Thermoelectric phenomena via an interacting particle system

We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat and charge transport in different but connected metallic substances. The electrons hop between energy-cells located alongside the spatial extension of the metal wire. When changing energy level, the system exchanges energy with the environment. At equilibrium the distribution satisfies the Fermi-Dirac occupation-law. Installing different temperatures at two connections induces an electromotive force (Seebeck effect) and upon forcing an electric current, an additional heat flow is produced at the junctions (Peltier heat). We derive the linear response behavior relating the Seebeck and Peltier coefficients as an application of Onsager reciprocity. We also indicate the higher order corrections. The entropy production is characterized as the anti-symmetric part under time-reversal of the space-time Lagrangian.Comment: 19 pages, 2 figures, submitted to Journal of Physics

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

Rectification of thermal fluctuations in ideal gases

We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced in [Van den Broeck, Kawai and Meurs, \emph{Microscopic analysis of a thermal Brownian motor}, to appear in Phys. Rev. Lett.], by an expansion of the Boltzmann equation and compare with the exact numerical solution.Comment: 18 page

In Vitro Models for Glaucoma Research: Effects of Hydrostatic Pressure

PURPOSE. The response of cells (e.g., optic nerve head [ONH] cells) to mechanical stress is important in glaucoma. Studies have reported the biological effects of hydrostatic pressure on ONH cells cultured on a rigid substrate. An apparatus, designed to independently vary hydrostatic pressure and gas tension (including oxygen tension) in culture medium, was used to evaluate the effects of pressure and tension on cell migration, shape, and α-tubulin architecture in a transformed cell line (DITNC1 rat cortical astrocytes). METHODS. During the assay period, cells were exposed to one of four experimental configurations: (1) control pressure and control gas tension; (2) high-pressure (7.4 mm Hg) and reduced gas tension; (3) control pressure and reduced gas tension; and (4) high-pressure and control gas tension. RESULTS. Calculations suggested that the cells in configurations 2 and 3 were hypoxic, as confirmed by direct measurements in configuration 2. No effects of hydrostatic pressure were observed on cell migration or α-tubulin architecture. However, cells cultured under low gas tension (configurations 2 and 3) showed increased migration at 48 and 72 hours (P \u3c 0.05). CONCLUSIONS. A hydrostatic pressure of 7.4 mm Hg has no effect on DITNC1 astrocytes cultured on rigid coverslips, whereas hypoxia associated with a fluid column creating this pressure does. These results differ from those in a previous report, the results of which may be explained by altered gas tensions in the culture medium. Steps are recommended for control of secondary effects when testing the effect of pressure on cultured cells

Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is via random matrix theory (RMT). Our objective is to firmly relate this theory to a microscopic model. We correct and extend previous work (arXiv:0912.1574) on the same topic. In particular, we obtain through a physically motivated scaling limit an ensemble of random matrices that is close to, but not identical to the standard transfer matrix ensembles (sometimes called TOE, TUE), corresponding to the Dyson symmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance is the same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1 class, we find a deviation from TOE. It remains to be seen whether or not this deviation vanishes in a thick-wire limit, which is the experimentally relevant regime. For the ideal ensembles, we also prove Ohm's law for all symmetry classes, making mathematically precise a moment expansion by Mello and Stone. This proof bypasses the explicit but intricate solution methods that underlie most previous results.Comment: Corrects and extends arXiv:0912.157

A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.Comment: v2 (55 pages): many improvements on the presentation, v3: correction of a few typos, to appear In Probability Theory and Related Field

Single-crossover dynamics: finite versus infinite populations

Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the {\em expected} type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.Comment: 21 pages, 4 figure

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field

The time to extinction for an SIS-household-epidemic model

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission

Toward a first-principles integrated simulation of tokamak edge plasmas

Performance of the ITER is anticipated to be highly sensitive to the edge plasma condition. The edge pedestal in ITER needs to be predicted from an integrated simulation of the necessary first-principles, multi-scale physics codes. The mission of the SciDAC Fusion Simulation Project (FSP) Prototype Center for Plasma Edge Simulation (CPES) is to deliver such a code integration framework by (1) building new kinetic codes XGC0 and XGC1, which can simulate the edge pedestal buildup; (2) using and improving the existing MHD codes ELITE, M3D-OMP, M3D-MPP and NIMROD, for study of large-scale edge instabilities called Edge Localized Modes (ELMs); and (3) integrating the codes into a framework using cutting-edge computer science technology. Collaborative effort among physics, computer science, and applied mathematics within CPES has created the first working version of the End-to-end Framework for Fusion Integrated Simulation (EFFIS), which can be used to study the pedestal-ELM cycles