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

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

The convex hull of the lattice points inside a curve

Let C be a smooth convex closed plane curve. The C -ovals C(R,u,v) are formed by expanding by a factor R , then translating by (u,v) . The number of vertices V(R,u,v) of the convex hull of the integer points within or on C(R,u,v) has order R 2/3 (Balog and Bárány) and has average size BR 2/3 as R varies (Balog and Deshouillers). We find the space average of V(R,u,v) over vectors (u,v) to be BR 2/3 with an explicit coefficient B , and show that the average over R has the same B . The proof involves counting edges and finding the domain D(q,a) of an integer vector, the set of (u,v) for which the convex hull has a directed edge parallel to (q,a) . The resulting sum over bases of the integer lattice is approximated by a triple integral