Nonextensive diffusion as nonlinear response

The porous media equation has been proposed as a phenomenological ``non-extensive'' generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous media equation in that it describes \emph{% generalized classical} diffusion, i.e. with $r/\sqrt Dt$ scaling, but with a generalized Einstein relation, and with power-law probability distributions typical of nonextensive statistical mechanics

Розвиток машинобудування в Україні в контексті забезпечення розширеного відтворення економіки

У статті досліджено сучасне становище сегменту машинобудування України з наголосом на забезпечення відтворювальних процесів усередині галузі.В статье исследовано современное положение сегмента машиностроения Украины с акцентом на обеспечение воспроизводственных процессов внутри отрасли.This article explores contemporary situation of Ukrainian machine building segment with an emphasis on providing reproductive processes within the industry

Lattice gas with ``interaction potential''

We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal gas behavior. {}From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numerical simulations to establish the validity of the model at macroscopic scale.Comment: 12 pages LaTeX, figures available on demand ([email protected]

Screening of heterogeneous surfaces: charge renormalization of Janus particles

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode-decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadropolar, etc., including mode-couplings. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.Comment: 2 figure

Is the Tsallis entropy stable?

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.Comment: 6 page

Chesapeake Bay Land Subsidence and Sea Level Change : an evaluation of past and present trends and future outlook

Ten Chesapeake Bay water level stations presently have a combined total of 647 years of water level measurements with record lengths varying between 35 years (1975-2009) at the Chesapeake Bay Bridge Tunnel, VA, and 107 years (1903-2009) at Baltimore, MD. All ten stations, with the exception of Gloucester Point, VA, are active stations in the National Water Level Observation Network of water level stations maintained by the U.S. National Oceanic and Atmospheric Administration, Center for Operational Oceanographic Products and Services. New technologies such as sea surface range measurements from earth-orbiting satellites now provide a global assessment of absolute sea level (ASL) trends relative to the center of a reference ellipsoid rather than fixed points on the earth’s surface to which relative sea level (RSL) measurements refer. New methodologies have also been applied to derive spatial averages of ASL trends over large regions with greater accuracy. Notwithstanding these advances, there is still no substitute for an accurate time series of water level measurements obtained locally, preferably one spanning several decades, when assessing RSL trends that will affect a specific community or township in the coming decades. RSL trends will determine local inundation risk whether due to vertical land movement (emergence or subsidence) or the ASL trend found as the sum of RSL trend and land movement when both are measured positive upward. In Chesapeake Bay, RSL trends are consistently positive (rising) while land movement is negative (subsiding). By choosing a common time span for the ten bay stations evaluated in this report, we are able to compare differences in RSL rise rates with approximately the same degree of confidence at each station. Uncertainty has been reduced by extracting the decadal signal present at all ten stations before using linear regression to obtain new RSL rise rates with smaller than usual confidence intervals, permitting both temporal and spatial comparisons to be made

Thermodiffusion in model nanofluids by molecular dynamics simulations

In this work, a new algorithm is proposed to compute single particle (infinite dilution) thermodiffusion using Non-Equilibrium Molecular Dynamics simulations through the estimation of the thermophoretic force that applies on a solute particle. This scheme is shown to provide consistent results for simple Lennard-Jones fluids and for model nanofluids (spherical non-metallic nanoparticles + Lennard-Jones fluid) where it appears that thermodiffusion amplitude, as well as thermal conductivity, decrease with nanoparticles concentration. Then, in nanofluids in the liquid state, by changing the nature of the nanoparticle (size, mass and internal stiffness) and of the solvent (quality and viscosity) various trends are exhibited. In all cases the single particle thermodiffusion is positive, i.e. the nanoparticle tends to migrate toward the cold area. The single particle thermal diffusion 2 coefficient is shown to be independent of the size of the nanoparticle (diameter of 0.8 to 4 nm), whereas it increases with the quality of the solvent and is inversely proportional to the viscosity of the fluid. In addition, this coefficient is shown to be independent of the mass of the nanoparticle and to increase with the stiffness of the nanoparticle internal bonds. Besides, for these configurations, the mass diffusion coefficient behavior appears to be consistent with a Stokes-Einstein like law

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass-asymmetry

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio $\mu$, including the limiting case $\mu=\infty$, for different mole fractions $x$. Within a large range of $x$ and $\mu$ the product of the diffusion coefficient of the heavy species $D_{2}$ and the total shear viscosity of the mixture $\eta_{m}$ is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function

Dynamic correlations in stochastic rotation dynamics

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for Stochastic Rotation Dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.Comment: 33 pages including 16 figure

Effect of cattle urine addition on the surface emissions and subsurface concentrations of greenhouse gases in a UK peat grassland

Grazing systems represent a substantial percentage of the global anthropogenic flux of nitrous oxide (N2O) as a result of nitrogen addition to the soil. The pool of available carbon that is added to the soil from livestock excreta also provides substrate for the production of carbon dioxide (CO2) and methane (CH4) by soil microorganisms. A study into the production and emission of CO2, CH4 and N2O from cattle urine amended pasture was carried out on the Somerset Levels and Moors, UK over a three-month period. Urine-amended plots (50 g N m−2) were compared to control plots to which only water (12 mg N m−2) was applied. CO2 emission peaked at 5200 mg CO2 m−2 d−1 directly after application. CH4 flux decreased to −2000 μg CH4 m−2 d−1 two days after application; however, net CH4 flux was positive from urine treated plots and negative from control plots. N2O emission peaked at 88 mg N2O m−2 d−1 12 days after application. Subsurface CH4 and N2O concentrations were higher in the urine treated plots than the controls. There was no effect of treatment on subsurface CO2 concentrations. Subsurface N2O peaked at 500 ppm 12 days after and 1200 ppm 56 days after application. Subsurface NO3− concentration peaked at approximately 300 mg N kg dry soil−1 12 days after application. Results indicate that denitrification is the key driver for N2O release in peatlands and that this production is strongly related to rainfall events and water-table movement. N2O production at depth continued long after emissions were detected at the surface. Further understanding of the interaction between subsurface gas concentrations, surface emissions and soil hydrological conditions is required to successfully predict greenhouse gas production and emission