A Very Fast and Momentum-conserving Tree Code

A Very Fast and Momentum-conserving Tree Code.

The tree code for the approximate evaluation of gravitational forces is extended and substantially accelerated by including mutual cell-cell interactions. These are computed by a Taylor series in Cartesian coordinates and in a completely symmetric fashion, such that Newton's third law is satisfied by construction and that therefore momentum is exactly conserved. The computational effort is furt...

Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities

The development and implementation of a tree code (TC) and fast multipole method (FMM) for the efficient, linear-scaling calculation of long-range electrostatic interactions of particle distributions with variable shape and multipole character are described. The target application of these methods are stochastic boundary molecular simulations with polarizable force fields and/or combined quantu...

VERY FAST TREE - STRUCTURED VECTOR QUANTIZATIONTodd

Very Fast Tree-structured Vector Quantization

Very fast tree-structured vector quantization employs scalar quantization decisions at each level, but chooses the dimension on which to quantize based on the coordinate direction of maximum variance. Because the quantization is scalar, searches are no more complex than scalar quantization − providing significant improvement in complexity over full-searched or even tree-structured vector quanti...

Thermal Conductivity for a Momentum Conserving Model

Abstract. We present here complete mathematical proofs of the results annouced in cond-mat/0509688. We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of harmonic oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute the current-current time correlation function and the t...