Scanning tunneling microscopy and kinetic Monte Carlo investigation of Cesium superlattices on Ag(111)

Cesium adsorption structures on Ag(111) were characterized in a low-temperature scanning tunneling microscopy experiment. At low coverages, atomic resolution of individual Cs atoms is occasionally suppressed in regions of an otherwise hexagonally ordered adsorbate film on terraces. Close to step edges Cs atoms appear as elongated protrusions along the step edge direction. At higher coverages, Cs superstructures with atomically resolved hexagonal lattices are observed. Kinetic Monte Carlo simulations model the observed adsorbate structures on a qualitative level.Comment: 8 pages, 7 figure

An invariant distribution in static granular media

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses.Comment: 4 pages 3 figure

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Large strain compressive response of 2-D periodic representative volume element for random foam microstructures

A numerical investigation has been conducted to determine the influence of Representative Volume Element (RVE) size and degree of irregularity of polymer foam microstructure on its compressive mechanical properties, including stiffness, plateau stress and onset strain of densification. Periodic two-dimensional RVEs have been generated using a Voronoi-based numerical algorithm and compressed. Importantly, self-contact of the foam’s internal microstructure has been incorporated through the use of shell elements, allowing simulation of the foam well into the densification stage of compression; strains of up to 80 percent are applied. Results suggest that the stiffness of the foam RVE is relatively insensitive to RVE size but tends to soften as the degree of irregularity increases. Both the shape of the plateau stress and the onset strain of densification are sensitive to both the RVE size and degree of irregularity. Increasing the RVE size and decreasing the degree of irregularity both tend to result in a decrease of the gradient of the plateau region, while increasing the RVE size and degree of irregularity both tend to decrease the onset strain of densification. Finally, a method of predicting the onset strain of densification to an accuracy of about 10 per cent, while reducing the computational cost by two orders of magnitude is suggested

The planar multiple obnoxious facilities location problem: A Voronoi based heuristic

Consider the situation where a given number of facilities are to be located in a convex polygon with the objective of maximizing the minimum distance between facilities and a given set of communities with the important additional condition that the facilities have to be farther than a certain distance from one another. This continuous multiple obnoxious facility location problem, which has two variants, is very complex to solve using commercial nonlinear optimizers. We propose a mathematical formulation and a heuristic approach based on Voronoi diagrams and an optimally solved binary linear program. As there are no nonlinear optimization solvers that guarantee optimality, we compare our results with a popular multi-start approach using interior point, genetic algorithm (GA), and sparse non-linear optimizer (SNOPT) solvers in Matlab. These are state of the art solvers for dealing with constrained non linear problems. Each instance is solved using 100 randomly generated starting solutions and the overall best is then selected. It was found that the proposed heuristic results are much better and were obtained in a fraction of the computer time required by the other methods.The multiple obnoxious location problem is a perfect example where all-purpose non-linear non-convex solvers perform poorly and hence the best way forward is to design and analyze heuristics that have the power and the exibility to deal with such a high level of complexity

Parameterization of a coarse-grained model of cholesterol with point-dipole electrostatics

© 2018, Springer Nature Switzerland AG. We present a new coarse-grained (CG) model of cholesterol (CHOL) for the electrostatic-based ELBA force field. A distinguishing feature of our CHOL model is that the electrostatics is modeled by an explicit point dipole which interacts through an ideal vacuum permittivity. The CHOL model parameters were optimized in a systematic fashion, reproducing the electrostatic and nonpolar partitioning free energies of CHOL in lipid/water mixtures predicted by full-detailed atomistic molecular dynamics simulations. The CHOL model has been validated by comparison to structural, dynamic and thermodynamic properties with experimental and atomistic simulation reference data. The simulation of binary DPPC/cholesterol mixtures covering the relevant biological content of CHOL in mammalian membranes is shown to correctly predict the main lipid behavior as observed experimentally