From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model

We consider a system of non-interacting charged particles moving in two dimensions among fixed hard scatterers, and acted upon by a perpendicular magnetic field. Recollisions between charged particles and scatterers are unavoidable in this case. We derive from the Liouville equation for this system a generalized Boltzmann equation with infinitely long memory, but which still is analytically solvable. This kinetic equation has been earlier written down from intuitive arguments.     

A study of the reduction of wave packets by simulation

Following the many-Hilbert-spaces theory of measurement by Machida and Namiki, it is possible to numerically simulate the quantum process of the reduction of wave packets, based on a model plausibly specifying Hilbert spaces. In neutron interferometry experiments such as those done by the Vienna group, each neutron belongs to a Hilbert space. When an interferometer environment is defined and neutrons allowed to interact with it, the degree of visibility degradation is calculated depending on the effectiveness of the interaction. The pile-up of numerous neutrons may or may not make an interfering pattern, depending on whether their interaction with the system is slight enough not to disperse or strong enough to disperse their phase differences after superposition. Thus it is shown that complete disappearance of visibility, i.e., reduction of wave packets, is expected for an infinitely large number of scatterers and/or an infinitely strong interaction, experienced by those neutrons.     

New theorems for bianisotropic media

The general volume equivalence theorem for bianisotropic scatterers is presented, where the equivalent electric and magnetic currents are determined by a pair of coupled vector integral equations. Moreover, using the general volume equivalence theorem and conventional image principle, image theory is developed for a bianisotropic body over an infinite perfect electric or magnetic conducting ground plane.     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

Longitudinal Optical Fields in Light Scattering from Dielectric Spheres and Anderson Localization of Light

Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to obtain a relatively low longitudinal field together with a strong resonant scattering efficiency. Therefore, random arrangements of structured (hollow or coated) spheres may be promising three‐dimensional disordered materials for reaching Anderson localization of light.     

Scattering of an unpolarized Bessel beam by spheres

The scattering process of an unpolarized Bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized Bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized Bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the Bessel beam.     

Solution of the three-dimensional inverse acoustic scattering problem on the basis of the Novikov-Henkin algorithm

A theoretical study of the practical abilities of the Novikov-Henkin algorithm, which is one of the most promising algorithms for solving three-dimensional inverse monochromatic scattering problems by functional analysis methods, is carried out. Numerical simulations are performed for model scatterers of different strengths in an approximation simplifying the reconstruction process. The resulting estimates obtained with the approximate algorithm prove to be acceptable for middle-strength scatterers. For stronger scatterers, an adequate reconstruction is possible on the basis of a rigorous solution.     

Homogenization theory for designing graded viscoelastic sonic crystals

In this paper,we propose a homogenization theory for designing graded viscoelastic sonic crystals(VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material.We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC.The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement.According to the relation of the effective loss factor to the filling fraction,a graded VSC plate is easily and quickly designed.Then,the graded VSC may have potential applications in the vibration absorption and noise reduction fields.     

Rayleigh approximation for axisymmetric scatterers

The Rayleigh approximation is known to be designed only for small ellipsoidal scatterers. We suggest an approach that allows one to find a simple, often analytical, long-wavelength approximation for nonellipsoidal particles. We apply the approach to axisymmetric scatterers and utilize Chebyshev particles to study the main properties of the obtained approximation. To a certain degree, it can be considered as an extension of the Rayleigh approximation to nonspheroidal scatterers.     

Hot Scatterers and Tracers for the Transfer of Heat in Collisional Dynamics

We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes. We study their ergodic properties in details and provide a useful formula for the cumulant generating function of the time integrated energy current. We observe that out of thermal equilibrium, the generating function is not analytic. When the set of temperatures of the scatterers is fixed by the condition that in average no energy is exchanged between the scatterers and the system, different behaviours may arise. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, the thermal conductivity is interpreted as a frequency of collision between tracers and scatterers.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Electronic motion in a model solid of short range potentials

The motion of an electron moving in a model solid which consists of an array of very short range scatterers is considered. This system introduces simplifications because the detailed nature of the individual scatterers enters in only a very simple fashion. The theory is developed for an arbitrary array of short range potentials and is then specialized to a periodic system. (Both infinite and semiinfinite [surface] cases are discussed.) The case of a system of periodically positioned scatterers, the inexactly known strengths of which are described by a Lorentzian distribution, is also considered. Finally, the theory is applied to the case of an electron, under the influence of a rational magnetic field, moving amid a periodic array of short range potentials.     

Scattering by acoustic boundary scatterers with small wave sizes and their reconstruction

The scattering efficiencies of hard and soft cylindrical scatterers are compared using the Novikov-Grinevich-Manakov functional algorithm designed to reconstruct two-dimensional scatterers. The existence of a rigid relationship between the amplitude and phase of the wave scattered by a quasi- point-like scatterer and by scatterers with small wave sizes in the form of a soft cylinder, a soft sphere, and an air bubble in a liquid is confirmed by numerical simulations.     

Acoustic anechoic layers with singly periodic array of scatterers: Computational methods,absorption mechanisms,and optimal design

The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incidence. The reflection characteristics of the anechoic layers with cavities and locally resonant scatterers are discussed. The backing is a steel plate followed by an air half space. Under this approximate zero transmission backing condition, the reflection reduction is induced by the absorption enhancement. The absorption mechanism is explained by the scattering/absorption cross section of the isolated scatterer. Three types of resonant modes which can induce efficient absorption are revealed. Due to the fact that the frequencies of the resonant modes are related to the size of the scatterers, anechoic layers with scatterers of mixed size can broaden the absorption band. A genetic optimization algorithm is adopted to design the anechoic layer with scatterers of mixed size at a desired frequency band from 2 kHz to l0 kHz for normal incidence, and the influence of the incident angle is also discussed.     

中红外散射的基质折射率效应研究

本文利用Mie散射理论对中红外波段三种不同类型散射体的散射和消光进行了研究,发现基质在三种不同类型散射体的散射和消光中所起作用完全不同。对于无吸收的高折射率散射体,基质折射率越大面积散射比(或面积消光比)越低;对于反常色散散射体,基质折射率越大面积散射比和面积肖光比越高;而对于金属散射体,基质折射率的大小对于散射和消光影响极小。     

Density of states in the presence of a strong magnetic field and random impurities

A supersymmetric formalism is used to rederive a recent beautiful result of Wegner concerning the density of state of an electron gas in the presence of a strong magnetic field and impurities. The derivation is simple and applicable to any (local) distribution of scatterers. Explicit formulae are given in two dimensions. A Poisson distribution of scatterers leads to an interesting condensation phenomenon when the magnetic field is increased.     

Free Path Lengths in Quasi Crystals

The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann–Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law.     

Effects of size and arrangement of virtual transducer on photoacoustic tomography

In this paper, we investigate the effects of the relative size and arrangement of a virtual transducer on the image quality in limited-view photoacoustic tomography. A virtual transducer refers to the acoustic scatterers used to reflect photoacoustic waves and improve the images reconstructed from incomplete PA signal. Size and spatial arrangement determine the performance of the virtual transducer. In this study, the scatterers utilized as virtual transducers are arranged in different manners, such as on a straight line or on an arc line. We find that virtual transducers with a big distributing angle can provide more significant image improvement than with a small distributing angle, which is similar to the true transducers. We also change the size of virtual transducer and study its influence on image quality. It is found that the bigger scatterers provide better images than the smaller ones. Especially, when the size of scatterers is reduced to the wavelength of photoacoustic wave, the image quality observably decreases, owing to the strong diffraction effect. Thus, it is suggested that the size of the acoustical scatterers should be much larger than the photoacoustic wavelength. The simulations are conducted, and the results could be helpful for the application and further study of virtual transducer theory in limited-view photoacoustic tomography.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

Electromagnetic radiation from filamentary sources in the presence of axially magnetized cylindrical plasma scatterers

Electromagnetic radiation from filamentary electric-dipole and magnetic-current sources of infinite length in the presence of gyrotropic cylindrical scatterers in the surrounding free space is studied. The scatterers are assumed to be infinitely long, axially magnetized circular plasma columns parallel to the axis of the filamentary source. The field and the radiation pattern of each source are calculated in the case where the source frequency is equal to one of the surface plasmon resonance frequencies of the cylindrical scatterers. It is shown that the presence of even a single resonant magnetized plasma scatterer of small electrical radius or a few such scatterers significantly affects the total fields of the filamentary sources, so that their radiation patterns become essentially different from those in the absence of scatterers or the presence of isotropic scatterers of the same shape and size. It is concluded that the radiation characteristics of the considered sources can efficiently be controlled using their resonance interaction with the neighboring gyrotropic scatterers.