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

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

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

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

Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.Comment: typos correcte

On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other

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

An Integrated Model of the Cardiovascular and Central Nervous Systems for Analysis of Microgravity Induced Fluid Redistribution

A recognized side effect of prolonged microgravity exposure is visual impairment and intracranial pressure (VIIP) syndrome. The medical understanding of this phenomenon is at present preliminary, although it is hypothesized that the headward shift of bodily fluids in microgravity may be a contributor. Computational models can be used to provide insight into the origins of VIIP. In order to further investigate this phenomenon, NASAs Digital Astronaut Project (DAP) is developing an integrated computational model of the human body which is divided into the eye, the cerebrovascular system, and the cardiovascular system. This presentation will focus on the development and testing of the computational model of an integrated model of the cardiovascular system (CVS) and central nervous system (CNS) that simulates the behavior of pressures, volumes, and flows within these two physiological systems

Numerical Modeling of Ophthalmic Response to Space

To investigate ophthalmic changes in spaceflight, we would like to predict the impact of blood dysregulation and elevated intracranial pressure (ICP) on Intraocular Pressure (IOP). Unlike other physiological systems, there are very few lumped parameter models of the eye. The eye model described here is novel in its inclusion of the human choroid and retrobulbar subarachnoid space (rSAS), which are key elements in investigating the impact of increased ICP and ocular blood volume. Some ingenuity was required in modeling the blood and rSAS compartments due to the lack of quantitative data on essential hydrodynamic quantities, such as net choroidal volume and blood flowrate, inlet and exit pressures, and material properties, such as compliances between compartments