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.     

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy’s law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials.     

Impurity transport in percolation media

An equation describing the impurity transport in a percolation medium is obtained and the inferences drawn from this equation are analyzed based on the scale invariance concept. A determining part in this analysis is allowance for the sinks inherent in such media. At distances shorter than the correlation length, the particles are transferred in the regime of subdiffusion; at large distances, the concentration asymptotics exhibits a characteristic “tail” shape. In the medium occurring in the state above the percolation threshold, the impurity transport over time periods longer than the characteristic time related to the correlation length is well described by the classical equation with a renormalized diffusion coefficient. In this case, the concentration tail has a Gaussian shape at moderate distances and tends to subdiffusion asymptotics at very long distances. A relation is established between the factor determining renormalization of the diffusion coefficient and the factor determining a decrease in the number of active impurity particles at large times.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Spin accumulation and domain wall magnetoresistance in 35 nm Co wires

An enhancement of the resistance due to the presence of only one or two isolated domain walls is clearly evidenced by transport measurements in 35 nm epitaxial Co wires, 20 &mgr;m long. The deduced relative change in the resistivity is at least 1 order of magnitude larger than the one predicted from a model based on the mixing of spin channels occurring over the length scale of the domain wall width [P. M. Levy and S. Zhang, Phys. Rev. Lett. 79, 5110 (1997)]. This inconsistency can be resolved by taking the effect of spin accumulation into account, which scales in the case of Co over the much larger distance of the spin diffusion length.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Spatial Heterogeneity Length Scales in Carbonate Rocks

Spatially resolved distributions of T ₂ relaxation times in carbonate rocks are measured with slice-selective multiple spin echo magnetic resonance imaging to study the length scales of heterogeneity in these samples. Single-voxel Carr–Purcell–Meiboom–Gill decays are fit to double exponential functions, and the results of those fits are combined into a histogram. We describe a novel qualitative method of assessing the importance of different length scales of heterogeneity, involving comparing various aspects of these histograms to the full-core T ₂ distributions. Using this technique, it is found that almost all individual voxels relax not only with more than one time constant but indeed with a range of relaxation times that approximates the full breadth of relaxation times for the entire core, indicating significant subvoxel heterogeneity. In addition, different voxels are found to exhibit relaxation times that differ by orders of magnitude, indicating significant heterogeneity between the scale of a voxel (1 mm) and that of the entire core (several centimeters). These results reflect the importance of a broad range of length scales of heterogeneity in these carbonate rocks. Authors' address: Yi-Qiao Song, Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877, USA     

Giant Hall effect in nonmagnetic granular metal films.

Nearly 3 orders of magnitude enhancement in the Hall coefficient is observed in Cu(x)-(SiO(2))(1--x) granular films. This large enhancement of the Hall coefficient not only is significantly larger than the prediction of the classical percolation theory, but also occurs at a metal concentration identified to be the quantum percolation threshold. Measurements of the electron dephasing length and magnetoresistance, plus the TEM characterization of microstructures, yield a physical picture consistent with the mechanism of the local quantum interference effect.     

Connectivity and percolation in simulated grain-boundary networks

Random percolation theory is a common basis for modelling intergranular phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.     

Knudsen diffusion in silicon nanochannels

Measurements on helium and argon gas flow through an array of parallel, linear channels of 12 nm diameter and 200 microm length in a single crystalline silicon membrane reveal a Knudsen diffusion type transport from 10(2) to 10(7) in Knudsen number Kn. The classic scaling prediction for the transport diffusion coefficient on temperature and mass of diffusing species, D(He) is proportional to square root T, is confirmed over a T range from 40 K to 300 K for He and for the ratio of D(He)/D(Ar) is proportional to square root (m(Ar)/m(He)). Deviations of the channels from a cylindrical form, resolved with electron microscopy down to subnanometer scales, quantitatively account for a reduced diffusivity as compared to Knudsen diffusion in ideal tubular channels. The membrane permeation experiments are described over 10 orders of magnitude in Kn, encompassing the transition flow regime, by the unified flow model of Beskok and Karniadakis.     

Influence of stagnant zones on transient and asymptotic dispersion in macroscopically homogeneous porous media

The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusion-limited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer.     

