On Spectral Asymptotics for Domains with Fractal Boundaries of Cabbage Type

The second term of the asymptotic expansion of the eigenvalue counting function N() is found for the Dirichlet Laplacian in a class of domains with fractal boundaries.     

分形凝聚粒子的光散射特性研究

粒子的形状和凝聚对光散射特性有着很大的影响.基于分形生长的受限扩散(DLA)模型,模拟了凝聚粒子的三维空间分形结构,并采用回转半径法计算了凝聚粒子的分形维数.利用离散偶极子近似(DDA)方法研究了纳米石墨凝聚粒子的光散射特性,对于原始粒子数不同的凝聚粒子及分形结构不同的凝聚粒子,数值计算了散射强度和偏振度随散射角的分布...     

多光束在分形粗糙表面散射的仿真

采用矩量法(MOM),分析了多光束在分形粗糙导体表面的散射分布.对在不同入射角、光束宽度控制因子、光束照射区宽度、表面均方根高度和表面分维数情况下的散射进行了数值仿真.仿真结果表明了各参量的变化对散射分布的影响.根据仿真计算结果给出了最佳的散射测量区域,为减少多光束测量的误差提供了一定的参考.     

Anisotropic Scattering in Accordance with Pomraning Phase Function

The emergent intensity I(0,μ) from the equation of transfer in anisotropically scattering medium with Pomraning phase function is derived in n ^th approximation by using Chandrasekhar’s discrete ordinate method. AMS classification: 85A25     

Scattering Solutions in Networks of Thin Fibers: Small Diameter Asymptotics

Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph Γ . We calculate the Lagrangian gluing conditions at vertices for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum, the gluing conditions are formulated in terms of the scattering data for each individual junction of the network. The authors were supported partially by the NSF grant DMS-0405927.     

Fractal Character of Dynamic Light Scattering of Particles

Dynamic light scattering signals from particles, exhibit fractal characteristics. This feature can be used to determine the particle size. The use of the fractal dimension, as a quantitative method to analyze the properties of dynamic light scattering signals from submicron particles, is presented. The analysis is performed directly on the time‐resolved scattered intensity, and the Box Dimensions of light scattering signals of particles with diameters 100, 200, 500 and 1000 nm. The experimental results show that the fractal dimensions of light scattering signals correlate well with particle size. In the submicron size range, the smaller the particles, the larger their fractal dimensions. Compared with the PCS technique, only several hundreds of samples are required in the fractal method. Therefore, the data processing is easily accomplished. However, this method only provides the mean particle size, but not the particle size distribution.     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

基于Mie散射理论的紫外光散射相函数研究

本文根据Mie散射理论,研究了四种典型大气条件下紫外光在大气传输中的散射相函数,并与常用的用于非紫外光散射相函数的三类经验公式进行了比较。研究结果表明:三种经验公式用于紫外光大气传输模拟存在一定的局限性。     

An Inverse Scattering Problem with Part of the Fixed-Energy Phase Shifts

Assume that q(r) is a real-valued, compactly supported potential, q(r)=0 for , . Let be an arbitrary fixed subset of non-negative integers such that , and be fixed-energy phase shifts corresponding to q(r). The main result is: Theorem. The data determine q(r) uniquely. Received: 3 March 1999 / Accepted: 27 April 1999     

The Phase Shifts for A-N Elastic Scattering

chiral soliton model with the gluon field, chiral doublet (σ, π)-field and chird singlet ω-meson field is employed to study A-nucleon elastic scattering phase shifts within the framework of the relativistic two-quark-cluster theory. The phase shifts are sensitive to the strange quark in the A-hyperon.     

Fractal Characteristics Investigation on Light Scattering from Two Dimensional Rough Surface

A normalized two dimensional band-limited Weierstrass fractal function is used for modeling the rough surface. Based on Kirchhoff theory, an analytic solution of the average scattering field and the variance of scattering intensity are derived with emphasis on examining the relation of fractal dimension with the scattering pattern. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated to a slope of linear equation.     

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation mad with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional very rough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximation at microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation and integral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancement on the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional veryrough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximationat microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation andintegral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancementon the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

激光照射金颗粒在散射效应下的相变传热

采用二维双温度模型结合散射作用所引起颗粒表面光强不均匀分布的结果,对单脉冲激光垂直照射金颗粒的相变传热进行研究,通过将界面能量平衡方程,成核动力学的界面追踪法相耦合来确定固液界面的位置并研究激光参数对烧结过程的影响.结果表明：当激光垂直照射金颗粒时,熔化现象主要发生在颗粒的两极且底部熔化开始时间早,熔化体积也比较小.激光的脉宽越短熔化开始时间越早,熔化体积越大.提高激光的能量密度,颗粒的熔化体积也随之增加.     

Coherent Scattering by Multiple Particles in Phase Doppler Interferometry

A theoretical model has been developed for studying the response of the phase Doppler interferometer when multiple particles are simultaneously present within the measurement probe volume. The developed model incorporates the geometrical optics theory for describing the coherent interaction between the scattered light signals of multiple particles, eachhaving different size, velocity, trajectory, and arrival time. The resulting Doppler signal is processed by a theoretical signal processor which can simulate the performance characteristic of different signal processing schemes that are widely used in phase Doppler interferometry, namely, zero-crossing counter, covariance, autocorrelation and DFT parocessors. The application of the developed model for studying the coherent scattering by two particles has been specifically addressed in this paper. It has been shown that a DFT processor can be used to simultaneously measure the size and velocity of the two particles in most instances. However, for more than two particles, the signal processing scheme becomes more complex because of a quadratic increase in the beat frequency components.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997