Monte Carlo simulations of 4d simplicial quantum gravity

Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues. One is that contrary to recent claims there is strong analytical and numerical evidence for the existence of an exponential bound that makes the partition function well-defined. The other is that there may be an ambiguity in the choice of the measure of the discrete model which could even lead to the existence of different universality classes.Comment: 16 pages, LaTeX, epsf, 4 uuencoded figures; contribution to the JMP special issue on "Quantum Geometry and Diffeomorphism-Invariant Quantum Field Theory

Effect of atomic scale plasticity on hydrogen diffusion in iron: Quantum mechanically informed and on-the-fly kinetic Monte Carlo simulations

We present an off-lattice, on-the-fly kinetic Monte Carlo (KMC) model for simulating stress-assisted diffusion and trapping of hydrogen by crystalline defects in iron. Given an embedded atom (EAM) potential as input, energy barriers for diffusion are ascertained on the fly from the local environments of H atoms. To reduce computational cost, on-the-fly calculations are supplemented with precomputed strain-dependent energy barriers in defect-free parts of the crystal. These precomputed barriers, obtained with high-accuracy density functional theory calculations, are used to ascertain the veracity of the EAM barriers and correct them when necessary. Examples of bulk diffusion in crystals containing a screw dipole and vacancies are presented. Effective diffusivities obtained from KMC simulations are found to be in good agreement with theory. Our model provides an avenue for simulating the interaction of hydrogen with cracks, dislocations, grain boundaries, and other lattice defects, over extended time scales, albeit at atomistic length scales

Exomoon simulations

We introduce and describe our newly developed code that simulates light curves and radial velocity curves for arbitrary transiting exoplanets with a satellite. The most important feature of the program is the calculation of radial velocity curves and the Rossiter-McLaughlin effect in such systems. We discuss the possibilities for detecting the exomoons taking the abilities of Extremely Large Telescopes into account. We show that satellites may be detected also by their RM effect in the future, probably using less accurate measurements than promised by the current instrumental developments. Thus, RM effect will be an important observational tool in the exploration of exomoons.Comment: 5 pages, 2 figures with 9 figure panels, accepted by EM&

Molecular Dynamics Simulations

A tutorial introduction to the technique of Molecular Dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NVT ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study of a glass-forming polymer melt under shear is mentioned.Comment: 38 pages, 11 figures, to appear in J. Phys.: Condens. Matte

Semiconvection: numerical simulations

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As in laboratory and geophysical cases convection takes place in a layered form. The proper translation between subsonic flows in a stellar interior and an incompressible (Boussinesq) fluid is given, and the validity of the Boussinesq approximation for the semiconvection problem is checked by comparison with fully compressible simulations. The predictions of a simplified theory of mixing in semiconvection given in a companion paper are tested against the numerical results, and used to extrapolate these to astrophysical conditions. The predicted effective He-diffusion coefficient is nearly independent of the double-diffusive layering thickness $d$. For a fiducial main sequence model (15 $M_\odot$) the inferred mixing time scale is of the order $10^{10}$ yr. An estimate for the secular increase of $d$ during the semiconvective phase is given. It can potentially reach a significant fraction of a pressure scale height.Comment: arXiv admin note: substantial text overlap with arXiv:1012.585

Simulations with Complex Measures

Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.Comment: 3 pages, postcript (95K), contribution to LAT93, UM-P-93/10