Anisotropic light diffusion: an oxymoron?

Light propagation in anisotropic random media is studied in the steady-state and time domains. Solutions of the anisotropic diffusion equation are compared to results obtained by the Monte Carlo method. Contrary to what has been reported so far, we find that even in the "diffusive regime" the anisotropic diffusion equation does not describe correctly the light propagation in anisotropic random media.     

Direct imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals

We visualize exciton diffusion in rubrene single crystals using localized photoexcitation and spatially resolved detection of excitonic luminescence. We show that the exciton mobility in this material is strongly anisotropic with long-range diffusion by several micrometers associated only with the direction of molecular stacking in the crystal, along the b axis. We determine a triplet exciton diffusion length of 4.0 ± 0.4 μm from the spatial exponential decay of the photoluminescence that originates from singlet excitons formed by triplet-triplet fusion.     

Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes

We developed a new monotone finite volume method for diffusion equations. The second-order linear methods, such as the multipoint flux approximation, mixed finite element and mimetic finite difference methods, are not monotone on strongly anisotropic meshes or for diffusion problems with strongly anisotropic coefficients. The finite volume (FV) method with linear two-point flux approximation is monotone but not even first-order accurate in these cases. The developed monotone method is based on a nonlinear two-point flux approximation. It does not require any interpolation scheme and thus differs from other nonlinear finite volume methods based on a two-point flux approximation. The second-order convergence rate is verified with numerical experiments.     

Deuterium stimulated-echo-type PGSE NMR experiments for measuring diffusion: application to a liquid crystal.

The accessibility of molecular self-diffusion coefficients in anisotropic materials, such as liquid crystals or solids, by stimulated-echo-type (2)H PGSE NMR is examined. The amplitude and phase modulation of the signal in the stimulated-echo-type sequence by the static quadrupole coupling during the encoding/decoding delays is suppressed by adjusting the pulse flip angles and the phase cycle. For nuclei that experience both nonnegligible quadrupole and dipole couplings, the application of magic echoes during the evolution periods of stimulated echo is demonstrated as a helpful technique in the case of slow diffusion. These findings are demonstrated by experimental results in the thermotropic liquid crystal of partially deuterated 8CB. The obtained diffusion coefficients are also compared to data obtained by a (1)H homonuclear-decoupling-type PGSE NMR method in the same material.     

Stabilizing effect of anisotropic thermal diffusion on the ablative Rayleigh-Taylor instability

Linear theory of the ablative Rayleigh-Taylor instability in anisotropic diffusive materials is presented. This analysis indicates that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. In the context of inertial confinement fusion, it is shown that anisotropic diffusion can be achieved using a laminated ablator made of successive layers of different diffusive properties. Numerical simulations confirm the theoretical predictions and indeed exhibit a significant stabilization of the ablation front for laminated ablators.     

Angular anisotropy of group averaged absorption coefficient and its effect on the behavior of diffusion approach in radiative transfer

Multi-group method, a generally accepted procedure for handling the radiative transfer equation, is accompanied by the group averaged absorption coefficient, and actually the coefficient is angularly anisotropic. In the paper, we present a brief discussion how the anisotropy of the coefficient makes the material absorb photons at different rate in each direction, also study its effect on the diffusion approach by comparing the results calculated using multi-group diffusion and multi-group discrete ordinate SN for the isotropic and anisotropic group averaged absorption coefficients respectively, and find that the anisotropy deteriorates the behavior of diffusion approach.     

Diffusion of particles over strongly anisotropic surface with traps

We investigate surface diffusion in a system of particles adsorbed on a two-dimensional strongly anisotropic lattice. There are two kinds of the lattice sites - ordinary sites and deep traps. Particles adsorbed in the ordinary sites can migrate over the surface, but particles adsorbed in traps are immobile. These particles do not move over the surface and they obstacle also the mobile particles migration (surface defects). Using kinetic Monte Carlo simulations we obtained coverage dependencies of the tracer, jump, and chemical diffusion coefficients. The coefficients are rather sensitive to the defect concentration. Even small admixture of the defects decreases drastically the fast diffusion. The effect is rather specific: strong dependence of the pre-exponential factor on the defect concentration and almost independent activation energy. The defect influence on the slow diffusion is weak. It results in strong decreasing of the surface diffusion anisotropy with the defect concentration. Such unusual behavior of the diffusion coefficients was observed in many experimental investigations of the surface diffusion of lithium, cesium, potassium, and strontium over strongly anisotropic W(1 1 2) and Mo(1 1 2) planes. It was shown that this specific behavior arises exclusively due to the surface anisotropy, and does not depend on the lateral interaction between the particles.     

Diffusion of two-dimensional excitons in pseudo-random potentials embedded in quantum well structures

Diffusion processes of excitons are investigated in quantum well structures where AlAs islands are embedded at the center of wells. The diffusion constant is measured by the transient grating method. It is found that with the AlAs insertion the diffusion is suppressed strongly at low temperatures and is anisotropic. Its dependence on carrier density is also revealed. A model calculation is discussed and compared with the experiment.     

Liouville mode in gauge/gravity duality

We establish solutions corresponding to AdS\(_4\) static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems.     

Modelling of anisotropic sintering in crystalline ceramics

We present a model that describes anisotropic shrinkage during sintering in a powder compact of aligned, elongated particles by deriving the anisotropic sintering stress and the anisotropic generalized viscosity as a function of material and geometric parameters. The powder compact consists of elongated particles, which are perfectly aligned and simply packed with elliptical pores at all the quadra-junctions between the particles. The model considers mass transport by grain boundary diffusion and surface diffusion. Shrinkage rates are calculated for a variety of geometries and are compared to kinetic Monte Carlo simulations.     

