Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning–Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

A continuum model of gas flows with localized density variations

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Macroscopic properties of fractured porous media

The macroscopic properties of fractured porous media locally governed by a Laplace equation are determined by several methods. The first one consists in discretizing the porous medium and the fractures and in solving the Laplace equation in the discretized structure. The other methods consist in successive upscalings. The first upscaling replaces the porous medium by a continuum with a given transport property. The second upscaling replaces the fractures by surfaces with equivalent properties. The results of the various methods give very close results. They suggest a simple approximation which is successful when the properties of the fluid and of the continuous porous medium are not too different.     

Nonlinear transport in the Boltzmann limit

Formal expressions for the irreversible fluxes of a simple fluid are obtained as functionals of the thermodynamic forces and local equilibrium time correlation functions. The Boltzmann limit of the correlation functions is shown to yield expressions for the irreversible fluxes equivalent to those obtained from the nonlinear Boltzmann kinetic equation. Specifically, for states near equilibrium, the fluxes may be formally expanded in powers of the thermodynamic gradients and the associated transport coefficients identified as integrals of time correlation functions. It is proved explicitly through nonlinear Burnett order that the time correlation function expressions for these transport coefficients agree with those of the Chapman-Enskog expansion of the nonlinear Boltzmann equation. For states far from equilibrium the local equilibrium time correlation functions are determined in the Boltzmann limit and a similar equivalence to the Boltzmann equation solution is established. Other formal representations of the fluxes are indicated; in particular, a projection operator form and its Boltzmann limit are discussed. As an example, the nonequilibrium correlation functions for steady shear flow are calculated exactly in the Boltzmann limit for Maxwell molecules.Research supported in part by NSF grant PHY 76-21453.     

Nonextensive nuclear liquid–gas phase transition

We study an effective relativistic mean-field model of nuclear matter with arbitrary proton fraction at finite temperature in the framework of nonextensive statistical mechanics, characterized by power-law quantum distributions. We investigate the presence of thermodynamic instability in a warm and asymmetric nuclear medium and study the consequent nuclear liquid–gas phase transition by requiring the Gibbs conditions on the global conservation of baryon number and electric charge fraction. We show that nonextensive statistical effects play a crucial role in the equation of state and in the formation of mixed phase also for small deviations from the standard Boltzmann–Gibbs statistics.     

Geometrical formulation of equilibrium phenomenological thermodynamics

An abstract geometric formulation of equilibrium phenomenological thermodynamics which generalizes and unifies that of Gibbs, Carathéodory, and others is given. As done by Hermann, one adapts here a contact manifold as the basic mathematical structure. Such a manifold for a thermodynamic system is constructed. The empirical laws of thermodynamics have been reformulated in terms of this manifold and by means of exterior differential forms. Such concepts as Gibbs phase rule, Gibbs-Duhem equation and thermodynamic potentials have been reexamined within such a general scheme.     

Derivation of the nonlinear hydrodynamic equations using multi-mode techniques

A general mode-mode coupling theory is developed for the microscopic mass, energy and momentum densities of a simple classical fluid. A projection operator method is employed to derive a generalized Langevin equation that contains nonlinearities of all orders with both convective and dissipative terms. A general nonequilibrium ensemble average, which contains local equilibrium as a special case, is employed to derive nonlinear transport equations that are nonlocal in both space and time.The nonlinear Euler and Navier-Stokes equations are recovered using a factorization procedure based on an inverse system size approximation. We show that in the context of mode-mode coupling theory, nonlinearities of all orders must be retained to derive the full nonlinear transport equations. We also slow that the space and time dependent nonequilibrium pressure and transport coefficients are functions of the nonequilibrium mass and internal energy densities. The thermodynamic closure relationships follow as a natural consequence of mode-mode coupling theory. For a system linearly displaced from equilibrium we demonstrate the role of the corrections to our factorization approximation in renormalizing the transport coefficients.     

Carrier dynamics around nano-scale Schottky contacts: a femtosecond near-field study

We report spatially and time-resolved measurements of ultrafast carrier dynamics around buried nano-scale Schottky contacts, performed with a novel femtosecond near-field scanning optical microscope. The experimental results are modeled by a self-consistent treatment of the drift–diffusion equation for the carriers and Poisson’s equation for the built-in electric field. We show that the built-in field suppresses electron transport towards and trapping into the metal particles at lower optically excited carrier densities. In contrast, efficient electron trapping into the metal occurs at higher electron densities, which screen the built-in field, allowing for efficient transport of electrons towards the Schottky contact.     

