The Steady State Distribution of the Master Equation

The steady states of the master equation are investigated. We give two expressions for the steady state distribution of the master equation a la the Zubarev-McLennan steady state distribution, i.e., the exact expression and an expression near equilibrium. The latter expression obtained is consistent with recent attempt of constructing steady state theormodynamics.Comment: 6 pages, No figures. A mistake was correcte

SEQUAL 2.1 User’s Manual

SEQUAL is a device simulation program which performs a quantum mechanical analysis of electron transport. The user need not be an expert in quantum mechanics to obtain useful results from this program, although an understanding of the subject is an invaluable aid in the interpretation of output. For this reason,, the theoretical formulation of the analysis is presented in some detail, following a brief introduction. The knowledgeable (or anxious) user may turn directly to the discussions of input and output in Chapters 3 and 4. The reader is cautioned, however, not to skip Chaper 2 entirely. At the heart of many a program error\u27 lies a misinterpretation of output

Physicochemical properties of concentrated Martian surface waters

Understanding the processes controlling chemical sedimentation is an important step in deciphering paleoclimatic conditions from the rock records preserved on both Earth and Mars. Clear evidence for subaqueous sedimentation at Meridiani Planum, widespread saline mineral deposits in the Valles Marineris region, and the possible role of saline waters in forming recent geomorphologic features all underscore the need to understand the physical properties of highly concentrated solutions on Mars in addition to, and as a function of, their distinct chemistry. Using thermodynamic models predicting saline mineral solubility, we generate likely brine compositions ranging from bicarbonate-dominated to sulfate-dominated and predict their saline mineralogy. For each brine composition, we then estimate a number of thermal, transport, and colligative properties using established models that have been developed for highly concentrated multicomponent electrolyte solutions. The available experimental data and theoretical models that allow estimation of these physicochemical properties encompass, for the most part, much of the anticipated variation in chemistry for likely Martian brines. These estimates allow significant progress in building a detailed analysis of physical sedimentation at the ancient Martian surface and allow more accurate predictions of thermal behavior and the diffusive transport of matter through chemically distinct solutions under comparatively nonstandard conditions

Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases

Both the right and left eigenfunctions and eigenvalues of the linearized homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are identified. It is shown that below a critical value of the parameter characterizing the inelasticity, one of the kinetic modes decays slower than one of the hydrodynamic ones. As a consequence, a closed hydrodynamic description does not exist in that regime. Some implications of this behavior on the formally computed Navier-Stokes transport coefficients are discussed.Comment: Submitted to PRL (13/04/10

Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about \emph{arbitrary}, far-from equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more consistant, extend discussio

Linear Response for Confined Particles

The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small perturbations of this nonuniform state is calculated from a linear Markov kinetic theory whose generator for the dynamics is exact in the short time limit. The kinetic equation is solved in terms of an effective mean field single particle dynamics determined by the local density and dynamical screening by a dielectric function for the non-uniform system. The autocorrelation function for the total force on the charges is discussed.Comment: 4 pages, 1 figure. Results presented at the "International Conference on Strongly Coupled Coulomb Systems", Camerino, Italy, July 2008. Submitted for publication in the conference proceedings (special issue of Journal of Physics A

Multispectral fingerprinting for improved in vivo cell dynamics analysis

Background: Tracing cell dynamics in the embryo becomes tremendously difficult when cell trajectories cross in space and time and tissue density obscure individual cell borders. Here, we used the chick neural crest (NC) as a model to test multicolor cell labeling and multispectral confocal imaging strategies to overcome these roadblocks. Results: We found that multicolor nuclear cell labeling and multispectral imaging led to improved resolution of in vivo NC cell identification by providing a unique spectral identity for each cell. NC cell spectral identity allowed for more accurate cell tracking and was consistent during short term time-lapse imaging sessions. Computer model simulations predicted significantly better object counting for increasing cell densities in 3-color compared to 1-color nuclear cell labeling. To better resolve cell contacts, we show that a combination of 2-color membrane and 1-color nuclear cell labeling dramatically improved the semi-automated analysis of NC cell interactions, yet preserved the ability to track cell movements. We also found channel versus lambda scanning of multicolor labeled embryos significantly reduced the time and effort of image acquisition and analysis of large 3D volume data sets. Conclusions: Our results reveal that multicolor cell labeling and multispectral imaging provide a cellular fingerprint that may uniquely determine a cell's position within the embryo. Together, these methods offer a spectral toolbox to resolve in vivo cell dynamics in unprecedented detail

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.Comment: 10 pages, 5 figure

Humidity-induced phase transitions of ferric sulfate minerals studied by in situ and ex situ X-ray diffraction

Phases encountered in the hydration of monoclinic and trigonal anhydrous Fe2(SO4)3 and evaporation of Fe2(SO4)3 solutions at room temperature were determined using in situ and ex situ X-ray diffraction (XRD) under dynamic relative humidity (RH) control at room temperature (22–25 °C). Both monoclinic and trigonal forms of Fe2(SO4)3 remain anhydrous at 11% RH or below, and undergo the following phase evolution sequence: anhydrous Fe2(SO4)3 → (ferricopiapite, rhomboclase) → kornelite → paracoquimbite at RH between 33 and 53% as a function of time. Evaporation of aqueous Fe2(SO4)3 solutions at 40% < RH < 60% results in precipitation of ferricopiapite and rhomboclase during evaporation, followed by a transition to kornelite and then paracoquimbite. Evaporation at RH < 33% produced an amorphous ferric-sulfate phase. The presence of some iron sulfate hydrates and their stability under varying RH are not only determined by the final humidity level, but also the intermediate stages and hydration history (i.e., either ferricopiapite or paracoquimbite can be a stable phase at 62% RH depending on the hydration history). The sensitivity to humidity change and path-dependent transitions of ferric sulfates make them potentially valuable indicators of paleo-environmental conditions and past water activity on Mars. The phase relationships reported herein can help in understanding the diagenesis of ferric sulfate minerals, and are applicable to geochemical modeling of mineral solubility in multi-component systems, an endeavor hindered by the need for fundamental laboratory studies of iron sulfate hydrates

Mass transport of an impurity in a strongly sheared granular gas

Transport coefficients associated with the mass flux of an impurity immersed in a granular gas under simple shear flow are determined from the inelastic Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution that retains all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the diffusion process instead of the conventional scalar coefficients. The mass flux is determined to first order in the deviations of the hydrodynamic fields from their values in the reference state. The corresponding transport coefficients are given in terms of the solutions of a set of coupled linear integral equations, which are approximately solved by considering the leading terms in a Sonine polynomial expansion. The results show that the deviation of these generalized coefficients from their elastic forms is in general quite important, even for moderate dissipation.Comment: 6 figure