Intensity correlations in filtered phase-diffusing light

Light undergoing phase diffusion displays a Lorentzian line shape: Here, electrical filtering techniques are used to examine the correlations among different spectral regions under this line shape. The experiment involves delayed self-heterodyne measurements of the output from a single-mode semiconductor laser. Two filters are tuned to isolate the signal contributions from opposite wings of the spectrum, and the transmitted intensities are shown to be strongly correlated in some regimes and strongly anticorrelated in others.     

Variational estimates of the diffusion coefficient of cosmic rays in a random magnetic field

A variational method is used to obtain estimates of the effective particle transport coefficients in a random static magnetic field. The particle propagation is described by an anisotropic diffusion equation. The diffusion coefficient parallel to the local magnetic field is much greater than the transverse diffusion coefficient. For large-scale magnetic-field variations the diffusion is described by effective coefficients. The variational approach can be used to find the effective parallel and perpendicular diffusion coefficients. It was shown that the instability growth rate of the magnetic field lines determines the upper estimate of the effective transverse diffusion coefficient. Zh. éksp. Teor. Fiz. 114, 398–405 (August 1998)     

Pulsed-Field-Gradient NMR Study of Anisotropic Molecular Translational Diffusion in nOCB Liquid Crystals

Pulsed-field-gradient nuclear magnetic resonance (NMR) combined with magic echo decoupling is applied to study anisotropic diffusion in samples with strong static dipolar spin interactions. The approach, due to its moderate demands on the NMR hardware, can be implemented on standard commercial equipment for routine diffusion studies of liquid crystals. Using a microimaging probe, measurement of diffusion in arbitrary spatial direction is possible. Hence, the principal components of the diffusion tensor are directly obtained. Anisotropic diffusion is investigated in the thermotropic mesophases of a homologous series of nOCB liquid crystals and an analogous compound with hydroxyl groups. The geometric average diffusion coefficient changes continuously at the isotropic–nematic phase transition. Experimental data are described in terms of the molecular translation models in the nematic phase and for the second-order nematic–smectic A phase transition. The diffusion anisotropy is higher for the sample with terminal hydroxyl groups suggesting significant molecular association via hydrogen bonding.     

Surface mass transport of Ag and In on vicinal Si(111)

Mass transport of Ag and In on vicinal Si(111) has been investigated by scanning Auger microscopy (SAM). Highly anisotropic surface diffusion and surface electromigration due to direct current were observed for Ag and In adatoms on 0°−, 0.5°−, 3°− and 6°−off vicinal Si(111) surfaces. The diffusion on the intermediate layer is strongly enhanced in the direction parallel to the step edge for Ag adatoms, while it is remarkably suppressed in the direction perpendicular to the step edge for In adatoms. The activation energy of the diffusion for the Ag adatoms ranged between 0.81 and 1.3 eV, while that for In adatoms increased from 0.31 to 0.66 eV with increasing the vicinal angle. The anisotropic diffusion transport is explained in terms of the step structure and the difference in the binding energy at the step site and the terrace site.     

Interface formation of iron on In-terminated InAs(001)

In situ scanning tunneling microscopy (STM) is used to investigate the nucleation and initial growth of iron on InAs(001) (4×2)/c(8×2) at room temperature and at 200 °C. Sequences of STM frames show the development at a specific location in the different stages of interface formation. At room temperature, initially 0.5 monolayer of iron grows in the form of small anisotropic clusters, which form long chains along [110] induced by the InAs substrate reconstruction. Further growth proceeds with the formation of isotropic 3d islands, resulting in a granular overlayer at higher coverages. Coalescence of the individual grains is strongly suppressed. At 200 °C the anisotropic chain structure is absent, but rectangular islands grow from the beginning. A decomposition of the substrate indicates intermixing. Room-temperature deposition followed by annealing at 200 °C leads to closed iron layers that are interspersed with pinholes, allowing diffusion of substrate material to the surface . PACS 68.37.Ef; 68.35.Ct; 68.55.Ac     

The influence of a static magnetic field on the fluctuation superconductivity

We study the influence of an external static magnetic field on the additional conductivity due to fluctuation superconductivity for bulk material and for thin films with the magnetic field normal to the film surfaces. Only a weak-coupling superconductor in the dirty limit is considered. This additional conductivity turns out to be anisotropic in general.     

Diffusion thermopower of (Ga,Mn)As/GaAs tunnel junctions

We report the observation of tunneling anisotropic magnetothermopower, a voltage response to a temperature difference across an interface between a normal and a magnetic semiconductor. The resulting voltage is related to the energy derivative of the density of states in the magnetic material, and thus has a strongly anisotropic response to the direction of magnetization in the material. The effect will have relevance to the operation of semiconductor spintronic devices, and may indeed already play a role in correctly interpreting the details of some earlier spin injection studies.     

Collective diffusion in a two-dimensional liquid composed of Janus particles

The collective diffusion of anisotropic particles in liquids plays a crucial role in many processes, such as self-assembly. The patchy particle, which is usually nearly spherical in shape, is an important anisotropic particle with different properties from other anisotropic particles like the ellipsoid liquid crystal particles. In the present study, molecular dynamics simulations are performed to study the collective diffusion of a two-dimensional anisotropic liquid system composed of Janus particles. The static structures and diffusion behaviours of anisotropic and isotropic Lennard-Jones liquids are compared. The long-time diffusion behaviour of an anisotropic liquid of nearly spherical Janus particles is found to be similar to that of an isotropic liquid because the orientation of the particles disappears over long-term averaging. The anisotropic properties of the Janus particles are mainly reflected in the spatial correlation of particle orientations and mid-time diffusion behaviour. The difference between nearly spherical anisotropic particles and rod-like particles is also discussed in this paper.