Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, the size, shape and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical results are presented for a representative example of a bianisotropic HCM, namely a Faraday chiral medium. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles.     

Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, the size, shape and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical results are presented for a representative example of a bianisotropic HCM, namely a Faraday chiral medium. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles.     

Quantitative analysis of depolarization of backscattered light by stochastically inhomogeneous dielectric particles

We determine the relationship between the depolarization properties of inhomogeneous particles and the statistical parameters of their internal refractive-index distributions. Our analysis demonstrates that the linear depolarization ratio of backscattered light by an inhomogeneous particle is approximately proportional to both the squared standard deviation and the squared correlation length of the particle's internal refractive-index distribution. We verify this result by conducting rigorous numerical studies using the finite-difference time-domain method. This improved understanding of light depolarization by inhomogeneous structures may enhance polarization-based biomedical optical imaging techniques.     

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.     

Second harmonic generation in composites of ellipsoidal particles with core–shell structure

We study the enhancement of the second-harmonic generation (SHG) coefficient in a random composite consisting of ellipsoidal particles with a core–shell structure in a linear dielectric host. The material making up the ellipsoidal core is assumed to be dielectric, but with a nonlinear susceptibility for SHG. The coating material is assumed to be metallic with a linear susceptibility. The effective SHG coefficient is derived and its expression is related to various local field factors. The numerical calculations of the effective SHG response per unit volume of nonlinear material can be greatly enhanced at certain frequencies. For coated ellipsoidal particles, the core–shell structure and the particle shape allow for tuning of the resonance through the choice of material parameters and/or the ratio of the core to shell volume fraction and the depolarization factor of the particles.     

Tilted and helical columnar phases for an axially symmetric discoidal system

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.     

Particle Sizing Using Frequency Domain Photon Migration

The transport properties of particulate process streams and their final product quality, are directly affected by critical parameters of particle size distribution, f(x), and volume, mass, or number density of particles or dispersed phase droplets. A method is proposed for the potential on-line monitoring of particle size distribution and volume fraction in real time, using frequency-domain photon migration measurements (FDPM). Theory, experimental measurements, and results for the determination of particle size distributions for both a polystyrene latex and a titanium dioxide suspension determined using the photon migration technique are presented. The critical issues associated with the application of photon migration to particulate and dispersed phase processes are discussed, including the effects of interparticle interactions on the transport of light.     

Modelling study on the three-dimensional neutron depolarisation response of the evolving ferrite particle size distribution during the austenite–ferrite phase transformation in steels

The magnetic configuration of a ferromagnetic system with mono-disperse and poly-disperse distribution of magnetic particles with inter-particle interactions has been computed. The analysis is general in nature and applies to all systems containing magnetically interacting particles in a non-magnetic matrix, but has been applied to steel microstructures, consisting of a paramagnetic austenite phase and a ferromagnetic ferrite phase, as formed during the austenite-to-ferrite phase transformation in low-alloyed steels. The characteristics of the computational microstructures are linked to the correlation function and determinant of depolarisation matrix, which can be experimentally obtained in three-dimensional neutron depolarisation (3DND). By tuning the parameters in the model used to generate the microstructure, we studied the effect of the (magnetic) particle size distribution on the 3DND parameters. It is found that the magnetic particle size derived from 3DND data matches the microstructural grain size over a wide range of volume fractions and grain size distributions. A relationship between the correlation function and the relative width of the particle size distribution was proposed to accurately account for the width of the size distribution. This evaluation shows that 3DND experiments can provide unique in situ information on the austenite-to-ferrite phase transformation in steels.     

Absorption and Scattering of Light by Highly Concentrated Two‐phase Flows

The spray cone emerging during an extended metal atomization process (called spray forming) has been investigated in order to quantify the influence of highly concentrated multiphase flows on phase‐Doppler‐anemometry (PDA) measurements. Using this non‐intrusive, optical measurement technique not only the local particle size and velocity distributions of the spray can be obtained but also additional information about the mass flux in the multiphase flow. Since standard phase‐Doppler systems can be easily applied to low concentrated particle systems (spherical particles with smooth surfaces and an optical transparent continuous phase taken for granted) the application of this measurement technique to highly concentrated multiphase flows is more complex. Both the laser light propagating from the PDA device to the probe volume and the scattered one going backward to the PDA receiving system are disturbed by passing the highly concentrated multiphase flow. The resulting significant loss in signal quality especially concerns the measurement of the smaller particles of the spray because of their reduced silhouette (in comparison with the bigger ones). Thus, the detection of the smallest particles becomes partially impossible leading to measurement of a distorted diameter distribution of the entire particle collective. In this study the distortions of the measured distributions dependent on the particle number concentration as well as on the path length of the laser light are discussed.     

Determination of Particle Size Distribution by Par-Tec® 100: Modeling and Experimental Results

Some particle size analyzers, such as the Par-Tec® 100 (Laser Sensor Technology, Redmond, WA, USA), measure the so-called cord length distribution (CLD) as the laser beam emitted from the sensor randomly crosses two edges of a particle (a cord length). The objectives of this study were to develop a model that can predict the response of the Par-Tec® 100 in measuring the CLD of a suspension for spherical and ellipsoidal particles and to infer the actual particle size distribution (PSD) using the measured CLD output. The model showed that the measured CLD is reasonably accurate for the spherical particles. However, this measurement progressively deteriorates as the shape of particles changes from spherical to ellipsoidal with large ratios of major to minor diameters. Experimental results obtained with spherical particles having a normal and a non-normal PSD indicated that the Par-Tec® 100 measurements deteriorate as the PSD deviates from a normal distribution. The information obtained from these experiments also showed that the model can reasonably predict the Par-Tec® response. Use of the inferred PSD rather than the measured CLD made a major improvement in estimating the actual PSD. Mean particle size analysis revealed that the Par-Tec® 100 volume-weighted mean particle size is closest to the unweighted mean particle size measured by sieve analysis.     

基于方向金字塔框架变换的遥感图像融合算法

为了综合利用多光谱遥感图像与全色遥感图像之间的互补信息,提出了一种方向金字塔框架变换(SPFT),并基于此变换提出了一种遥感图像融合算法。具体融合过程是将多光谱图像的每个波段分别与高分辨力全色图像进行融合,首先将高分辨力全色图像与多光谱图像的待融合波段进行直方图匹配,然后对该波段图像以及直方图匹配后的高分辨力全色图像分别进行方向金字塔框架变换分解,融合过程就是对两图像方向金字塔框架变换分解后的系数进行组合,最后对组合后的系数进行方向金字塔框架逆变换即可得到该波段图像与高分辨力全色图像的融合图像。实验结果表明该算法在性能上优于基于亮度-色调-饱和度(1HS)的彩色空间变换以及基于离散小波框架变换(DWFT)的遥感图像融合方法,尤其对源图像之间存在配准误差的情况。     

Measurement of Size,Number Concentration and Velocity of Aerosol Particles using an optical particle counter

An aerosol measurement instrument is presented which allows for the simultaneous measurement of the size distribution, number concentration and velocities of particles. A commercial optical particle counter (OPC) was modified in terms of optics and signal evaluation to provide the required measurement information. The design of this instrument allows the definition of a cubic measuring volume by purely optical means. This is achieved by an aperture/lens system which projects a sharply defined light beam into a stream of aerosol flow. Light scattered from single particles at average angles of 90° is collected by two opposite receiver units, each projecting light on to a separate photomultiplier. The intensity of the scattered light with this instrument is found to be an unambiguous function of the particle size. The total number of particles detected per unit time results in the particle flux. The particle velocity can be calculated, in principle, through the correlation of the signal length and the optical length of the measuring volume, provided that the particles have a straight trajectory through the measuring volume and the measuring volume length in the mean flow direction is well defined. The absence of sharpness in real optical projections effects a border zone of definite length, in which the illumination declines to zero. This leads, together with the low-pass filtering of the particle signals, to an increase in the length of the signal slopes, causing some difficulties in the determination of the signal length. A digital signal evaluation technique was developed that renders possible the clear differentiation between the slope and the kernel region of the signal. The latter represents the motion of particles through the completely illuminated region, which can be a more accurate parameter to define the signal length. In addition to the signal length determination, a cross-correlation technique was tested for its potential to obtain particle velocity. the instrument has two interlaced measuring volumes of nearly the same size, which are shifted for this special application in the main flow direction by 20 μm. The phase difference between the signals from the two photomultipliers, together with the optical distance, yields the particle velocity.     

Spatial Density Distributions and Correlations in a Quasi-one-Dimensional Polydisperse Granular Gas

By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.     

