Search

Diffusion of rare earth elements has been characterized in synthetic forsterite and natural olivine ([Fo.sub.90]) under dry conditions. Experiments were prepared by enclosing source material [mixtures of rare-earth element (La, Dy, or Yb) aluminate and synthetic forsterite powders in 3:1 proportions] and polished forsterite in platinum capsules. For buffered experiments on natural olivine, samples were placed with the source in AgPd capsules, sealed under vacuum in silica glass ampoules with a solid buffer (NNO, IW, or graphite). In some experiments, ground natural olivine was also incorporated into the source material. Prepared capsules were annealed in 1 atm furnaces for one hour to several weeks at 850 to 1300[degrees]C. REE distributions in olivine were profiled by Rutherford backscattering spectrometry (RBS). The following Arrhenius relation is obtained for Dy diffusion in forsterite: [D.sub.Dy] = 8.0 x [10.sup.-10] exp(-289 [+ or -] 21 kJ [mol.sup.-1]/RT) [m.sup.2]/s. Diffusivities of Yb and La in forsterite and for Dy in natural olivine are similar. Experiments run on natural olivine show little dependence of diffusion on crystallographic orientation. The Arrhenius relation yields diffusivities about three orders of magnitude smaller than those determined for REE diffusion in olivine by Spandler et al. (2007) and suggests that timescales for preservation of REE signatures in olivine-hosted melt inclusions may be relatively long. REE diffusivities in olivine are an order of magnitude faster than those of [REE.sup.+3] in enstatite (Cherniak and Liang 2007) and in diopside under most conditions (Van Orman et al. 2001). Hence, REE signatures in olivine are more likely to be altered by diffusion than those of clinopyroxene or orthopyroxene. Keywords: Rare earth elements, olivine, diffusion, Rutherford backscattering spectrometry DOI: 10.2138/am.2010.3345

Effects of isolated transport barriers on the global mixing and fluxes of a tracer are investigated, where a barrier is defined as a local minimum in effective diffusivity. An idealized 1D model with a prescribed diffusivity profile, with or without forcing, is used to show that the structure, flux, and decay rates of the tracer are all very sensitive to the barrier geometry, particularly when it is deep and narrow. Although the tracer gradients and the variance dissipation are concentrated to the barrier region, the flux shows a more global response to the barrier, decreasing everywhere. The harmonic mean of effective diffusivity is proposed as a useful first-order predictor of the global transport. This 1D model is used to diagnose the isentropic transport in the upper troposphere and lower stratosphere with offline transport calculations driven by the Met Office winds. The global tracer variance in these calculations decays approximately exponentially, and the time-mean decay rate and tracer structure are well captured by the gravest 1D eigenmode with the time-averaged effective diffusivity. However, the decay rate and the flux of the full solution are 15%-20% smaller than those of the eigenmode because of a negative temporal correlation between the effective diffusivity and the gradient. The vertical and decadal variations of the decay rates are consistent with the corresponding variations in the harmonic mean effective diffusivity. To the extent that the global mixing is sensitive to the local barrier properties, and to the extent that the latter are sensitive to the errors in advecting winds and model numerics, modeling of global atmospheric transport remains a challenge. This may explain, at least partially, the disparate model estimates reported in the literature.

Refractory oxide melts of the binary system MgO-[Al.sub.2][O.sub.3] have been studied by molecular dynamics simulation using an advanced ionic interaction model derived from first-principles. The simulations reproduce well experimental densities, structure factors, and transport properties. Anomalous behavior of the latter was observed as a function of melt composition. The minimum in the Al self-diffusion and the respective maximum in the shear viscosity around Mg[Al.sub.4][O.sub.7] composition are explained by structural changes in the melt. Keywords: Molecular dynamics simulation, [Al.sub.2][O.sub.3], MgO, melt, structure, viscosity, diffusion

Diffusion tensors are estimated from magnetic resonance images (MRIs) that are diffusion-weighted, and those images inherently contain noise. Therefore, noise in the diffusion-weighted images produces uncertainty in estimation of the tensors and their derived parameters, which include eigenvalues, eigenvectors, and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors. Although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters, we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise. The aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images. Whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters, such as fractional anisotropy (FA), depends critically on the morphology of the diffusion tensor that is being estimated. The wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction (PD) of isotropic (or oblate) tensor. We also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors, demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations. Simulation studies are also used to understand more thoroughly our theoretical results. Our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors, oblate tensors, or multiple tensors. Index Terms--Acquisition scheme, bootstrap, diffusion tensor, fiber tracks, principal direction.

