Joan Adler

Bootstrap Percolation: visualizations and applications

Bootstrap percolation models describe systems as diverse as magnetic materials, fluid flow in rocks and computer storage systems. The models have a common feature of requiring not just a simple connectivity of neighbouring sites, but rather an environment of other suitably occupied sites. Different applications as well as the connection with the mathematical literature on these models is presented. Visualizations that show the compact nature of the clusters are provided.

Simulated annealing in ocular adaptive optics

We present what is to our knowledge a first hardware realization of a simulated annealing algorithm in an adaptive optics system designed to image the retina of the human eye. The algorithm is applied to the retinal image itself without the need for wavefront sensors in the system. We find that this optimization algorithm can be an alternative to the traditional Hartmann-Shack sensing. We also compare the simulated annealing algorithm to the stochastic parallel gradient descent algorithm.

ION-IMPLANTATION-INDUCED DEFECTS IN DIAMOND AND THEIR ANNEALING : EXPERIMENT AND SIMULATION

The nature of damage induced by ion-impact and its annealing are studied both experimentally and theoretically. The experimental methods employed include measurements of the changes in electrical conductivity, in material density and in Raman spectra. These are measured for natural type IIa diamonds containing different amounts of ion-implantation induced damage and subjected to different annealing temperatures (up to 1300 K for 20 min). The simulations performed are based on Molecular Dynamics (MD) computations using the Tersoff potential. A deeply buried highly damaged region is created inside the diamond sample by imparting high momenta to lattice atoms aimed towards the same point in the crystal. The nature of the damage so created is statistically analyzed yielding information on the formation of threefold-coordinated atoms in the damage region. The transformation that the damaged region undergoes as a result of “annealing” (up to 4000 K for 50 ps) is investigated. Both experiment and theory show that diamond which contains a low density of point defects can anneal back to diamond whereas, for damage levels beyond a certain level, it tends to graphitize. The stable defect in damaged diamond seems to be, according to both experiment and theory, the 〈100〉 split interstitial. Electrically, point defects in diamond act as donor centers.

Measurement of the Branching Fractions for D0 ---> pi- e+ electron-neutrino and D0 ---> K- e+ electron-neutrino and Determination of (V (c d) / V (c s))**2

Measurements of the exclusive branching fractions B(D^0→π^-e^+ν_e) and B(D^0→K^-e^+ν_e), using data collected at the ψ(3770) with the Mark III detector at the SLAC e^+e^- storage ring SPEAR, are used to determine the ratio of the Kobayashi-Maskawa matrix elements │V_(cd)/V_(cs)│^2 =0.057_(-0.015)^(+0.038)±0.005.

Atomistic study of structural correlations at a liquid–solid interface

Abstract Structural correlations at a liquid–solid interface were explored with molecular dynamics simulations of a model aluminium system using the Ercolessi–Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium crystalline positions while liquid atoms were free to move. The density profile at the interface was investigated for different substrate crystallographic orientations and temperatures. An exponential decay of the density profile was observed, ρ ( z )∼e − κz , leading to the definition of κ as a quantitative measure of the ordering at the liquid solid interface. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found.

Resonant substructure in Kππ decays of charmed D mesons

Abstract Dalitz plot analyses of four Kππ decays of the D 0 and D + mesons are presented. The relative amounts of K ∗ π, Kϱ and non-resonant Kππ in each decay mode are determined, and isospin amplitudes and phases are derived. These results are compared with predictions from QCD. The K − π + π + mode has a non-uniform, non-resonant contribution; attempts to fit this distribution are described.

Transformation of Diamond (sp3) to Graphite (sp2) Bonds by Ion-Impact

The formation of point defects in diamond induced by an energetic displacement of a carbon atom out of its lattice site and the relaxation of the thereby disrupted crystal are studied by molecular dynamics simulations with the Tersoff potential. The displacement energy for Frenkel pair creation is calculated to be 52 eV, in agreement with experiments. It is found that the split interstitial, with a bonding configuration which resembles graphite, is the most stable defect, and the disrupted region around it is rich in sp2-like (graphitic) bonds. This region extends several nanometers and is likely to be the elementary electrically conductive cell experimentally found in radiation-damaged diamond.

The dynamical critical exponent of the two-, three- and five-dimensional kinetic Ising model

Abstract We present Monte Carlo simulation results for the dynamical critical exponent z of the two-, three- and five-dimensional kinetic Ising model. We used Glauber as well as Metropolis dynamics. Both type of dynamics lead to the same z-values in two and three dimensions. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems (up to (169984)2, (3072)3 and (48)5). For the two-dimensional case we obtain z = 2.21 ± 0.03 and for the three-dimensional case z = 2.08 ± 0.03. For the five-dimensional Glauber case, the requirement z = 2 gives a critical point J/kBTc = 0.11391 from Monte Carlo simulations, whereas new series expansions with four more terms give 0.113935 ± 0.000015 for this ratio.

Low-concentration series in general dimension

We discuss recent work on the development and analysis of low-concentration series. For many models, the recent breakthrough in the extremely efficient no- free-end method of series generation facilitates the derivation of 15th-order series for multiple moments in general dimension. The 15th-order series have been obtained for lattice animals, percolation, and the Edwards-Anderson Ising spin glass. In the latter cases multiple moments have been found. From complete graph tables through to 13th order, general dimension 13th-order series have been derived for the resistive susceptibility, the moments of the logarithms of the distribution of currents in resistor networks, and the average transmission coefficient in the quantum percolation problem, 11th-order series have been found for several other systems, including the crossover from animals to percolation, the full resistance distribution, nonlinear resistive susceptibility and current distribution in dilute resistor networks, diffusion on percolation clusters, the dilute Ising model, dilute antiferromagnet in a field, and random field Ising model and self-avoiding walks on percolation clusters. Series for the dilute spin-1/2 quantum Heisenberg ferromagnet are in the process of development. Analysis of these series gives estimates for critical thresholds, amplitude ratios, and critical exponents for all dimensions. Where comparisons are possible, our series results are in good agreement with bothε-expansion results near the upper critical dimension and with exact results (when available) in low dimensions, and are competitive with other numerical approaches in intermediate realistic dimensions.

Ordering at Solid-Liquid Interfaces Between Dissimilar Materials

In an earlier report we explored structural correlations at a liquid-solid interface with molecular dynamics simulations of a model aluminium system using the Ercolessi-Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium fcc crystalline positions while liquid atoms were free to move. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found. In the present paper we extend this study to the case of a fixed bcc substrate in contact with liquid aluminium. We find surprisingly similar results for the density profiles of both (100) and (110) substrates. However, there is a far greater in-plane ordering in the (100) than for the (110) system. For the (100) substrates we observe adsorption of liquid atoms into the terminating plane of the bcc (100) substrate, effectively transforming the bcc (100) plane into an fcc (100) plane.