Rapid Determination of Multiple Reaction Pathways in Molecular Systems: The Soft-Ratcheting Algorithm

We discuss the ``soft-ratcheting'' algorithm which generates targeted stochastic trajectories in molecular systems with scores corresponding to their probabilities. The procedure, which requires no initial pathway guess, is capable of rapidly determining multiple pathways between known states. Monotonic progress toward the target state is not required. The soft-ratcheting algorithm is applied to an all-atom model of alanine dipeptide, whose unbiased trajectories are assumed to follow overdamped Langevin dynamics. All possible pathways on the two-dimensional dihedral surface are determined. The associated probability scores, though not optimally distributed at present, may provide a mechanism for estimating reaction rates

Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

We present the first calculation of an intrinsically relativistic quantity in fully non-linear cosmolog- ical large-scale structure studies. Traditionally, non-linear structure formation in standard {\Lambda}CDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent ap- proximation to the Einstein equations, a gravito-magnetic vector potential - giving rise to frame dragging - is present in the metric in addition to the usual Newtonian scalar potential. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in {\Lambda}CDM and examine its magnitude relative to the scalar potential. We also discuss some possible observable effects.Comment: 5 pages, 3 figur