  Non-equilibrium (NE) molecular dynamics (MD), or NEMD, gives a "direct"
simulation of thermal conductivity kappa. Heat H(x) is added and subtracted in
equal amounts at different places x. After steady state is achieved, the
temperature T(x) is found by averaging over finite sections. Usually the aim is
to extract a value of dT/dx from a place distant from sources and sinks of
heat. This yields an effective kappa(L) for the thermal conductivity, L being
the system size. The result is then studied as a function of L, to extract the
bulk limit kappa. Here instead, our heat is H(x)~sin(qx), where q=2pi/L. This
causes a steady-state temperature T_0 + Delta T sin(2pi x/L). A thermal
conductivity kappa(q) is extracted, which is well converged at the chosen q (or
L). Bulk conductivity kappa requires taking the q to 0 limit. The method is
tested for liquid and crystalline argon. One advantage is reduced computational
noise at a given total MD run time. Another advantage is that kappa(q) has a
more physical meaning than kappa(L). It can be easily studied using
Peierls-Boltzmann transport theory. New formulas for kappa(q) in simplified
Debye-type models give new insight about extrapolation to q to 0 or 1/L to 0.
In particular, it is shown that kappa(L$ is unlikely to behave as kappa -C/L,
and much more likely to behave as kappa-C'/sqrt(L). Convergence problems
encountered in computational cells with very large aspect ratios
L(parallel)/L(perp) are also analyzed. Some details are contained in the
"Supplemental Material" file.