Bunching and antibunching in the fluorescence of semiconductor nanocrystals

The fluorescence of single-colloidal CdSe quantum dots is investigated at room temperature by means of the autocorrelation function over a time scale of almost 12 orders of magnitude. Over a short time scale, the autocorrelation function shows complete antibunching, indicating single-photon emission and atomiclike behavior. Over longer time scales (up to tens of seconds), we measure a bunching effect that is due to fluorescence intermittency and that cannot be described by fluctuations between two states with constant rates. The autocorrelation function also exhibits nonstationary behavior related to power-law distributions of On and Off times.     

New experimental constraints on non-Newtonian forces below 100 microm

We have searched for large deviations from Newtonian gravity by means of a finite-frequency microcantilever-based experiment. Our data eliminate from consideration mechanisms of deviation that posit strengths approximately 10(4) times Newtonian gravity at length scales of 20 microm. This measurement is 3 orders of magnitude more sensitive than others that provide constraints at similar length scales.     

Distribution of slip tracks in single crystals of Ni3Fe alloy

The results of an experimental investigation of the distribution of slip tracks in a primary system in single crystals of Ni₃Fe alloy, oriented for a single slip, are presented. Investigations were carried out over a range of scales which differed by three orders of magnitude. Histograms of the distances between slip tracks at different scale levels are constructed. Self-similar track distributions in the primary slip system over the range of scales investigated are established. Tomsk State Architectural-Construction University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 51–56, April, 1998.     

Torsion vector and variableG

In the Einstein-Cartan theory coupled to a classical spin fluid only the traceless part of the torsion field can be related to spin. Here the theory is generalized by allowing intrinsic dilation currents which couple algebraically to the torsion trace. The intrinsic dilation current is interpreted as the relative change of intrinsic length scales relative to the gravitational length scale. By a dilation current conservation law, one finds the scale function between the atomic length scales and the gravitational length scales. This is in effect a dynamic unification of the atomic and gravitational units of measurement. The theory is applied to the Friedmann-Robertson-Walker cosmology, and physical effects in the solar system are considered.     

High Conductivity Mediated by Thermal Excitation of Solectrons

We study the quantum dynamics and statistics of electrons interacting with nonlinear excitations of a classical thermal lattice of atoms on a semi‐phenomenological basis. By theoretical estimates based on tight‐binding approximations, Wigner distributions and computer simulations we show the existence of fast and nearly loss‐free motions of electrons along crystallographic axes of a nonlinear lattice. Using mass‐action relations we estimate the density of moving bound states between electrons and lattice solitons and estimate analytically and by simulations Wigner momentum distributions which are non‐Maxwellian. Calculating the currents from these bimodal distributions we show that thermally excited solectrons in nonlinear media may lead to a considerable transport enhancement. Our estimates and simulations demonstrate that in a temperature window, where solectrons are excited and are relatively stable, conductivity and diffusion may be enhanced by up to two orders of magnitude. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport length scales in disordered graphene-based materials: strong localization regimes and dimensionality effects

We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path and charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). The electronic systems are found to undergo a conventional Anderson localization in the zero-temperature limit, in agreement with localization scaling theory. Localization lengths in weakly disordered ribbons are found to strongly fluctuate depending on their edge symmetry, but always remain several orders of magnitude smaller than those computed for 2D graphene for the same disorder strength. This pinpoints the role of transport dimensionality and edge effects.     

Cluster size distribution at criticality

Monte Carlo studies of the cluster size distribution for the site percolation problem on the triangular lattice are extended to lattices with up to 4 × 10¹¹ sites. Agreement with the predictions of scaling theory at p_c is excellent over a range of cluster sizes spanning five orders of magnitude.     

Time-dependent tunneling spectroscopy for studying surface diffusion confined in nanostructures

By confining a diffusion atom in a nanometer region using surface potential heterogeneity, we have successfully employed a time-dependent tunneling spectroscopy to quantitatively study its random motion. A hopping rate in the range of 1-10(4) Hz, approximately 3 orders of magnitude faster than those accessible by the existing diffusion methods based on scanning tunneling microscopy, was demonstrated for single Cu atoms diffusing in the faulted half unit cell of Si(111)-(7 x 7). Our technique is potentially useful to detect fast diffusion processes such as H quantum diffusion at atomic scale.