Percolation theory and the conductivity of random close packed mixtures of hard spheres

The conductivity of random close packed mixtures of conducting and insulating spheres has been measured. The composition dependence and the critical percolation density are similar to what has been observed in crystalline systems.     

Orientational structure in a monolayer of dipolar hard spheres

Off-lattice Monte Carlo simulations have been employed to investigate the orientational structure in a quasi-2-dimensional system of dipolar hard spheres covering both the fluid and crystal regions. The study includes pattern formation resulting from the competition of the long range dipolar interaction with localized interactions typical of those encountered in thin magnetic films.     

Orientational structure of dipolar hard spheres near a hard neutral wall

Spherical boundaries are used in a Monte Carlo simulation to calculate the angular structure of dipolar hard spheres near a neutral hard wall.     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.     

Dense random packings of hard and compressible spheres

The sublattices of the tetrahedrally co-ordinated random network of Connell and Temkin are related to the dense random packing of equal spheres. Thus, by relaxation of the atomic co-ordinates of the former, the dependence of the pair distribution function and packing fraction of the latter on sphere compressibility can be investigated. The results are compared with experimental data on NiP alloys.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.     

Noncollinear magnetic order in quasicrystals

Based on Monte Carlo simulations, the stable magnetization configurations of an antiferromagnet on a quasiperiodic tiling are derived theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the superposition of geometric frustration with the quasiperiodic ordering leads to a three-dimensional noncollinear antiferromagnetic spin structure. The structure can be divided into several ordered interpenetrating magnetic supertilings of different energy and characteristic wave vector. The number and the symmetry of subtilings depend on the quasiperiodic ordering of atoms.     

Noncollinear orientation of external magnetic field and flux lines penetrating an isotropic hard superconductor

Penetration by Abrikosov flux lines of an isotropic hard superconductor in the critical state induced by changes in the orientation of external magnetic field has been theoretically investigated. The analysis has been based on the microscopic nonlocal model taking into account forces of bulk and surface pinning, alongside magnetic forces of interaction of the row of penetrating vortices with existing flux lines, Meissner currents, and vortex images. New vortices penetrate a superconductor only when the angle through which the field is rotated is larger than a certain critical value. It has been determined that the alignment of entering vortices is essentially different from that of the applied magnetic field. The feasibility of detecting noncollinearity effects is discussed. Zh. éksp. Teor. Fiz. 114, 1804–1816 (November 1998)     

Noncollinear magnetic ordering in a magnetic dimer supported on a metallic substrate

Self-consistent electronic structure calculations for a magnetic dimer supported on a metal surface are performed on the basis of the microscopic Hamiltonian for itinerant electrons. The possibility of a noncollinear ground state in the absence of spin-orbit interaction and magnetic frustration is shown. The effective exchange interaction of moments is determined by the number of quasi-localized d-electrons per atom and, in general, is not described by the Heisenberg model.     

Noncollinear states in a chain of single-domain magnetic particles

The ground state of a chain of single-domain magnetic particles has been theoretically analyzed. The conditions under which this state corresponds to a noncollinear structure in zero external magnetic field are determined. Such noncollinear states are due to the features of the long-range magnetostatic interactions in the systems without the center of inversion.     

Spectropolarised ray-tracing simulations in densely packed particulate medium

Light scattering from particulate medium is simulated using the Monte Carlo ray-tracing technique. The medium is modelled as a randomly packed medium of ellipsoidal grains with stochastically rough surfaces, with an optional thin coating. Optical properties are modelled using a wavelength-dependent complex refractive index and taking Fresnelian reflections and refractions from the interfaces. The size and shape of the grains are assumed to be large and smooth enough for geometric optics to apply reasonably well.The ray-tracing technique uses parallel, weighted rays for computing simultaneously over a wide wavelength spectrum and a small roughness range, and scaling to obtain a large range of sizes and absorbities simultaneously. Polarisation is fully accounted for. The multiobservation technique is effectively used at each scattering point. The scattering from thinner sample layers is also received as a subresult.Simulations are run for a set of model samples to study the effects and sensitivities regarding the values of certain parameters. It has been found that the size and composition of the grains affect the scattering in a unique and invertible way. The shape of the grain causes similar significant effects that must certainly be taken into account if any accuracy is required, although inverting for the shape is difficult without further constraints. The packing density has a small but observable effect. Polarisation can be used to study the composition of low-albedo objects.     

Noncollinear magnetic states in iron-chromium-type multilayers

A model of noncollinear magnetic ordering in Fe/Cr-type multistructures was suggested. The model was based on the idea of charge (and, as a consequence, spin) density redistribution near a metal-metal interface. A peculiar state of the whole structure characterized by strong short-range antiferromagnetic ordering in the interlayer and a pronounced dependence of magnetic characteristics on the properties of the boundary between iron and chromium layers was shown to be formed in a certain temperature range. Inhomogeneous antiferromagnetic structures with a vector order parameter were found, and the effective exchange coupling between neighboring iron layer moments was calculated using the Ginzburg-Landau expansion of the thermodynamic potential. The results were used to discuss the experimental data on Fe/Cr superlattices obtained in neutron scattering and magnetization measurements.     

A first-order phase transition defines the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the “freezing point” in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the “entropy of fusion”. This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.     

Wave propagation through a dielectric layer containing densely packed fibers

This paper presents the theoretical formulation for the propagation of electromagnetic wave through a dielectric layer containing a random dense distribution of fibers. The diameter of the fibers is comparable to the inter-fiber spacing and wavelength of the incident radiation, but is much smaller than the thickness of the layer. Discontinuity of refractive index across the boundaries of the dielectric layer resulted in multiple internal reflection of both the primary source wave and the scattered waves. As a result the incident waves on the fibers consist of the multiply-reflected primary waves, scattered waves from other fibers, and scattered-reflected waves from the boundaries. The effective propagation constant of the dielectric fiber layer was developed by utilizing the Effective field-Quasicrystalline approximation. The influence of the refractive index of the dielectric medium on the radiative properties of a dense fiber layer was examined by means of numerical analyses.     

Correlation functions for inhomogeneous magnetic field in random media with application to a dense random pack of spheres

In porous media subject to applied magnetic field, the internal field arises out of susceptibility contrast of the constituents. We have examined the spatial inhomogeneity of the internal fields in a random pack of spheres using numerical computation. We find that the pair-correlation function of the internal field (K2) is a close approximation to the structure factor of the material, thus K2 can be used to characterize pore geometry. The magnetic length scale LambdaM exhibited in K2 is shown to be related to the fluid transport in the medium.