Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of nonlocal phonon thermal conductivity simulations showing the
  ballistic to diffusive crossover   Simulations (e.g. Zhou et al., Phys. Rev. B 79, 115201 (2009)) show nonlocal
effects of the ballistic/diffusive crossover. The local temperature has
nonlinear spatial variation not contained in the local Fourier law
$\vec{j}(\vec{r})=-\kappa\vec{\nabla}T(\vec{r})$. The heat current
$\vec{j}(\vec{r})$ depends not just on the local temperature gradient
$\vec{\nabla}T(\vec{r})$, but also on temperatures at points $\vec{r}^{ \
\prime}$ within phonon mean free paths, which can be micrometers long. This
paper uses the Peierls-Boltzmann transport theory in non-local form to analyze
the spatial variation $\Delta T(\vec{r})$. The relaxation-time approximation
(RTA) is used because full solution is very challenging. Improved methods of
extrapolation to obtain the bulk thermal conductivity $\kappa$ are proposed.
Callaway invented an approximate method of correcting RTA for the $\vec{q}$
(phonon wavevector or crystal momentum) conservation of N (normal as opposed to
Umklapp) anharmonic collisions This method is generalized to the non-local case
where $\kappa(\vec{k})$ depends on wavevector of the current $\vec{j}(\vec{k})$
and temperature gradient $i\vec{k}\Delta T(\vec{k})$.

32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys