Incorporation of Effects of Diffusion into Advection-Mediated Dispersion in Porous Media

The distribution of solute arrival times, W(t;x), at position x in disordered porous media does not generally follow Gaussian statistics. A previous publication determined W(t;x) in the absence of diffusion from a synthesis of critical path, percolation scaling, and cluster statistics of percolation. In that publication, W(t;x) as obtained from theory, was compared with simulations in the particular case of advective solute transport through a two-dimensional model porous medium at the percolation threshold for various lengths x. The simulations also did not include the effects of diffusion. Our prediction was apparently verified. In the current work we present numerical results related to moments of W(x;t), the spatial solute distribution at arbitrary time, and extend the theory to consider effects of molecular diffusion in an asymptotic sense for large Peclet numbers, P_e. However, results for the scaling of the dispersion coefficient in the range 1<P_e<100 agree with those of other authors, while results for the dispersivity as a function of spatial scale also appear to explain experiment.     

A Geometry Model for Tortuosity of Flow Path in Porous Media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.     

A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media

A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.     

A New Method for the Analysis of Relative Permeability in Porous Media

By combining three-dimensional digital microtomography techniques with the lattice Boltzmann method,a new methodology is used to analyse the relative permeability of multiphase flow in porous media.The results indicate that the two coupling coefficients K12 and K21 have the same magnitude,therefore the Onsager reciprocity still holds,the results also agree well with the results of pipe flow numerical experiments.     

Fractal Character for Tortuous Streamtubes in Porous Media

An analytical model for fractal dimension of tortuous streamtubes in porous media is derived. The proposed fractal dimension for tortuous streamtubes in porous media is expressed as a function of porosity and scale, and there is no empirical constant in the proposed expression. The model predictions for the fractal dimension of tortuous streamtubes in porous media are in good agreement with those by the box-counting method and with the observations of other researchers.     

Biot／Squirt Model in Viscoelastic Porous Media

Viscoelastic wave equations are derived for both the Biot flow and squirt-flow involved.The relationship between phase velocity or attenuation of viscoelastic wave and macro parameters of the reservoir is clarified in a porous extensive dilatancy anisotropy medium.Numerical models clearly demonstrate that the viscoelastic property of rocks,not the squirt-flow,causes the dispersion and attenuation in the low-frequency range.The attenuation of the quasi SV-wave,SH-wave and the quasi P-wave depend strongly on the directions of permeabilities.Furthermore,the trends of attenuation of the quasi P-wave fast and the quasi SV-wave are inversed in both the high-frequency and low-frequency ranges.Our numerical result is in agreement with the experimental result that was carried out for the Biot/Squirt model by Jorge [Geophys.65(2000)202].     

Solitons in Plasmas: A Lie Symmetry Approach

This paper talks about the stationary solitons for Langmuir waves in plasmas that are described by the Nonlinear Schrödinger’s equation with power law nonlinearity. The integration is carried out by the usage of Lie symmetry in presence of perturbation terms.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation II

This paper is a continuation of the previous study (Šamaj in J. Stat. Phys. 137:1–17, 2009), where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov’s fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).     

A Geometry Model for Tortuosity of Streamtubes in Porous Media with Spherical Particles

A geometry model for tortuosity of tortuous streamtubes in porous media with spherical particles is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and hence of different configurations. The proposed model is a function of porosity with no empirical constant imposed on it.The model predictions are found to be in good agreement with the available experimental data.     

Experimental Determination of Transmittance of Porous Cerium Dioxide Media in the Spectral Range of 300–1,100 nm

Abstract

A spectroscopy system is developed to measure radiative characteristics of participating media in the spectral range of 300–1,100 nm. The system incorporates a short-arc radiation source, double monochromator, optical chopper synchronized with a lock-in amplifier, and a silicon detector. Measurements of overall spectral transmittance are performed with two types of cerium dioxide samples with average porosities of 0.08 and 0.72, respectively. For both sample types, the spectral variation of the transmittance indicates mixed contribution by absorption and scattering to the observed attenuation in the considered spectral range. All samples are characterized by high opacity to radiation up to approximately 400 nm.     

Zero-Point Vacancy Concentration in a Model Quantum Solid: A Reversible-Work Approach

We investigate the influence of anharmonic effects on the zero-point vacancy concentration in a boson system model in the solid phase at T=0 K. We apply the reversible-work method to compute the vacancy formation free energy and the vacancy concentration in the system. A comparison of our results with those obtained using the harmonic approximation show that anharmonic effects reduce the formation free energy by ∼25%, leading to an increase of the zero-point vacancy concentration by more than an order of magnitude.     

Localization in One Dimensional Random Media:¶A Scattering Theoretic Approach

We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization. Received: 23 September 1999 / Accepted: 13 March 2000     

Pattern Structure and Properties of Invasion Percolation in Porous Media

The percolation clusters with varying occupy probability are constructed.Invasion percolation(IP)in percolation cluster is investigated by means of IP alporithm without trapping.The pattern constructions of IP in percolation clusters are obviously different from that of visocous fingering(VF) in percolation clusters.The fractal dimension Df of IP increases with increasing the percolation probability P.The geometry and the topology of the porous media have strong effects on the pattern structure of IP.For large M(the node numbers occupied by the injected fluid),the rescaled value is Rg/M^1/Df,which asymptotically approaches a constant value,and Rg is the gyration radius of IP cluster,Moreover,the chemical dimension Dl and the shortest path exponent dmin are obtained.     

\mathcal{A} -invariance: An Axiomatic Approach to Quantum Relativity

The sort of approach claimed by the title of this article is realizable, at least, within the framework of ADG where we do not assume any “spacetime” supplying the dynamics we employ. The latter classical type of argument can naturally be included herewith along with its concomitant impediments that are emanated therefrom and are essentially “absorbed”, technically speaking, by the proposed mechanism. So our approach, being “manifoldless” (thence, no smoothness, in the standard sense) does not contain any such issue, as before, according to the very definitions, being thus “singularities”-free. As a consequence, the equations that one would be able to formulate within the present set-up will be, by the very essence of the matter, already the quantized ones. Dedicated to Professor Rafael D. Sorkin on the occasion of his 60th birthday with much friendship and recognition of his creative pursuit in theoretical physics.     

Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media

Based on the lattice Boltzmann method and general theory of fluids flowing in porous media, a numerical model is presented for the diffusion-reaction-transport (DRT) processes in porous media. As a test, we simu]ate a DRT process in a two-dimensional horizontal heterogeneous porous medium. The influence of gravitation in this case can be neglected, and the DRT process can be described by a strongly heterogeneous diagnostic test strip or a thin confined piece of soil with stochastically distributing property in horizontal directions. The results obtained for the relations between reduced fluid saturation S, concentration c1, and concentration c2 are shown by using the visualization computing technique. The computational efficiency and stability of the model are satisfactory.     

A Geometric Approach to Time Evolution Operators of Lie Quantum Systems

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrödinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.     

Determinant Representation for Some Transition Probabilities in the TASEP with Second Class Particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.     

Using Digital Imaging to Characterize Threshold Dynamic Parameters in Porous Media Based on Lattice Boltzmann Method

Digital images (DI) and lattice Boltzmann method (LBM) are used to characterize the threshold dynamic parameters of porous media. Two-dimensional representations of the porous structure are reconstructed from segmentation of digital images obtained from a series of tiny samples. The threshold pressure gradients and threshold Péclet numbers are researched on seven test samples by using LBM. Numerical results are in agreement with that obtained by integrating Darcy’s law. The results also indicate that fluids can flow through porous media only if the fluid force is large enough to overcome threshold pressure gradient in porous media. One synthetic case is used to further illustrate the applicability of the proposed technique. In addition, the dynamical rules in our model are local, therefore it can be run on parallel computers with well computational efficiency.     

A New Approach to Black hole Spin in X-Ray Binaries

A new approach of detecting the black hole spin in x-ray binaries is proposed based on the model of the coexistence of the Blandford-Znajek （BZ） and magnetic coupling （MC） processes, in which the BZ process is used to power the jet emissions from x-ray binaries, and high frequency quasi-periodic oscillations （QPOs） are explained by a rotating hotspot in the inner region of the accretion disc surrounding a fast-spinning black hole. It is shown that the black hole spins of several x-ray binaries （XTE J1550-564, GRO d1665-40 and GRS 1915＋105） can be constrained in a rather narrow range, provided that QPOs and jets coexist in these sources.     

Slicing and Dicing the Genome: A Statistical Physics Approach to Population Genetics

The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics. The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small numbers of sequences. We present a method that compares the total number of haplotypes (distinct sequences) with the model prediction. By chopping the DNA sequence into pieces we condense the immense information hidden in sequence space into a function for the number of haplotypes versus subsequence size. The details of this curve are robust to statistical fluctuations and are seen to reflect the process parameters. This procedure allows for a clear visualization of the quality of the fit and, crucially, the numerical complexity grows only linearly with the number of sequences. Our procedure is tested against both simulated data as well as empirical mtDNA data from China and provides excellent fits in both cases.