model is solved by an extension of standard quasiparticle gas theory of
bulk solids. Both structure and heat flow are constrained by periodic boundary
conditions. Diffusive transport is fully included, while ballistic transport by
phonons of long mean free path is diminished in a specific way. Heat current
J(x) and temperature gradient dT(x')/dx' have a non-local relationship, via
k(x-x'), over a distance |x-x'| determined by phonon mean free paths. In MD
modeling of bulk conductivity, finite computer resources limit system size.
Long mean free paths, comparable to the scale of heating and cooling, cause
undesired finite-size effects that have to be removed by extrapolation. The
present model allows this extrapolation to be quantified. Calculations based on
the Peierls-Boltzmann equation, using a generalized Debye model, show that
extrapolation involves fractional powers of 1/L. It is also argued that heating
and cooling should be distributed sinusoidally (de/dt~cos(2pi x/L)) to improve
convergence of numerics.

2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th