Construction of Simulation Wavefunctions for Aqueous Species: D3O+

This paper investigates Monte Carlo techniques for construction of compact wavefunctions for the internal atomic motion of the D3O+ ion. The polarization force field models of Stillinger, et al and of Ojamae, et al. were used. Initial pair product wavefunctions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair product wavefunctions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair product wavefunctions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair product wavefunctions, the traditional variational theorem permits identification of wavefunction features with significant potential for further optimization. The most important explicit correlation variable found for the D3O+ ion was the vector triple product {\bf r}$_{OD1}\cdot$({\bf r}$_{OD2}\times${\bf r}$_{OD3}$). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wavefunction with an error of 5-6% in the zero point energy.Comment: 17 pages including 6 figures, typos correcte

Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisation

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology. Moreover, we provide here for the first time a theoretical analysis of the new Monte Carlo simulation technique in Kuznetsov et al. (2011) and of its multilevel variant for computing expectations of functions depending on the historical trajectory of a Levy process. We derive rates of convergence for both methods and show that they are uniform with respect to the "jump activity" (e.g. characterised by the Blumenthal-Getoor index). We also present a modified version of the algorithm in Kuznetsov et al. (2011) which combined with the multilevel methodology obtains the optimal rate of convergence for general Levy processes and Lipschitz functionals. This final result is only a theoretical one at present, since it requires independent sampling from a triple of distributions which is currently only possible for a limited number of processes

A New Monte Carlo Method for Time-Dependent Neutrino Radiation Transport

Monte Carlo approaches to radiation transport have several attractive properties compared to deterministic methods. These include simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them particularly interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents an attractive approach for use in neutrino radiation-hydrodynamics simulations of core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport

Thermodynamics of a Trapped Unitary Fermi Gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value $T_c=0.23(2)epsilon_F$ in the bulk, as predicted by the present authors in their Monte Carlo calculations.Comment: 5 pages, 4 figures, published versio