Chord length distributions and small-angle scattering

Chord length distributions describe size, shape and spatial arrangement of geometrical objects (particles). The chord length distribution is in principle proportional to the second derivative of the correlation function of small-angle scattering. It is calculable from a relative measurement of the scattering intensity I(h). In structure research, the characterization of numerous particle systems can be achieved by comparing experimental chord distributions with theoretical ones, provided the latter are available with sufficiently high precision for a lot of fundamental, universal shapes. Both sides of this concept are exemplified: – the step from a relative measurement of the scattering intensity of an isotropic two-phase sample to the chord length distribution (errors in and in , limited h-interval, corresponding to the region (1-2) nm < r in real space, must be observed); as well as the geometric matter of calculation of chord distributions as fingerprints for basic geometric figures, including the non-convex case. Received 15 March 1999 and Received in final form 26 April 2000     

Coarsening and self-organization in dilute diblock copolymer melts and mixtures

This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns.We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.     

Phase transitions in a system of unstable particles

A study is reported of phase separation in a system of particles created at a constant rate and having a finite lifetime. It is shown that (1) phase separation is possible if the particle lifetime exceeds a certain critical value, (2) the particle-density difference between the phases depends on particle lifetime, and (3) the correlation function in the two-phase region oscillates (with damping) as a function of spatial coordinates, which implies correlation between the phase locations. Fiz. Tverd. Tela (St. Petersburg) 40, 741–745 (April 1998)     

Optical equivalence of isotropic ensembles of ellipsoidal particles in the Rayleigh-Gans-Debye and anomalous diffraction approximations and its consequences

Light scattering by isotropic ensembles of ellipsoidal particles is considered in the Rayleigh-Gans-Debye approximation. It is proved that randomly oriented ellipsoidal particles are optically equivalent to polydisperse randomly oriented spheroidal particles and polydisperse spherical particles. Density functions of the shape and size distributions for equivalent ensembles of spheroidal and spherical particles are presented. In the anomalous diffraction approximation, equivalent ensembles of particles are shown to also have equal extinction, scattering, and absorption coefficients. Consequences of optical equivalence are considered. The results are illustrated by numerical calculations of the angular dependence of the scattering phase function using the T-matrix method and the Mie theory.     

Particle Size Distribution Analysis of Industrial Colloidal Slurries using ultrasonic spectroscopy

Several solid-liquid suspensions containing submicron particles at moderate to high concentrations (5 to 50 volume percent) are encountered in industrial slurry processing. Measurements of ultrasonic attenuation spectra are used in a newly developed AcoustoPhor particle analysis system to get particle size distributions of such colloidal suspensions. This paper deals with the performance evaluation of the AcoustoPhor system. The automated ultrasonic spectrometer component of the AcoustoPhor system was tested using a reference silicone liquid for its accuracy and precision. The particle size distribution (PSD) estimation capabilities were evaluated using a set of well-dispersed slurries covering a wide range of particle concentrations. Sensitivity to process variations was evaluated in field tests at a pigment manufacturing plant. The AcoustoPhor system appears to be capable of providing reliable PSD data for inorganic pigment slurries with particle diameters ranging from 0.01 to 100 micrometers at particle concentrations as high as 50 volume percent.     

Scaling laws for the spatial distributions of the plasma parameters in the positive column of a dc oxygen discharge

Comprehensive self-consistent simulations of the positive column plasma of a dc oxygen discharge are performed with the help of commercial CFDRC software (), which enables one to carry out computations in an arbitrary 3D geometry using fluid equations for heavy components and a kinetic equation for electrons. The main scaling laws for the spatial distributions of charged particles are determined. These scaling laws are found to be quite different in the parameter ranges that are dominated by different physical processes. At low pressures, both the electrons and negative ions in the inner discharge region obey a Boltzmann distribution; as a result, a flat profile of the electron density and a parabolic profile of the ion density are established there. In the ion balance, transport processes prevail, so that ion heating in an electric field dramatically affects the spatial distribution of the charged particles. At elevated pressures, the volume processes prevail in the balance of negative ions and the profiles of the charged particle densities in the inner region turn out to be similar to each other.     

Transition radiation emitted by a particle moving along the axis of a perfectly conducting conical surface

The spatial field distribution is determined for the transition radiation emitted by a relativistic particle moving along the axis of a perfectly conducting circular conical surface with a fixed apex. Emission from particles moving away from and towards the apex is examined. Expressions are obtained that can be used to calculate the angular distribution of radiation intensity for various apex angles between 0 and π. Significant differences are demonstrated between the spatial distributions of radiation generated by outgoing and incoming particles.