A diffusion Monte Carlo study of small para-Hydrogen clusters

Ground state energies and chemical potentials of parahydrogen clusters are calculated from 3 to 40 molecules using the diffusion Monte Carlo technique with two different pH2-pH2 interactions. This calculation improves a previous one by the inclusion of three-body correlations in the importance sampling, by the time step adjustement and by a better estimation of the statistical errors. Apart from the cluster with 13 molecules, no other magic clusters are predicted, in contrast with path integral Monte Carlo results

Correlated sampling in quantum Monte Carlo: a route to forces

In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate numerical forces and potential energy surfaces in diffusion Monte Carlo. It employs a novel coordinate transformation, earlier used in variational Monte Carlo, to greatly reduce the statistical error. Results are presented for first-row diatomic molecules.Comment: 5 pages, 2 postscript figure

The Path Integral Monte Carlo Calculation of Electronic Forces

We describe a method to evaluate electronic forces by Path Integral Monte Carlo (PIMC). Electronic correlations, as well as thermal effects, are included naturally in this method. For fermions, a restricted approach is used to avoid the ``sign'' problem. The PIMC force estimator is local and has a finite variance. We applied this method to determine the bond length of H$_2$ and the chemical reaction barrier of H+H$_2\longrightarrow$H$_2$+H. At low temperature, good agreement is obtained with ground state calculations. We studied the proton-proton interaction in an electron gas as a simple model for hydrogen impurities in metals. We calculated the force between the two protons at two electronic densities corresponding to Na ($r_s=3.93$) and Al ($r_s=2.07$) using a supercell with 38 electrons. The result is compared to previous calculations. We also studied the effect of temperature on the proton-proton interaction. At very high temperature, our result agrees with the Debye screening of electrons. As temperature decreases, the Debye theory fails both because of the strong degeneracy of electrons and most importantly, the formation of electronic bound states around the protons.Comment: 18 pages, 10 figure

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde

The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile

A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically

Contact problem for bonded nonhomogeneous materials under shear loading

The present paper examines the contact problem related to shearpunch through a rigid strip bonded to a nonhomogeneous medium.The nonhomogeneous medium is bonded to another nonhomogeneousmedium. The strip is perpendicular to the y-axis and parallelto the x-axis. It is assumed that there is perfect bonding atthe common plane surface of two nonhomogeneous media. UsingFourier cosine transforms, the solution of the problem is reducedto dual integral equations involving trigonometric cosinefunctions. Later on, the solution of the dual integral equationsis transformed into the solution of a system of two simultaneousFredholm integral equations of the second kind. Solvingnumerically the Fredholm integral equations of the second kind,the numerical results of resultant contact shear are obtained andgraphically displayed to demonstrate the effect of nonhomogeneityof the elastic material.Peer Reviewe

Contact problem for bonded nonhomogeneous materials under shear loading

The present paper examines the contact problem related to shear punch through a rigid strip bonded to a nonhomogeneous medium. The nonhomogeneous medium is bonded to another nonhomogeneous medium. The strip is perpendicular to the y-axis and parallel to the x-axis. It is assumed that there is perfect bonding at the common plane surface of two nonhomogeneous media. Using Fourier cosine transforms, the solution of the problem is reduced to dual integral equations involving trigonometric cosine functions. Later on, the solution of the dual integral equations is transformed into the solution of a system of two simultaneous Fredholm integral equations of the second kind. Solving numerically the Fredholm integral equations of the second kind, the numerical results of resultant contact shear are obtained and graphically displayed to demonstrate the effect of nonhomogeneity of the elastic material

The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile

A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.Peer Reviewe