Series expansion studies of random sequential adsorption with diffusional relaxation

We obtain long series (28 terms or more) for the coverage (occupation fraction) $\theta$, in powers of time $t$ for two models of random sequential adsorption with diffusional relaxation using an efficient algorithm developed by the authors. Three different kinds of analyses of the series are performed for a wide range of $\gamma$, the rate of diffusion of the adsorbed particles, to investigate the power law approach of $\theta$ at large times. We find that the primitive series expansions in time $t$ for $\theta$ capture rich short and intermediate time kinetics of the systems very well. However, we see that the series are still not long enough to extract the kinetics at large times for general $\gamma$. We have performed extensive computer simulations employing an efficient event-driven algorithm to confirm the $t^{-1/2}$ saturation approach of $\theta$ at large times for both models, as well as to investigate the short and intermediate time behaviors of the systems.Comment: 35 pages. revtex. 16 eps figures. Series expansion coefficients are attached at the end of the soure/LaTex file (named diff.tex). uses fleqn.st

A size-consistent Gr\"uneisen-quasiharmonic approach for lattice thermal conductivity

We propose a size-consistent Gr\"uneisen-quasiharmonic approach (GQA) to calculate the lattice thermal conductivity $\kappa_l$ where the Gr\"uneisen parameters that measure the degree of phonon anharmonicity are calculated directly using first-principles calculations. This is achieved by identifying and modifying two existing equations related to the Slack formulae for $\kappa_l$ that suffer from the size-inconsistency problem when dealing with non-monoatomic primitive cells (where the number of atoms in the primitive cell $n$ is greater than one). In conjunction with other thermal parameters such as the acoustic Debye temperature $\theta_a$ that can also be obtained within the GQA, we predict $\kappa_l$ for a range of materials taken from the diamond, zincblende, rocksalt, and wurtzite compounds. The results are compared with that from the experiment and the quasiharmonic Debye model (QDM). We find that in general the prediction of $\theta_a$ is rather consistent among the GQA, experiment, and QDM. However, while the QDM somewhat overestimates the Gr\"uneisen parameters and hence underestimates $\kappa_l$ for most materials, the GQA predicts the experimental trends of Gr\"uneisen parameters and $\kappa_l$ more closely. We expect the GQA with the modified Slack formulae could be used as an effective and practical predictor for $\kappa_l$, especially for crystals with large $n$.Comment: 8 pages, 6 figure

Linear scaling computation of the Fock matrix. IX. Parallel computation of the Coulomb matrix

We present parallelization of a quantum-chemical tree-code [J. Chem. Phys. {\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91 -- 98 % efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63 -- 81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).Comment: 7 pages, 6 figure

In-plane dominant anisotropy stochastic magnetic tunnel junction for probabilistic computing: A Fokker-Planck study

Recently there is considerable interest to realize efficient and low-cost true random number generators (RNGs) for practical applications. One important way is through the use of bistable magnetic tunnel junctions (MTJs). Here we study the magnetization dynamics of an MTJ, with a focus to realize efficient random bit generation under the assumption that the orientation dependence of the energy of the nanomagnet is described by two perpendicular in-plane anisotropies. We find that a high rate of random bit generation is achievable away from the pure easy-axis situation by tuning a single parameter $H_z$ so that it is either (a) toward a barrierless-like single easy plane situation when $H_z$ reduces to zero, or (b) toward a stronger easy plane situation when $H_z$ becomes increasingly negative where transitions between low energy states are confined in the stronger easy plane that contains the saddle points. We find that the MTJs maintain their fast magnetization dynamical characteristics even in the presence of a magnetic field. Our findings provide a valuable guide to achieving efficient generation of probabilistic bits for applications in probabilistic computing.Comment: 10 pages, 5 figure

First-principles study of the lattice dynamics of Sb2S3

We present a lattice dynamics study of orthorhombic antimony sulphide (Sb2S3) obtained using density-functional calculations in conjunction with the supercell force-constant method. The effect of Born effective charges is taken into account using a mixed-space approach, resulting in the splitting of longitudinal and transverse optical (LO-TO) phonon branches near the zone center. Zone-center frequencies agree well with Raman scattering experiments. Due to the slow decay of the interatomic force constants (IFC), a minimal 2x4x2 supercell (Pnma setting) with 320 atoms is crucial for an accurate determination of the dispersion relations. Smaller supercells result in artificial acoustic phonon softening and unphysical lifting of degeneracies along high symmetry directions. We propose a scheme to investigate the convergence of the IFC with respect to the supercell sizes. The phonon softening can be attributed to the periodic images that affect the accuracy of the force constants, and the truncation of long-ranged forces. The commensuration of the q-vectors with the supercell size is crucial to preserve degeneracies in Sb2S3 crystals.Comment: 7 pages 4 figures, 3 table