Anisotropy and multiple scattering in thick mammalian tissues

A dual-channel Mach-Zehnder interferometer using heterodyne detection allowed us to measure simultaneously parallel and perpendicular polarization components through various mammalian tissues at a wavelength of lambda = 633 nm. By contrast with liver tissue, squeletic muscles of a few millimeters thickness exhibit strong anisotropic properties that change the direction of the linear polarization of the light. This rotation of the initial plane of polarization is to be distinguished from the depolarization that is due to the multiple light scattering that goes along with large temporal fluctuations. Complementary photos under linearly polarized light illustrate the behavior difference between liver (isotropic medium) and muscle (anisotropic medium).     

Sizing of colloidal particles with light scattering: corrections for beginning multiple scattering

Static light scattering is widely used for sizing of particles with radii in the range of 50 nm up to several micrometers. These experiments usually require very low particle concentrations (<10(-4)) for prevention of multiple scattering. As a consequence, nonabsorbing samples that are suited for light-scattering investigations must be transparent so that the transmittance of the incident light is typically above 95%. Investigations of less translucent samples require corrective terms for the beginning of multiple scattering to retrieve the particle-size distribution successfully. We applied a computationally convenient first-order approximation for the multiple-scattering problem that has Hartel's approach in its first steps. When incorporated into our inversion technique, this approximation functions well for samples with transmittances above 30%. We present examples of applications to experimental data.     

Motions of charged particles in plasmas

The motion of a single charged particle in magnetic and electric fields B and E is described by the basic non-relativistic equation of motion in which radiation damping is neglected.

With emphasis on vector methods, data are obtained for the drift-free reference case of motion in a circular helix, and then the drift velocity perpendicular to B due to electric field perturbation of the circular case is used to obtain the familiar gravitational and curved magnetic line drifts. Application of the gravitational drift to the plasma physics Rayleigh-Taylor instability is examined critically in the light of information which can be obtained from the macroscopic equation of motion for a plasma in a magnetic field.

For a spatially perturbed magnetic field a guiding centre treatment using the standard orthogonal curvilinear co-ordinate system of differential geometry yields, after time averaging, the first-order Alfvén and curvature drifts, the latter being in agreement with the result obtained less rigorously from the electric drift velocity. The magnetic field geometry is described in terms of an extended set of Frenet-Serret partial derivatives which involve six scalar quantities, five of which are independent when a scalar magnetic potential exists. After time averaging there also exists a first order velocity component of unusual form parallel to B. For the usually encountered case of B irrotational, this component vanishes.

The three equations of motion for the components of the particle velocity are also obtained in terms of this curvilinear co-ordinate system, and when time averaged the equation of motion for the particle velocity component parallel to B enables the spatial adiabatic invariance of a spiralling particle's magnetic moment to be rapidly established.

The case of B dependent on the time, which can lead to radial compression of a plasma, is discussed from drift and non-drift view points, and the difference between Larmor's frequency and the gyrofrequency is emphasized. A simple microscopic treatment of the polarization drift is also included.

Finally the historical and mathematical significance of adiabatic invariance is discussed, with particular reference to the magnetic moment in plasma physics.     

The interaction between charged dust particles in a plasma

A solution to the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles, considered as Debye atoms forming a Debye molecule, is studied by numerical methods. It is demonstrated that attractive forces between the particles arise when two conditions are satisfied. First, the Debye screening radius, corresponding to the electron density at a half average spacing between particles, must be equal to approximately half of this distance. In this case, the attraction arises at a distance equal approximately to the average spacing between particles. Second, charges of one sign must be concentrated predominantly on the particles. Should the particles possess only a small fraction of charges of one sign, they will repulse at any distance. Estimates of the electrostatic pressure and surface tension in a gas of dust particles are obtained.     

On the theory and simulation of multiple Coulomb scattering of heavy-charged particles

The Moliere theory of multiple Coulomb scattering is modified to take into account the difference between processes of scattering off atomic nuclei and electrons. A simple analytical expression for angular distribution of charged particles passing through a thick absorber is found. It does not assume any special form for a differential scattering cross section and has a wider range of applicability than a gaussian approximation. A well-known method to simulate multiple Coulomb scatterings is based on treating 'soft' and 'hard' collisions differently. An angular deflection in a large number of 'soft' collisions is sampled using the proposed distribution function, a small number of 'hard' collision are simulated directly. A boundary between 'hard' and 'soft' collisions is defined, providing a precise sampling of a scattering angle (1% level) and a small number of 'hard' collisions. A corresponding simulating module takes into account projectile and nucleus charged distributions and exact kinematics of a projectile-electron interaction.     

Clustering of charged particles in isotropic turbulence

A statistical model is given of the formation of ordered structures (clusters) in a homogeneous isotropic turbulent field. The suggested model is based on the kinetic equation for the probability density function of relative velocity of a pair of particles. The solution of the problem is treated for a steady-state rarefied system of dispersed particles in view of pair interaction.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 908–916.Original Russian Text Copyright © 2004 by V. M. Alipchenkov, L. I. Zaichik, and O. F. Petrov.     

基于拉伸振动精确化理论求解含孔厚板弹性波散射问题

针对采用弹性力学平面问题求解波动/振动时常产生较大误差的问题,基于厚板拉伸振动精确化方程,采用复变函数方法对含孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。给出了含椭圆孔厚板拉压弹性波散射与动应力集中的数值结果。研究结果表明:动应力集中系数与分布取决于入射波数、平板厚度、椭圆偏心率等无量纲化参数。     

Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams

In this paper, we present an efficient numerical method for the simulation of multiple scattering by random discrete particles illuminated by focused Gaussian beams with arbitrary incidence. Specifically, the Davis first-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The surface integral equations are applied to formulate the scattering problems involving multiple discrete particles with a random distribution and are numerically discretized by the method of moments. The resultant matrix equation is solved by employing the characteristic basis function method based on the use of macrobasis functions constructed according to the Foldy-Lax multiple scattering equations. Since this method only requires the solution of small-size matrix equations associated with isolated particles and it is also readily parallelized, the computational burden can be significantly relieved. Some numerical results are included to illustrate the validity of the present method and to show the scattering behaviors of random discrete particles when they are illuminated by focused Gaussian beams.     

Quasi-stationary distribution of relativistic particles in a bent crystal

It is shown that a quasi-stationary distribution of the transverse energies of relativistic particles (protons) moving in a bent crystal has a characteristic width of less than a few thousandths of an electron-volt.     

Theory of multiple scattering in a fractal medium

An analysis is made of multiple scattering of particles whose ranges have a power-law distribution corresponding to a fractal medium. The small-angle approximation is used to derive an expression for the angular distribution of particles which have traversed a specific path. The results of numerical calculations are presented. Pis’ma Zh. Tekh. Fiz. 25, 34–40 (June 12, 1999)     

Electromagnetic scattering of high-permittivity particles on a substrate

We contribute to the study of the optical properties of high-permittivity nanostructures deposited on surfaces. We present what we believe is a new computational technique derived from the coupled-dipole approximation (CDA), which can accommodate high-permittivity scatterers. The discretized CDA equations are reformulated by use of the sampling theory to overcome different sources of inaccuracy that arise for high-permittivity scatterers. We first give the nonretarded filtered surface Green's tensor used in the new scheme. We then assess the accuracy of the technique by comparing it with the standard CDA approach and show that it can accurately handle scatterers with a large permittivity.     

Attenuation of an electromagnetic wave by charged dust particles in a sandstorm

We calculate the light scattering properties of the partially charged dust particles with the Mie theory for electromagnetic waves with different frequencies, and the attenuation coefficients of an electromagnetic wave propagating in a sandstorm are also calculated. The results show that the electric charges distributed on the sand surface have a significant effect on the attenuation of the electromagnetic wave, especially for a frequency lower than 40 GHz, and attenuation coefficients increase with the magnitude of charges carried by the dust particles (expressed by the charge-to-mass ratio in this paper). For the higher frequency electromagnetic wave, such as visible light, the effect of charges carried by sand particles on its attenuation is very little, which can be ignored.     

Longitudinal dynamics of a nonrelativistic bunch of charged particles in a traveling wave field

The longitudinal dynamics of a nonrelativistic bunch of charged particles in a traveling wave field has been studied. A Lagrange function for this motion is constructed and the Lagrange equation describing longitudinal envelopes of the bunch is derived.     

Collisionality in an ensemble of identical charged particles in a closed magnetic trap

A strict proof of the theorem of infinite collisionality in an ensemble of identical charged particles in a closed magnetic trap is presented.     

Role of multiple scattering in cross-correlated light scattering with a single laser beam

Previous systems for measuring cross-correlated light scattering by small particles suspended in a liquid with multiple-scattering suppression have illuminated the particles with two laser beams. It is shown that multiple-scattering suppression should also occur in cross correlation for a system that employs a single laser beam and two closely spaced detectors with wide fields of view. The single-scattering, double-scattering, and single-double-scattering cross-term contributions to the intensity cross-correlation function are calculated. It is found that the two cross terms, when added together, are unimportant for both autocorrelation and cross correlation. The amplitude of the double-scattering term can be greatly diminished by judicious detector spacing because the spatial coherence area in the detector plane for double scattering is much smaller than that for single scattering.