On the Onsager Variation Principle and its Generalization for Nonlinear Irreversible Thermodynamics

The Onsager variation principle is examined from the viewpoint of the thermodynamic analogue of the D'Alembert principle in mechanics when the irreversible processes are linear and thus the system is near equilibrium. The thermodynamic D'Alembert principle is shown to be a precursor to the Onsager variation principle. The thermodynamic D'Alembert principle is then generalised to the cases of nonlinear irreversible processes occurring removed from equilibrium and a generalised form of the Onsager variation principle is obtained under some restricting conditions. The restricted variation principle so deduced has an accompanying exact differential form generalising the Clausius entropy differential (equilibrium Gibbs relations) and contains in it the essence of the thermodynamics of irreversible processes in systems where non-linear transport processes occur. An example is given for the nonlinear dissipation function in the variation functional. The evolution equations for fluxes are shown to yield those known in the literature.     

Green–Kubo Expressions for a Granular Gas

The transport coefficients for a gas of smooth, inelastic hard spheres are obtained from the Boltzmann equation in the form of Green–Kubo relations. The associated time correlation functions are not simply those constructed from the fluxes of conserved densities. Instead, fluxes constructed from the reference local homogeneous distribution occur as well. The analysis exposes some complexities to be expected in the application of linear response methods to granular systems.     

浸没在多孔介质中的竖直管沸腾换热实验研究

本文对竖直管外填充固体颗粒情况下，蒸馏水和无水乙醇两种工质的池沸腾换热现象进行了实验研究，分析了颗粒直径以及工质热物性对竖直管液池沸腾换热特性，包括沸腾滞后的影响规律，证明了在填充固体颗粒条件下，竖直管的池沸腾换热可以得到一定程度的强化，在低热负荷区，强化效果尤为明显。大颗粒对沸腾滞后现象有较好的缓解作用。在高热负荷区，由于气膜的出现，沸腾机理将有所改变。     

On Thermodynamic Limits of Entropy Densities

We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.     

基于格子Boltzmann大密度比模型的多孔介质内气泡动力学行为数值模拟

基于格子Boltzmann两相流大密度模型,研究气泡穿过多孔介质的动力学行为.研究发现:当孔隙率较大时,气泡只变形不破裂,能完整地通过多孔介质;而孔隙率较小时,气泡变形更加剧烈且发生破裂,穿过多孔介质所需的时间更长.另外,当障碍物表面接触角(θ)较小时,气泡均能完整地通过多孔介质,随着接触角的增大,气泡开始发生破裂,且...     

Stochastic langevin model for flow and transport in porous media

We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies.     

Nonlinear Diffusion and Transient Osmosis

We investigate both analytically and numericallythe concentration dynamics of a solution in two containers connected bya narrow and short channel, in which diffusion obeys a porous medium equation.We also consider the variation of the pressure in the containers due tothe flow of matter in the channel.
In particular, we identify a phenomenon, which depends on the transport of matteracross nano-porous membranes, which we call ``transient osmosis'.
We find that nonlinear diffusion of the porous medium equation type allows numerous differentosmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion.Experimental results suggest one possible candidate for transiently osmotic processes.     

Alternative ensemble averages in molecular dynamics simulation of hard spheres

ABSTRACT

We consider application to the hard sphere (HS) model of the mapped-averaging framework for generating alternative ensemble averages for thermodynamic properties. Specifically, we develop and examine new formulas for the pressure, the singlet and pair densities, and the cavity-correlation function inside the HS core; the pressure formula in particular is constructed such that it gives an ensemble average that exactly corrects the second-order virial equation of state. The force plays a central role in mapped-averaging expressions, and we write them in a way that accounts for the impulsive, event-driven nature of the HS dynamics. Comparison between results obtained conventionally versus mapped averaging finds that the latter has some advantage at low density, while both perform equally well (in terms of uncertainties for a given amount of sampling) at higher densities.     

Application of nmr spectroscopy to determine the thermodynamic characteristics of water bound to OX-50 nanosilica

We have used low-temperature 1H NMR spectroscopy to determine the thermodynamic characteristics of water bound to OX-50 nanosilica (SBET ≈ 50 m2/g) in different media: aqueous, air, chloroform medium, and gaseous methane. We demonstrate the difference between the hydration parameters of silica OX-50 on going from an aqueous suspension to a hydrated powder. We present the water cluster size distributions in the studied systems, calculated from the Gibbs–Thomson equation. We found that the average water cluster size in suspension is considerably larger than the cluster sizes in hydrated powders.     

Effective medium method of slightly compressible elastic media permeated with air-filled bubbles

An effective medium method is developed for the slightly compressible elastic media permeated with air-filled bubbles, according to the nonlinear oscillation of the bubble, which happens when compressional wave travels through the porous media. The effective Lame coefficients of the porous medium and the nonlinear elastic wave equation are deduced, based on the fact that the micro-unit of the effective medium should have the same stress and strain as the micro-unit of the porous media. The linearized properties obtained by this method are in good agreement with the results of Gaunaurd’s classic theory [Gaunaurd G.C. and überall H., J. Acoust. Soc. Am., 1978, 63: 1699–1711]. Furthermore, the nonlinear coefficient, which is an important property of the porous media, can also be acquired by this method. __________ Translated from Acta Acustica, 2006 (in Chinese) (in press)