Diffusion spectrum imaging (DSI) can map complex fiber microstructures in tissues by characterizing their 3-D water diffusion spectra. However, a long acquisition time is required for adequate q-space sampling to completely reconstruct the 3-D diffusion probability density function. Furthermore, to achieve a high q-value encoding for sufficient spatial resolution, the diffusion gradient duration and the diffusion time are usually lengthened on a clinical scanner, resulting in a long echo time and low signal-to-noise ratio of diffusion-weighted images. To bypass long acquisition times and strict gradient requirements, the reduced-encoding DSI (RE-DSI) with a bi-Gaussian diffusion model is presented in this study. The bi-Gaussian extrapolation kernel, based on the assumption of the bi-Gaussian diffusion signal curve across biological tissue, is applied to the reduced q-space sampling data in order to fulfill the high q-value requirement. The crossing phantom model and the manganese-enhanced rat model served as standards for accuracy assessment in RE-DSI. The errors of RE-DSI in estimating fiber orientations were close to the noise limit. Meanwhile, evidence from a human study demonstrated that RE-DSI significantly decreased the acquisition time required to resolve complex fiber orientations. The presented method facilitates the application of DSI analysis on a clinical magnetic resonance imaging system. Index Terms--Bi-Gaussian model, diffusion spectrum imaging, manganese-enhanced rat model, phantom model.

Determination of aqueous diffusion coefficients of solutes through fractured media is essential for understanding and modeling contaminant transport at many hazardous waste disposal sites. Development of experimental methods and measurements for the characterization of diffusion in fractured glass media is necessary for the design and performance assessment of glassified radionuclear waste disposal facilities. We report on the use of time-lag diffusion experimental method to assess the diffusion behavior of three different solutes (Cs, Sr, and pentafluoro benzoic acid) in fractured, immobilized low activity waste (ILAW) glass forms. A fractured media time-lag diffusion experimental apparatus, which allows the measurement of diffusion coefficients, has been designed and built for this purpose. Use of time-lag diffusion method, a considerably easier experimental method than the other available methods, was not previously demonstrated for measuring diffusion in fractured waste glass media. Hydraulic conductivity, porosity, and diffusion coefficients of a solute were experimentally measured in fractured glass blocks using this method for the first time. Results agree with the range of properties reported for similar rock media earlier, indicating that the time-lag experimental method can effectively characterize the diffusion coefficients of fractured ILAW glass media. Data presented are rare and useful for the design of vitrified glass disposal facilities. DOI: 10.1061/(ASCE)0733-9372(2008)134:10(879) CE Database subject headings: Measurement; Diffusion; Cracking; Glass; Waste management.

The analytical solution of the differential-form momentum equation for the outflow distribution along a continuous multiple-port diffuser is derived. The solution is verified by comparison with available experimental data. The outflow patterns along the diffuser are determined by the range of two dimensionless parameters, which measure the effects of wall friction and port momentum, respectively. A concept of flow uniformity of lateral discharge is explored, and an analytical formula for the evaluation of uniformity is derived. A simple formula is also proposed which may be useful in the design of the multiple-port diffuser. DOI: 10.1061/(ASCE)0733-9429(2008) 134:9(1383) CE Database subject headings: Water discharge; Flow patterns; Outflow; Infiltration; Diffusion.

