Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

Complexation of DNA with positive spheres: phase diagram of charge inversion and reentrant condensation

The phase diagram of a water solution of DNA and oppositely charged spherical macroions is studied. DNA winds around spheres to form beads-on-a-string complexes resembling the chromatin 10 nm fiber. At small enough concentration of spheres these "artificial chromatin" complexes are negative, while at large enough concentrations of spheres the charge of DNA is inverted by the adsorbed spheres. Charges of complexes stabilize their solutions. In the plane of concentrations of DNA and spheres the phases with positive and negative complexes are separated by another phase, which contains the condensate of neutral DNA-spheres complexes. Thus when the concentration of spheres grows, DNA-spheres complexes experience condensation and resolubilization (or reentrant condensation). Phenomenological theory of the phase diagram of reentrant condensation and charge inversion is suggested. Parameters of this theory are calculated by microscopic theory. It is shown that an important part of the effect of a monovalent salt on the phase diagram can be described by the nontrivial renormalization of the effective linear charge density of DNA wound around a sphere, due to the Onsager-Manning condensation. We argue that our phenomenological phase diagram or reentrant condensation is generic to a large class of strongly asymmetric electrolytes. Possible implication of these results for the natural chromatin are discussed.Comment: Many corrections to text. SUbmitted to J. Chem. Phy

Pair-factorized steady states on arbitrary graphs

Stochastic mass transport models are usually described by specifying hopping rates of particles between sites of a given lattice, and the goal is to predict the existence and properties of the steady state. Here we ask the reverse question: given a stationary state that factorizes over links (pairs of sites) of an arbitrary connected graph, what are possible hopping rates that converge to this state? We define a class of hopping functions which lead to the same steady state and guarantee current conservation but may differ by the induced current strength. For the special case of anisotropic hopping in two dimensions we discuss some aspects of the phase structure. We also show how this case can be traced back to an effective zero-range process in one dimension which is solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur

A Phylogenetic Analysis of the African Plant Genus Palisota (family Commelinaceae) based on Chloroplast DNA Sequences

The plant genus Palisota (family Commelinaceae, or spiderwort family) consists of approximately 20 species and is distributed throughout the forests of tropical Africa. The genus exhibits several unusual morphological characteristics, and as a result has been difficult to classify based on morphology. Molecular phylogenetic studies have placed it near the base of Commelinaceae, but the exact placement of Palisota within the family is not clear. As the African continent has become more arid in recent geological times, the forests have receded, reducing the habitat for Palisota species and potentially impacting speciation and extinction rates within the genus. The goal of this study is to sequence the chloroplast-encoded gene rbcL in several additional species of Palisota and its relatives in order to: 1) determine the phylogenetic relationship of the genus with respect to other members of Commelinaceae; 2) evaluate phylogenentic relationships among species of Palisota; and 3) infer relative speciation/extinction rates within the genus. Additionally, we are exploring the use of other molecular regions for phylogenetic analysis with the genus

Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System

An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class particles can be changed due to creation and annihilation reactions. It is shown that the system undergoes a discontinuous phase transition in contrast to the case where the density of the second-class particles is finite and the phase transition is continuous.Comment: Revised, 8 pages, 1 EPS figure. Accepted for publication in Journal of Statistical Mechanics: theory and experimen

Simulation tools for future interferometers

For the design and commissioning of the LIGO interferometer, simulation tools have been used explicitly and implicitly. The requirement of the advanced LIGO interferometer is much more demanding than the first generation interferometer. Development of revised simulation tools for future interferometers are underway in the LIGO Laboratory. The outline of those simulation tools and applications are discussed

Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure