Parallel Diffusion Coefficient Research Articles

Anisotropic translational diffusion in the nematic phase: Dynamical signature of the coupling between orientational and translational order in the energy landscape

We find in a model system of thermotropic liquid crystals that the translational diffusion coefficient parallel to the director D(parallel) first increases and then decreases as temperature drops through the nematic phase, and this reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant. We argue, based on an energy landscape analysis, that the coupling between orientational and translational order can play a role in inducing the nonmonotonic temperature behavior of D(parallel). Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion.

Magnetic resonance imaging of tissue and vascular layers in the cat retina

Purpose: To report the visual resolution of multiple cell and vascular “layers” in the cat retina using MRI. Materials and Methods: T2- and diffusion-weighted MRI at 4.7 Tesla was performed. Layer-specific thickness, T2, spin density, apparent diffusion coefficient perpendicular (ADC) and parallel (ADC) to the retinal surface were tabulated. T1-weighted MRI was acquired before and after intravenous administration of Gd-DTPA and subtraction images were obtained. Histology was performed for validation. Results: Three distinct “layers” were observed. The inner strip nearest to the vitreous (exhibiting large T2, ADC, spin density with Gd-DTPA enhancement) overlapped the ganglion cell layer, bipolar cell layer, and the embedded retinal vascular layer. The middle strip (exhibiting small T2, ADC, spin density without Gd-DTPA enhancement) overlapped the photoreceptor cell layer and the inner and outer segments. The outer strip (exhibiting large T2, ADC, spin density with GdDTPA enhancement) overlapped the tapetum and choroidal vascular layer. T2, spin density, ADC and ADC of different “layers” were tabulated. The inner strip was slightly thicker than the other two strips. The total thickness, including neural and nonneural retina, was 358 13 m( N 6) by MRI and 319 77 m( N 5) by histology. Conclusion: MRI provides a noninvasive tool to study the retina with laminar specificity without depth limitation.

Cosmic rays X. The cosmic ray knee and beyond: diffusive acceleration at oblique shocks

Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where highly oblique shocks exist. We examine numerically (using Monte-Carlo simulations) the effect of the diffusion coefficients on the energy gain and the acceleration rate, by testing the role between the obliquity of the magnetic field to the shock normal, and the significance of both perpendicular cross-field diffusion and parallel diffusion coefficients to the acceleration rate. We find (and justify previous analytical work – Jokipii 1987, ApJ, 313, 842) that in highly oblique shocks the smaller the perpendicular diffusion gets compared to the parallel diffusion coefficient values, the greater the energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray spectrum in high energies, between 10 15 eV and about 10 18 eV is claimed, as we estimate the upper limit of energy that cosmic rays could gain in plausible astrophysical regimes; interpreted by the scenario of cosmic rays which are injected by three different kind of sources, (a) supernovae which explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet stars, where the two latter explode into their pre-supernovae winds.

Molecular dynamics simulation of the nematic liquid crystal phase in the presence of an intense magnetic field

The influence of an intense external field on the dynamics of the nematic liquid crystal phase is investigated using a molecular dynamics simulation for the Gay-Berne nematogen under isobaric-isothermal conditions. The molecular dynamics as a function of the second-rank orientational order parameter P<2> for a system consisting of a nematic liquid crystal in the presence of an intense magnetic field is compared with that of a similar system without the field. The translational motion of molecules is determined as a function of the translational diffusion coefficient tensor and the anisotropy and compared with the values predicted theoretically. The rotational dynamics of molecules is analyzed using the first- and the second-rank orientational time correlation functions. The translational diffusion coefficient parallel with respect to the director is constrained by the intense field, although the perpendicular one is decreased as the P<2> is increased, just as it is in the system without the field. However, no essential effect of the strong magnetic field is observed in the rotational molecular dynamics. Further, the rotational diffusion coefficient parallel with respect to the director obtained from the first-rank orientational time correlation function in the simulation is qualitatively in agreement with that in the real nematic liquid crystalline molecules. The P<2> dependence of the rotational diffusion coefficient for the system with the intense magnetic field shows a tendency similar to that for the system without the field.

Magnetic resonance imaging of tissue and vascular layers in the cat retina

To report the visual resolution of multiple cell and vascular "layers" in the cat retina using MRI. T2- and diffusion-weighted MRI at 4.7 Tesla was performed. Layer-specific thickness, T2, spin density, apparent diffusion coefficient perpendicular (ADC(perpendicular)) and parallel (ADC(parallel)) to the retinal surface were tabulated. T1-weighted MRI was acquired before and after intravenous administration of Gd-DTPA and subtraction images were obtained. Histology was performed for validation. Three distinct "layers" were observed. The inner strip nearest to the vitreous (exhibiting large T2, ADC, spin density with Gd-DTPA enhancement) overlapped the ganglion cell layer, bipolar cell layer, and the embedded retinal vascular layer. The middle strip (exhibiting small T2, ADC, spin density without Gd-DTPA enhancement) overlapped the photoreceptor cell layer and the inner and outer segments. The outer strip (exhibiting large T2, ADC, spin density with Gd-DTPA enhancement) overlapped the tapetum and choroidal vascular layer. T2, spin density, ADC(perpendicular) and ADC(parallel) of different "layers" were tabulated. The inner strip was slightly thicker than the other two strips. The total thickness, including neural and nonneural retina, was 358 +/- 13 microm (N = 6) by MRI and 319 +/- 77 microm (N = 5) by histology. MRI provides a noninvasive tool to study the retina with laminar specificity without depth limitation.

Ulysses observations of Jovian relativistic electrons in the interplanetary space near Jupiter: Determination of perpendicular particle transport coefficients and their energy dependence

Intensities of ∼1–10 MeV relativistic electrons in several energy channels of the high-energy telescope (HET) on Ulysses increase dramatically during its flybys of Jupiter in 1992 and 2004. Perpendicular diffusion coefficients of these particles are derived by fitting the spatial profile of Jovian electron intensity to a diffusion-convection model of particle transport. It is found that the latitudinal diffusion coefficient during the 2004 Jupiter flyby has to be enhanced from its value during the 1992 Jupiter flyby and it is also enhanced relative to the radial perpendicular diffusion. Such an enhancement of latitudinal particle transport was implied previously through the observations of Jovian electrons, cosmic rays and solar energetic particles at high heliographic latitudes, and now this requirement extends further to low latitude region of the heliosphere. Energy dependence of the perpendicular diffusion coefficient is obtained quite precisely through the variation in the slope of energy spectrum of Jovian electrons. The perpendicular diffusion coefficient increases with energy, which can put a tight constraint on models of the particle transport coefficient. The newest nonlinear guiding center (NLGC) theory of perpendicular diffusion is consistent with this observation, but only when it is combined with a parallel diffusion coefficient from the quasilinear theory in a slab magnetic turbulence without dynamic damping.

A fully 3-D anisotropic numerical model of the DI-B in situ diffusion experiment in the Opalinus clay formation

In situ diffusion experiments have been performed at underground research laboratories in clay formations to overcome the limitations of laboratory diffusion experiments and investigate possible scale effects. The DI-B experiment is a long-term, natural-scale, in situ diffusion experiment performed in a packed section in a borehole drilled vertically into the anisotropic Opalinus clay formation at Mont Terri in Switzerland. A cocktail of non-radioactive tracers was used. Tracers were monitored for one year at the test interval and measured at samples taken from an overcored interval. Contrary to the methods used so far for the interpretation of in situ experiments which rely on 2-D models and disregard diffusion across bedding, here we present a fully 3-D anisotropic finite element model of the DI-B experiment. The numerical model has been calibrated with iodide and deuterium data. The fully anisotropic 3-D model provides reliable estimates of effective diffusion coefficients and accessible porosities for deuterium and iodide which are within the range of published values. We show that a simple 2-D model can be safely used to interpret data along central profiles although it may lead to biased estimates when applied to profiles located near the edges of the test interval. Computed concentrations in the borehole are much less sensitive to changes in model parameters than concentrations along profiles. Computed concentrations close to the borehole are most sensitive to the accessible porosity while concentrations at distances greater than 0.085 m are most sensitive to the diffusion coefficient parallel to the bedding. Computed concentrations along some profiles are sensitive to the effective diffusion perpendicular to bedding.

Cosmic rays & diffusive shock acceleration at highly oblique non-relativistic shocks

Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where highly oblique shocks exist. We examine numerically (using Monte Carlo simulations) the effect of the diffusion coefficients on the energy gain and the acceleration rate, by testing the role between the obliquity of the magnetic field at the shock normal, and the significance of both perpendicular cross-field diffusion and parallel diffusion coefficients to the acceleration rate. We find (and justify previous analytical work - Jokipii 1987) that in highly oblique shocks the smaller the perpendicular diffusion gets compared to the parallel diffusion coefficient values, the greater the energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray spectrum at high energies, between 10 15 eV and about 10 18 eV is claimed, as we estimate the upper limit of energy that cosmic rays could gain in plausible astrophysical regimes; interpreted by the scenario of cosmic rays which are injected by three different kind of sources, (a) supernovae which explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet stars, where the two latter explode into their pre-supernovae winds.

Transport properties and distribution of water molecules confined in hydrophobic nanopores and nanoslits.

The transport properties, including the diffusivity and viscosity, of water confined in hydrophobic nanopores and nanoslits were studied by molecular dynamics simulations. The results show that the diffusion coefficient in nanopores and nanoslits is markedly lower than that in the bulk. But the viscosity is much larger than that in bulk. The parallel diffusion coefficient is obviously larger than the perpendicular ones. The diffusion coefficient in the channel pore is ever less than that in the slit pore at the same pore width, but the viscosity is larger. The temperature and density affect significantly the diffusivity and viscosity in nanopores and nanoslits. Lower density water exhibits some special characteristics on density profiles in nanopores and nanoslits at lower temperatures, and the density profiles show a change from homogeneous to inhomogeneous as the pore width is reduced. Even clusters occurred in micropores.

Random walks of molecular motors arising from diffusional encounters with immobilized filaments

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation in two and three dimensions. Results are obtained for the fraction of bound motors, their average velocity, displacement, and dispersion. The analytical results are in good agreement with results from Monte Carlo simulations and confirm the behavior predicted by scaling arguments. The diffusion coefficient parallel to the filament becomes anomalously large since detachment and subsequent reattachment, in the presence of directed motion of the bound motors, leads to a broadening of the density distribution. The occurrence of protofilaments on a microtubule is modeled by internal states of the binding sites. After a transient time, all protofilaments become equally populated.

Atomistic Molecular Dynamics Simulation of Hexakis(pentyloxy)triphenylene: Structure and Translational Dynamics of Its Columnar State

Atomistic molecular dynamics computer simulations have been performed on the columnar state of the discogen hexakis(pentyloxy)triphenylene (HAT5). The parameters of the empirical model potential have been taken from the AMBER and OPLS force fields. A 10 ns simulation run has been carried out in Berendsen's ensemble at pressure P = 0.1 MPa and temperature T = 375 K to study bulk and molecular structure. The bulk structure has been characterized by obtaining structural parameters that compare favorably with those deduced from X-ray diffraction experiments. 1 3 C and 2 H NMR data suggest two completely different pictures of the position of the pendant chains with respect to the plane of the aromatic core: one, called diablo-like, with the chains in the triphenylene plane; the other, octopus-like, with the chains out of this plane and, alternatively, above and below it. Our simulated data are consistent with an intermediate situation. In agreement with all NMR data, we find that the chains become more and more disordered, moving away from the core. We have observed a decrease of the disorder of the lateral chains in going from gas phase to condensed bulk state. Information on translational dynamics has been obtained by performing a 1 ns simulation in the microcanonical ensemble; these calculations definitely assess the one-dimensional fluid character of the columnar state. We have found that the mean square displacement has a solidlike behavior in the plane perpendicular to the column axis. The translational dynamics along the direction parallel to it is dominated by the reciprocal, fluidlike sliding motion of the columns as a whole. If this collective dynamics is removed, also the parallel diffusion coefficient turns out to be solidlike.

Anisotropy and nonequilibrium effects on the light scattered from suspension in a nematic solvent.

We investigate the effects produced on the light scattering spectrum by the anisotropic diffusion of impurities in an incompressible nematic solvent. The spectrum is calculated by using a fluctuating hydrodynamic description when the system is both in a fully thermodynamic equilibrium state and in a nonequilibrium steady state induced by a dye-concentration gradient. In the former state, the isotropic pretransitional phase as well as the nematic phase of the solvent are considered. This spectrum is symmetric (Lorentzian) with respect to the frequency shifts, but anisotropic through its explicit dependence on the ratio of the diffusion coefficients of the dye parallel and normal to the mean molecular axis of the nematic. The values of these coefficients were taken from experimental measurements of diffusion of methylred and nitrosodimethylaniline in a N -( p -methoxybenzylidene)- p -butylaniline (MBBA) solvent. This anisotropy changes the height and the width at mid height with respect to the isotropic case in amounts which for MBBA vary up to 36% and 26%. We also calculate the spectrum in the presence of a concentration gradient of the dye and find that its presence gives rise to an asymmetry of the spectrum in its dependence on the frequency shift; its maximum increases and is displaced with respect to its equilibrium position. The size and direction of this shift are proportional to the magnitude of the dye-concentration gradient and depend on its relative orientation with respect to the scattering vector. For small dimensionless concentration gradients ( approximately 10(-2) ), this effect is maximum when these vectors are parallel and the scattering angle is low ( approximately 1 degrees ). The maximum degree of departure from equilibrium is significant and turns out to be approximately 55%. In view of the significant changes in the spectrum, our theoretical analysis suggests that these effects might be observable.

Perpendicular diffusion coefficient for charged particles of arbitrary energy

The problem of perpendicular diffusion by a particle in a turbulent plasma is a problem of enduring interest and one that has yet to be fully solved. Analytic models do not agree with either observations or numerical simulations. Recently, a nonlinear guiding center theory (NLGC) was developed byMatthaeus et al.[2003]which, for the first time, appears to be consistent with numerical simulations in both the high‐energy and low‐energy particle regimes, provided that the transverse magnetic field is complex. Flux surfaces with high transverse complexity are characterized by the rapid separation of nearby magnetic field lines, and we show that the combination of slab and two‐dimensional turbulence (a “two‐component” model) is necessary to produce transverse complexity and that slab turbulence alone, for example, is insufficient. The nonlinear theory is expressed through the solution of an integral equation for the perpendicular diffusion coefficient κxx, which we solve approximately. Our approximate solution is in excellent agreement with the exact solution of the integral equation. The physical content of the NLGC theory is revealed clearly by the approximate solution and it is shown how κxxscales with parameters such as the energy density in magnetic fluctuations, mean field strength, particle gyroradius, MHD turbulence correlation length scales, parallel diffusion coefficient, etc. Unlike the integral equation formulation, which is not readily amenable to inclusion in models and numerical codes that require the perpendicular diffusion coefficient explicitly, the approximate model derived here is easily incorporated into, for example, heliospheric cosmic ray modulation models. Finally, the perpendicular diffusion coefficient is used to evaluate (1) the particle acceleration timescale for diffusive shock acceleration at perpendicular shocks and (2) the diffusion coefficient for cosmic ray modulation throughout the heliosphere.

Extensions of the 3‐Dimensional Plasma Transport Code E3D

AbstractOne important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2‐D code packages like B2‐Eirene or UEDGE are under development. A 3‐dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm.The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra‐variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation.

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.

Effects of the Sector Structure of the Interplanetary Magnetic Field on Galactic Cosmic Ray Anisotropy

We study the effects of the sector structure of the interplanetary magnetic field (IMF) on the Galactic cosmic ray (GCR) anisotropy at solar minimum by using Global Network neutron monitor data. The hourly neutron monitor data for 1976 were averaged for the positive (+) and negative (–) IMF sectors (+ and – correspond to the antisolar and solar directions of magnetic field lines, respectively) and then processed by the global survey method. We found that the magnitude of the GCR anisotropy vector is larger in the positive IMF sector and that the phase shifts toward early hours. The derived GCR components Ar, Aθ, and Aϕ for the different + and – sectors are then used to calculate the angle ψ (≈ 46°) between the IMF lines and the Sun–Earth line, the solar wind velocity U (≈ 420 km/s), the ratio of the perpendicular (K⊥) and parallel (K||) diffusion coefficients K⊥/K|| = α (≈ 0.33), and other parameters that characterize the GCR modulation in interplanetary space.

Brownian motion in confinement

This research modifies an earlier approach based on the single-wall reflection method to predict the perpendicular and parallel diffusion coefficients of a Brownian sphere in confinement. The modified version provides predictions that match experimental data reported in the literature more accurately than those provided by other available models, including the linear superposition approximation, the coherent superposition approximation, and Oseen's equation.

Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord.

