Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring

We study a generalized two-species model on a ring. The original model [1] describes ordinary particles hopping exclusively in one direction in the presence of an impurity. The impurity hops with a rate different from that of ordinary particles and can be overtaken by them. Here we let the ordinary particles hop also backward with the rate q. Using Matrix Product Ansatz (MPA), we obtain the relevant quadratic algebra. A finite dimensional representation of this algebra enables us to compute the stationary bulk density of the ordinary particles, as well as the speed of impurity on a set of special surfaces of the parameter space. We will obtain the phase structure of this model in the accessible region and show how the phase structure of the original model is modified. In the infinite-volume limit this model presents a shock in one of its phases.Comment: Adding more references and doing minor corrections, 16 pages and 3 Eps figure

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Thermal performance of two heat exchangers for thermoelectric generators

Thermal performance of heat exchanger is important for potential application in integrated solar cell/module and thermoelectric generator (TEG) system. Usually, thermal performance of a heat exchanger for TEGs is analysed by using a 1D heat conduction theory which ignores the detailed phenomena associated with thermo-hydraulics. In this paper, thermal and mass transports in two different exchangers are simulated by means of a steady-state, 3D turbulent flow k -e model with a heat conduction module under various flow rates. In order to simulate an actual working situation of the heat exchangers, hot block with an electric heater is included in the model. TEG model is simplified by using a 1D heat conduction theory, so its thermal performance is equivalent to a real TEG. Natural convection effect on the outside surfaces of the computational model is considered. Computational models and methods used are validated under transient thermal and electrical experimental conditions of a TEG. It is turned out that the two heat exchangers designed have a better thermal performance compared with an existing heat exchanger for TEGs, and more importantly, the fin heat exchanger is more compact and has nearly half temperature rise compared with the tube heat exchanger

Absence of phase coexistence in disordered exclusion processes with bypassing

Adding quenched disorder to the one-dimensional asymmetric exclusion process is known to always induce phase separation. To test the robustness of this result, we introduce two modifications of the process that allow particles to bypass defect sites. In the first case, particles are allowed to jump l sites ahead with the probability p_l ~ l^-(1+sigma), where sigma>1. By using Monte Carlo simulations and the mean-field approach, we show that phase coexistence may be absent up to enormously large system sizes, e.g. lnL~50, but is present in the thermodynamic limit, as in the short-range case. In the second case, we consider the exclusion process on a quadratic lattice with symmetric and totally asymmetric hopping perpendicular to and along the direction of driving, respectively. We show that in an anisotropic limit of this model a regime may be found where phase coexistence is absent.Comment: 18 pages, 10 figures, to appear in JSTA

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Air Pollution Exposure Assessment for Epidemiologic Studies of Pregnant Women and Children: Lessons Learned from the Centers for Children’s Environmental Health and Disease Prevention Research

The National Children’s Study is considering a wide spectrum of airborne pollutants that are hypothesized to potentially influence pregnancy outcomes, neurodevelopment, asthma, atopy, immune development, obesity, and pubertal development. In this article we summarize six applicable exposure assessment lessons learned from the Centers for Children’s Environmental Health and Disease Prevention Research that may enhance the National Children’s Study: a) Selecting individual study subjects with a wide range of pollution exposure profiles maximizes spatial-scale exposure contrasts for key pollutants of study interest. b) In studies with large sample sizes, long duration, and diverse outcomes and exposures, exposure assessment efforts should rely on modeling to provide estimates for the entire cohort, supported by subject-derived questionnaire data. c) Assessment of some exposures of interest requires individual measurements of exposures using snapshots of personal and microenvironmental exposures over short periods and/or in selected microenvironments. d) Understanding issues of spatial–temporal correlations of air pollutants, the surrogacy of specific pollutants for components of the complex mixture, and the exposure misclassification inherent in exposure estimates is critical in analysis and interpretation. e) “Usual” temporal, spatial, and physical patterns of activity can be used as modifiers of the exposure/outcome relationships. f) Biomarkers of exposure are useful for evaluation of specific exposures that have multiple routes of exposure. If these lessons are applied, the National Children’s Study offers a unique opportunity to assess the adverse effects of air pollution on interrelated health outcomes during the critical early life period

Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics

We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.Comment: 11 pages, 3 figure

One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle

The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle and the density profile of the ordinary particles are calculated exactly. The phase diagram for the correlation length is identified. As a byproduct, the average and the variance of the particle density of the one-dimensional partially asymmetric simple exclusion process with open boundaries are also computed.Comment: 23 pages, 1 figur

Bethe Ansatz Solution for a Defect Particle in the Asymmetric Exclusion Process

The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time limit behaviour of the generating function of the distance travelled by the defect particle. This allows us to recover steady state properties known from the matrix approach such as the velocity, and obtain new results such as the diffusion constant of the defect particle. In the case where the defect particle is a second class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is Gaussian. Moreover the variance (diffusion constant) grows as L to the power 1/2 where is the system size. This behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system. In the case where the defect particle produces a shock, our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by Ferrari and Fontes.Comment: Latex, 23 page

Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries

The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, that is still integrable: the spectrum of this new matrix can be also described in terms of Bethe roots for special values of the parameters. However, due to the algebraic framework used to write the Bethe equations in the previous works, the nature of the excitations and the full structure of the eigenvectors were still unknown. This paper explains why the eigenvectors of the modified transition matrix are physically relevant, gives an explicit expression for the eigenvectors and applies it to the study of atypical currents. It also shows how the coordinate Bethe Ansatz developped for the excitations leads to a simple derivation of the Bethe equations and of the validity conditions of this Ansatz. All the results obtained by de Gier and Essler are recovered and the approach gives a physical interpretation of the exceptional points The overlap of this approach with other tools such as the matrix Ansatz is also discussed. The method that is presented here may be not specific to the asymmetric exclusion process and may be applied to other models with open boundaries to find similar exceptional points.Comment: references added, one new subsection and corrected typo