Some closure operations in Zariski-Riemann spaces of valuation domains: a survey

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains

Spin Model for Inverse Melting and Inverse Glass Transition

A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower energy associated with the non-interacting states yields a "paramagnetic" phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange, analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified

Epitaxial Growth Kinetics with Interacting Coherent Islands

The Stranski-Krastanov growth kinetics of undislocated (coherent) 3-dimensional islands is studied with a self-consistent mean field rate theory that takes account of elastic interactions between the islands. The latter are presumed to facilitate the detachment of atoms from the islands with a consequent decrease in their average size. Semi-quantitative agreement with experiment is found for the time evolution of the total island density and the mean island size. When combined with scaling ideas, these results provide a natural way to understand the often-observed initial increase and subsequent decrease in the width of the coherent island size distribution.Comment: 4 pages, 4 figure

Simulations of the grand design galaxy M51: a case study for analysing tidally induced spiral structure

We present hydrodynamical models of the grand design spiral M51 (NGC 5194), and its interaction with its companion NGC 5195. Despite the simplicity of our models, our simulations capture the present day spiral structure of M51 remarkably well, and even reproduce details such as a kink along one spiral arm, and spiral arm bifurcations. We investigate the offset between the stellar and gaseous spiral arms, and find at most times (including the present day) there is no offset between the stars and gas to within our error bars. We also compare our simulations with recent observational analysis of M51. We compute the pattern speed versus radius, and like the observations, find no single global pattern speed. We also show that the spiral arms cannot be fitted well by logarithmic spirals. We interpret these findings as evidence that M51 does not exhibit a quasi-steady density wave, as would be predicted by density wave theory. The internal structure of M51 derives from the complicated and dynamical interaction with its companion, resulting in spiral arms showing considerable structure in the form of short-lived kinks and bifurcations. Rather than trying to model such galaxies in terms of global spiral modes with fixed pattern speeds, it is more realistic to start from a picture in which the spiral arms, while not being simple material arms, are the result of tidally induced kinematic density `waves' or density patterns, which wind up slowly over time.Comment: 23 pages, 20 figures, accepted for publication in MNRA

Strain-Dependence of Surface Diffusion: Ag on Ag(111) and Pt(111)

Using density-functional theory with the local-density approximation and the generalized gradient approximation we compute the energy barriers for surface diffusion for Ag on Pt(111), Ag on one monolayer of Ag on Pt(111), and Ag on Ag(111). The diffusion barrier for Ag on Ag(111) is found to increase linearly with increasing lattice constant. We also discuss the reconstruction that has been found experimentally when two Ag layers are deposited on Pt(111). Our calculations explain why this strain driven reconstruction occurs only after two Ag layers have been deposited.Comment: 4 pages, 3 figures, Phys. Rev. B 55 (1997), in pres

Elastic Constants of Quantum Solids by Path Integral Simulations

Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the (NVT) ensemble using an estimator for elastic constants. The other method is based on simulations in the (NpT) ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good agreement with available experimental data on elastic constants is found for helium 3. Predictions are made for the thermal expectation value of the kinetic energy of solid helium 3.Comment: 9 pages doublecolumn, 6 figures, submitted to PR