A numerical study was carried out to understand the effect of CO enrichment on flame temperature and NO formation in counterflow C[H.suv.4]/air diffusion flames. The results indicate that when CO is added to the fuel, both flame temperature and NO formation rate are changed due to the variations in adiabatic flame temperature, fuel Lewis number, and chemical reaction. At a low strain rate, the addition of carbon monoxide causes a monotonic decrease in flame temperature and peak NO concentration. However, NO emission index first slightly increases, and then decreases. At a moderate strain rate, the addition of CO has negligible effect on flame temperature and leads to a slight increase in both peak NO concentration and NO emission index, until the fraction of carbon monoxide reaches about 0.7. Then, with .a further increase in the fraction of added carbon monoxide, all three quantities quickly decrease. At a high strain rate, the addition of carbon monoxide causes increase in flame temperature and NO formation rate, until a critical carbon monoxide fraction is reached. After the critical fraction, the further addition of carbon monoxide leads to decrease in both flame temperature and NO formation rate. [DOI: 10.1115/1.2906222] Keywords: diffusion flame, N[O.sub.x]. fuel enrichment, carbon monoxide

This paper reports the results of several thousand analyses of the Mg content of calcite from 31 samples from the Ubehebe Peak contact aureole, Death Valley, California. All data reported are from metamorphic calcite formed during mixed volatile-mineral reactions in which dolomite remained in the rock. The Mg content generally increases toward the intrusive contact and bend with increasing temperature, but it varies strongly. Indeed, probability distributions for each sample are near Gaussian, possess a relatively small skewness (-l.72 to 3.32), and a variance that is a multiple of the estimated measuring uncertainty. These findings complicate direct application of the Mg content in calcite for use as an accurate thermometer. The purpose of the study presented in the second part of the paper is to explore the significance of these systematic variations of Mg composition of calcite to aid the interpretation of contact metamorphic temperatures recorded in carbonates. We developed forward models to evaluate the effect of growth zoning, volume diffusion, and the formation of submicroscopic exsolution lamellae ( Keywords: Calcite-dolomite thermometry, contact metamorphism, Ubehebe Peak, mineral growth, fluid infiltration

This paper presents a field study of installation effects of deep mixed columns on properties of the sensitive Ariake marine clay. Cone penetration tests were performed in the field to evaluate the change in the strength of the surrounding clay with time. Soil samples were taken before and after column installation to evaluate variations of physical, mechanical, and chemical properties of the surrounding clay. Test results indicated that the water content of the surrounding clay decreased while the concentration of cations increased as sampling locations approached the columns. Shear strength of the surrounding clay decreased during the installation but recovered after a short period of curing. Shear strength continued to increase with time over a period of 70 days. Based on the regression results, the surrounding soil after the installation of the columns took approximately 10 days to recover to the strength value before installation. On average, the shear strength of the surrounding clay increased over the original strength by approximately 23% after 40 days and 50% after 70 days, respectively. Discussion is presented on strength changes and key influence factors including soil disturbance and fracturing, thixotropy, consolidation, and diffusion of cations from deep mixed columns to the surrounding clay. CE Database subject headings: Soil mixing; Clays; Field tests; Soil properties; Cracking; Shear strength; Diffusion.

A new experimental method is presented where transport and partitioning of elements in grain boundaries is investigated by using thin films. As a model system, the element exchange between a nanocrystalline thin film of olivine (F[O.sub.30]) and a San Carlos olivine single crystal (F[O.sub.89]), which is mediated by grain diffusion through a polycrystalline Zr[O.sub.2] layer was studied. Double layers of Zr[O.sub.2] and olivine on polished single crystals have been prepared by pulsed laser deposition and annealed in the temperature range between 900 and 1050 [degrees] C at controlled oxygen fugacity. Starting and annealed samples were analyzed by SEM, RBS, and SIMS. From the chemical analysis by RBS and SIMS, the reaction mechanism could be classified according to the reaction mechanism map of Dohmen and Chakraborty (2003). Most of the samples show a combined grain boundary/volume diffusion-controlled reaction behavior according to this scheme. During the anneal, a linear concentration gradient for the Fe/(Fe + Mg) ratio evolved within the Zr[O.sub.2] layer, where Fe strongly prefers the Zr[O.sub.2] grain boundary compared to Mg. The depth profiles for the Fe/(Fe + Mg) ratio have been simulated in detail. From the simulation Fe-Mg volume (in olivine) and grain boundary diffusion coefficients, as well as the partition coefficient and the storage capacity for the grain boundary, have been extracted. The chemical diffusion coefficient of Fe-Mg within the Zr[O.sub.2] grain boundary at 900 [degrees] C is on the order of 1 x [10.sup.-15] [m.sup.2]/s. Volume and grain boundary diffusion coefficients obtained using the new method are in good agreement with literature data. An additional observation is that grains within the polycrystalline fayalite-rich olivine layer grow by a grain rotation mechanism until an equilibrium texture is attained. Keywords: Diffusion, kinetics, element exchange, thin films, olivine, zirconia

Computing the morphological similarity of diffusion tensors (DTs) at neighboring voxels within a DT image, or at corresponding locations across different DT images, is a fundamental and ubiquitous operation in the postprocessing of DT images. The morphological similarity of DTs typically has been computed using either the principal directions (PDs) of DTs (i.e., the direction along which water molecules diffuse preferentially) or their tensor elements. Although comparing PDs allows the similarity of one morphological feature of DTs to be visualized directly in eigenspace, this method takes into account only a single eigenvector, and it is therefore sensitive to the presence of noise ill the images that can introduce error intothe estimation of that vector. Although comparing tensor elements, rather than PDs, is comparatively more robust to the effects of noise, the individual elements of a given tensor do not directly reflect the diffusion properties of water molecules. We propose a measure for computing the morphological similarity of DTs that uses both their eigenvalues and eigenvectors, and that also accounts for the noise levels present in DT images. Our measure presupposes that DTs in a homogeneous region within or across DT images are random perturbations of one another in the presence of noise. The similarity values that are computed using our method are smooth (in the sense that small changes in eigenvalues and eigenvectors cause only small changes in similarity), and they are symmetric when differences in eigenvalues and eigenvectors are also symmetric. In addition, our method does not presuppose that the corresponding eigenvectors across two DTs have been identified accurately, an assumption that is problematic in the presence of noise. Because we compute the similarity between DTs using their eigenspace components, our similarity measure relates directly to both the magnitude and the direction of the diffusion of water molecules. The favorable performance characteristics of our measure offer the prospect of substantially improving additional postprocessing

Symplectites composed of Cr-rich spinel plus one or more of the minerals orthopyroxene, clinopyroxene, pyrope garnet, Mg-rich amphibole, and phlogopite, are common in depleted peridotites recovered from kimberlites. The symplectites are unusual for being fine-grained intergrowths in a much coarser matrix of grains, and for having high concentrations of Ca and Al in an environment generally depleted in these elements. Various processes, and combinations of processes, including diffusion, discontinuous precipitation, metamorphism, and metasomatism create and alter the symplectites. Clinopyroxene + spinel symplectites are the most basic symplectites and are assumed to be precursors to all other types of symplectites. These symplectites resemble cellular intergrowths formed in alloys during cooling, by processes of diffusion and by discontinuous precipitation. Garnet in symplectites is interpreted to form by prograde mineral reactions between matrix minerals and symplectites. Symplectites containing amphibole and phlogopite are pyroxene + spinel [+ or -] garnet symplectites that have been modified by metasomatism. Keywords: Symplectite, discontinuous precipitation, garnet, harzburgite, mantle

In predicting the chloride diffusivity of concrete as a three-phase material, the morphological characteristics of the three phases, the physical properties of each phase constituent material, and the interactions of the three phases in the concrete matrix should all be taken into account. The present paper attempts to develop an analytical method to achieve this. A three-phase composite sphere model for the concrete matrix is proposed to represent the heterogeneous nature of concrete and a closed form solution for the chloride diffusivity of concrete is derived. After verifying the derived closed form solution with experimental results, the effects of key factors that affect the chloride diffusivity of concrete, namely the chloride diffusivity and thickness of the interfacial transition zone (ITZ), the maximum aggregate diameter, and the aggregate gradation are examined in a quantitative manner. It is found in the paper that the most important factor influencing the chloride diffusivity of concrete is the chloride diffusivity of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given relative chloride diffusivity of ITZ to cement paste at 10 is almost four times that for a given relative chloride diffusivity of ITZ to cement paste at 2. The second most important factor is the thickness of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given ITZ thickness at 0.05 mm increases by 76% as compared to that for a given ITZ thickness at 0.02 mm. The least important factors are the maximum aggregate diameter and aggregate gradation. The extent to which they influence the chloride diffusivity of concrete is in the range of 10-55%. The paper concludes that the closed form solution derived here can predict the chloride diffusivity of concrete with reasonable accuracy. DOI: 10.1061/(ASCE)0899-1561(2008)20:3(205) CE Database subject headings: Concrete; Chlorides; Diffusivity; Closed form solutions; Predictions.