Anisotropy of water diffusion in axon tracts, as determined by diffusion-weighted MRI, has been assumed to reflect the restriction of water diffusion across axon membranes. Reduction in this anisotropy has been interpreted as degeneration of axons. These interpretations are based primarily on a priori reasoning that has had little empirical validation. We used the experimental advantages of the sea lamprey spinal cord, which contains several very large axons, to determine whether intraaxonal diffusion is isotropic and whether anisotropy is attributable to restriction of water mobility by axon surface membranes. Through the application of magnetic resonance microimaging, we were able to measure the purely intraaxonal diffusion characteristics of the giant reticulospinal axons (20-40 microm in diameter). The intraaxonal apparent diffusion coefficients of water parallel (longitudinal ADC, l-ADC) and perpendicular (transverse ADC, t-ADC) to the long axis were 0.98 +/- 0.06 (10(-3) mm2 sec) and 0.97 +/- 0.11 (10(-3) mm2 sec), respectively. In white matter regions that included multiple axons, l-ADCs were almost identical regardless of axon density in the sampled axon tract. By comparison, t-ADCs were reduced and varied inversely with the number of axons (and thus axolemmas) in a fixed cross-sectional area. Thus, diffusion was found to be isotropic when measured entirely within a single axon and anisotropic when measured in regions that included multiple axons. These findings support the hypothesis that the cell membrane is the primary source of diffusion anisotropy in fiber tracts of the central nervous system.

Transport of cosmic rays in chaotic magnetic fields

The transport of charged particles in disorganized magnetic fields is an important issue which concerns the propagation of cosmic rays of all energies in a variety of astrophysical environments, such as the interplanetary, interstellar and even extragalactic media, as well as the efficiency of Fermi acceleration processes. We have performed detailed numerical experiments using Monte Carlo simulations of particle propagation in stochastic magnetic fields in order to measure the parallel and transverse spatial diffusion coefficients and the pitch angle scattering time as a function of rigidity and strength of the turbulent magnetic component. We confirm the extrapolation to high turbulence levels of the scaling predicted by the quasilinear approximation for the scattering frequency and parallel diffusion coefficient at low rigidity. We show that the widely used Bohm diffusion coefficient does not provide a satisfactory approximation to diffusion even in the extreme case where the mean field vanishes. We find that diffusion also takes place for particles with Larmor radii larger than the coherence length of the turbulence. We argue that transverse diffusion is much more effective than predicted by the quasilinear approximation, and appears compatible with chaotic magnetic diffusion of the field lines. We provide numerical estimates of the Kolmogorov length and magnetic line diffusion coefficient as a function of the level of turbulence. Finally we comment on applications of our results to astrophysical turbulence and the acceleration of high energy cosmic rays in supernovae remnants, in superbubbles, and in jets and hot spots of powerful radiogalaxies.

Stray field gradient NMR reveals effects of hydrogen bonding on diffusion coefficients of pyridine in mesoporous silica

The diffusion of pyridine confined in mesoporous silica MCM-41 (d(pore) = 3.3 nm) was studied with stray field gradient (SFG) NMR diffusometry as a function of the filling factor of the mesopores at room temperature, employing a laboratory-built SFG setup. The translational diffusion of pyridine in MCM-41 is found to be anisotropic and the diffusion parallel to the pores' cylinder axes is much faster than that perpendicular to them. The parallel diffusion coefficient depends strongly on the filling level of the guest liquid inside the pores. For a filling level of 25, which corresponds approximately to a monomolecular layer of pyridine molecules hydrogen bonded to surface-SiOH groups, a parallel diffusion coefficient of D-parallel to = 1.0 X 10(-9) m(2) s(-1) is found, which is slower than the diffusion coefficient of the bulk liquid (D = 1.6 X 10(-9) m(2) s(-1)). For higher filling factors the parallel diffusion coefficient increases and at a filling factor of 85 a diffusion coefficient of D-parallel to = 6.8 X 10(-9) m(2) s(-1) is reached. The perpendicular diffusion coefficient of D-perpendicular to = 3.7 +/- 2.0 X 10(-11) m(2) s(-1) is independent of the filling factor. Employing additional N-15 MAS data for the pyridine inside the mesopores, a microscopic model of the diffusion is proposed, which depends on the exchange of the slowly diffusing hydrogen-bonded surface pyridine molecules with fast-diffusing free pyridine molecules inside the pores. Copyright (C) 2001 John Wiley & Sons, Ltd.