2D Lattice Liquid Models

A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on the rectangular honeycomb lattice of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability, and peculiar anomalous diffusions in their time-averaged mean square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.Comment: REVTeX4, 14 pages in double colomn, 12 figures; added references with some comments, typos fixe

Analysis of a non-reversible Markov chain speedup by a single edge

We present a Markov chain example where non-reversibility and an added edge jointly improve mixing time: when a random edge is added to a cycle of $n$ vertices and a Markov chain with a drift is introduced, we get mixing time of $O(n^{3/2})$ with probability bounded away from 0. If only one of the two modifications were performed, the mixing time would stay $\Omega(n^2)$.Comment: 15 pages, 5 figure

MASSCLEANcolors - Mass Dependent Integrated Colors for Stellar Clusters Derived from 30 Million Monte Carlo Simulations -

We present Monte Carlo models of open stellar clusters with the purpose of mapping out the behavior of integrated colors with mass and age. Our cluster simulation package allows for stochastic variations in the stellar mass function to evaluate variations in integrated cluster properties. We find that UBVK colors from our simulations are consistent with simple stellar population (SSP) models, provided the cluster mass is large, Mcluster >= 10^6 M_Sun. Below this mass, our simulations show two significant effects. First, the mean value of the distribution of integrated colors moves away from the SSP predictions and is less red, in the first 10^7 to 10^8 years in UBV colors, and for all ages in (V - K). Second, the 1\sigma dispersion of observed colors increases significantly with lower cluster mass. The former we attribute to the reduced number of red luminous stars in most of the lower mass clusters and the later we attribute to the increased stochastic effect of a few of these stars on lower mass clusters. This later point was always assumed to occur, but we now provide the first public code able to quantify this effect. We are completing a more extensive database of magnitudes and colors as a function of stellar cluster age and mass that will allow the determination of the correlation coefficients among different bands, and improve estimates of cluster age and mass from integrated photometry.Comment: 11 pages, 5 figures, submitted to Astrophysical Journal Letter