The effect of the insulating shield thickness on the steady-state diffusion-limiting current of sphere cap microelectrodes is investigated. Theoretical steady-state limiting currents are obtained by using a simulation procedure, which relies on the explicit finite difference method with a fixed time grid and an exponentially spatial grid. The results obtained indicate that the current increases by decreasing the thickness of the insulating sheath or by increasing the aspect ratio of the sphere cap (h/a, where h is the height of the sphere cap and a is the electrode basal radius), similarly to other types of microelectrodes with different electrode geometry, such as disks and finite cones. The simulated data are fitted to approximate analytical expressions to describe the dependence of the limiting current on both h/a and RG (RG = b/a, where b is the overall tip radius) parameter. Theoretical currents are also compared with experimental data, which are obtained with a range of mercury-coated platinum microelectrodes having different RG and h/a values. The measurements are performed by using cyclic voltammetry at 1 [mVs.sup.-1], in aqueous solutions containing Ru[([NH.sub.3]).sub.6-[Cl.sub.3] as electroactive species. A good agreement (within 3%) between theoretical and experimental steady-state currents is found. Finally, SECM operating in the feedback mode is used to assess the validity of the shape parameters found by voltammetry for sphere cap microelectrodes, whose insulating shields are of a thickness comparable to the electrode radius.

The lateral mobility of the thiolate ligands on the surface of Au nanoparticles was probed by EPR spectroscopy. This was achieved by using bisnitroxide ligands, which contained a disulfide group (to ensure attachment to the Au surface) and a cleavable ester bridge connecting the two spin-labeled branches of the molecule. Upon adsorption of these ligands on the surface of Au nanoparticles, the two spin-labeled branches were held next to each other by the ester bridge as evidenced by the spin--spin interactions. Cleavage of the bridge removed the link that kept the branches together. CW and pulsed EPR (DEER) experiments showed that the average distance between the adjacent thiolate branches on the Au nanoparticle surface only marginally increased after cleaving the bridge and thermal treatment. This implies that the lateral diffusion of thiolate ligands on the nanoparticle surface is very slow at room temperature and takes hours even at elevated temperatures (90[degrees]C). The changes in the distance distribution observed at high temperature are likely due to ligands hopping between the nanoparticles rather than diffusing on the particle surface.

Currently there are two approaches to treat ion exchange equilibrium between the exchanger phase and solution phase: the chemical reaction equilibrium and the Donnan equilibrium. Nevertheless, theoretical calculation of the ion distribution between these two phases remains impossible using these two approaches because of the difficulty in obtaining the activity coefficient of an ion in the exchanger phase for a solution mixture containing two or more types of electrolytes. Our analysis of ion diffusion in an electric field showed that the exchange process of electrostatic adsorption can be treated as a diffusion process. A new equilibrium equation was obtained by treating ion exchange as a diffusion process. The new equation can be used to predict the ion distribution between the exchanger and solution phases without knowing the activity coefficients of the adsorbed ions. The new approach was tested and verified using published experimental data for a Na-Ca-illite system. The experimental data and the theoretical predictions matched very well. The new ion distribution equation can provide another way to calculate ion exchange equilibrium for a well-dispersed suspension of dilute bulk solution containing two types of electrolytes. Abbreviation: DDL, diffuse double layer.

Time-dependent fluctuations in the catalysis rate ([delta]k(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion [delta][[omega].sub.0](t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy ([delta]E(t)) as a contributor to [delta]k(t) and relate the latter to [delta][[omega].sub.0](t). The resulting relation between [delta]k(t) and [delta][[omega].sub.0](t) is a dynamic analog of the solvato-chromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated [delta]E(t) on fluctuations in the radiative component ([[delta].sub.[gamma]r.sup.-1](t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between [delta][[gamma].sup.-1.sub.r](t) and [delta][[omega].sub.0](t) is obtained. Experimental tests will determine whether the correlation functions for [delta]k(t), [delta][[omega].sub.0](t), and [delta][[gamma].sup.-1.sub.r] are indeed similar for any enzyme. Measurements of dielectric dispersion, [epsilon]([omega]), for the enzyme discussed elsewhere will provide further insight into the correlation function for [delta]E(t). They also will determine whether fluctuations in the nonradiative component [[gamma].sup.-1.sub.nr] of the lifetime decay has a different origin, fluctuations in distance for example. fluorescence | single enzyme

In the context of drug eluting stent, we present two-dimensional numerical models of mass transport of the drug in the wall and in the lumen to study the effect of the drug diffusion coefficients in the three principal media (blood, vascular wall, and polymer coating treated as a three-compartment problem) and the impact of different strut apposition configurations (fully embedded, half embedded, and not embedded). The different conditions were analyzed in terms of their consequence on the drug concentration distribution in the arterial wall. We apply the concept of the therapeutic window to the targeted vascular wall region and derive simple metrics to assess the efficiency of the various stent configurations. Although most of the drug is dispersed in the lumen, variations in the blood flow rate within the physiological range of coronary blood flow and the diffusivity of the drug molecule in the blood were shown to have a negligible effect on the amount of drug in the wall. Our results reveal that the amount of drug cumulated in the wall depends essentially on the relative values of the diffusion coefficients in the polymer coating and in the wall. Concerning the strut apposition, it is shown that the fully embedded strut configuration would provide a better concentration distribution. [DOI: 10.1115/1.2768381] Keywords: drug eluting stents, drug delivery, diffusion, therapeutic window, restenosis

Using inelastic electron tunneling spectroscopy (IETS) to measure the vibronic structure of nonequilibrium molecular transport, aided by a quantitative interpretation scheme based on Green's function-density functional theory methods, we are able to characterize the actual pathways that the electrons traverse when moving through a molecule in a molecular transport junction. We show that the IETS observations directly index electron tunneling pathways along the given normal coordinates of the molecule. One can then interpret the maxima in the IETS spectrum in terms of the specific paths that the electrons follow as they traverse the molecular junction. Therefore, IETS measurements not only prove (by the appearance of molecular vibrational frequencies in the spectrum) that the tunneling charges, in fact, pass through the molecule, but also can be used to determine the transport pathways and how they change with the geometry and placement of molecules in junctions. molecular electronics | molecular junctions | molecular transport

Using the algebra transformation method, we develop and demonstrate the use of the [delta]-[P.sub.1] approximation to improve steady-state radiative-transfer estimates on spatial scales comparable to the mean free path. We show that the [delta]-[P.sub.1] approximation agrees well with Monte Carlo simulation from source to infinity when we choose an appropriate parameter f(fractional portion that scatters directly forward) in the [delta]-Eddington phase function. We also provide the empirical formula to determine the parameter f. OCIS codes: 030.0030, 290.0290, 290.7050.

The authors examine the use of closed-form analytical solutions to describe diffusion flames in flow fields. Topics include kinetic energy, fuel sources, and strain fields.

During optical mapping of the heart, the signal represents a weighted average of the transmembrane potential. Researchers sometimes illuminate the epicardium and record over a cut surface. My goal is to compare their signal to the photon density within an intact tissue. Does cutting the tissue affect the signal? Index Terms--Optical mapping, photon diffusion equation, transmembrane potential.

The well known Fisher model is utilized to measure and compare the Ge diffusivity in micro- and nanocrystalline Si layers. The diffusivities in nanograins and nanograin boundaries are found to be one order of magnitude higher when compared to micrograins and micrograin boundaries while the activation energy in nano- as well as micrograin boundaries are same.

We show, by numerical simulations, how the particles diffuse with respect to the magnetic field flux tubes. In the numerical model, we can vary both the degree of turbulence anisotropy and the ratio of particle gyroradius over the turbulence correlation length. We find that the magnetic flux tube structure changes with the anisotropy, as clearly seen from the flux tube cross sections, and that increasing the gyroradius particles are progressively less tied to magnetic field lines. Surprisingly, perpendicular transport decreases for very large gyroradii. Index Terms--Anisotropy, diffusion, magnetic turbulence, plasma transport.