Droplet collision simulation by multi-speed lattice Boltzmann method

Realization of the Shan-Chen multiphase flow lattice Boltzmann model is considered in the framework of the higher-order Galilean invariant lattices. The present multiphase lattice Boltzmann model is used in two dimensional simulation of droplet collisions at high Weber numbers. Results are found to be in a good agreement with experimental findings

A note on the invariant distribution of a quasi-birth-and-death process

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution

Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [ P. Asinari and I. V. Karlin Phys. Rev. E 79 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed

Separable and Low-Rank Continuous Games

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in separable games. We show that these games admit finitely supported Nash equilibria. Motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. We present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. Using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game

Exit times in non-Markovian drifting continuous-time random walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.Comment: 9 pages, 3 color plots, two-column revtex 4; new Appendix and references adde

A Portrait of Five Undergraduate Students Who Serve as Caregivers While Taking University Courses

The purpose of this study was to identify characteristics specific to adults who are caregivers while taking classes from an institution of higher education. We recruited 5 university attending adults through a subject pool and through announcements in various classes through the university setting. Measures on depression, burden, daily activities, and general background were used to assess the experiences of the participants. Self-reports indicated high levels of selfefficacy with regard to the care process, minimal depression, low to moderate levels of burden, and high resiliency among those surveyed. These results indicate while registered as a full time student (12 credits or more) daily activities remain high, while overall levels for depression and reported burden remain relatively low. This group of providers suggests a desire to continue with current responsibilities of providing care to the family member. More intensive analysis is needed to explain the resilient nature of this group. Degree seeking may provide a buffer from the traditional burden and depression often experienced by other caregivers who are not attending college

Stochastic Chemical Reactions in Micro-domains

Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a master-diffusion equation for the joint probability density of a mobile reactant and the number of bound substrate in a confined domain. We use the equation to calculate the fluctuations in the number of bound substrate molecules as a function of initial reactant distribution. A second model is presented based on a Markov description of the binding and unbinding and on the mean first passage time of a molecule to a small portion of the boundary. These models can be used for the description of noise due to gating of ionic channels by random binding and unbinding of ligands in biological sensor cells, such as olfactory cilia, photo-receptors, hair cells in the cochlea.Comment: 33 pages, Journal Chemical Physic

Universality of Long-Range Correlations in Expansion-Randomization Systems

We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent $\chi$ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of $\chi$, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.Comment: 23 pages, 15 figure

Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments