Perturbation Theory for Isotropic Landau-Lifschitz Equation Based on Inverse Scattering Transformation

The perturbation theory for the Landau-Lifschitz equation for isotropic chain with correction, which is based on the inverse scattering transform (IST), is developed to treat Landau-Lifschitz equation for a spin chain with axis asymmetry. The time-evolution equation of parameters and a formula for the first-order correction is given by treating the equation with axis symmetry as a perturbation to the isotropic equation. PACS numbers 05.45.Yv, 42.65.-k, 42.50.Md.Supported by the National Science Foundation of China under Grant NO. 10474076 and No. 10375041.     

Exact Stationary States of a Two-Dimensional Transport Model

Previous calculations of transport coefficients of particle systems in two or more dimensions have used computer simulations or various approximations, like those implicit in the Boltzmann equation or in the standard probability theory of diffusion. Here an exactly solved model of crystal growth in three dimensions is transformed into a 2D model of steady particle transport. Then the exact, many-body stationary distribution and exact transport coefficients can be found as well as correlation functions. The model is highly asymmetric. In the transverse direction, particles are strongly attracted, so that long transverse rows of particles tend to form at low temperature. Kinks in these rows are rare, so the transverse positions of kinks effectively move continuously on a large distance scale.     

Determinant of Wave Operator as a Measure for Resonance and Bound States in One-Dimensional Potential Scattering System

The determinant of the wave operator or its transposed operator (source operator) works as a measure for resonance and bound states in one-dimensional potential scattering system. This fact is based on an identity proved here: the determinant of the wave or source operator equals to the transmission coefficient, which represents the field amplitude in the forward side of the scatterer. Utilizing this measure, resonance and bound states in one-dimensional system are properly assigned without solving wave equation. In future, local enhancement of optical near-field in three-dimensional system, i.e., local plasmon resonance will be treated, generalizing the present method.     

Response of Charged Particles in a Storage Ring to Gravitational Waves

The influence of gravitational waves on the charged particles in a storage ring is studied. It shows thatthe gravitational waves might be directly detected by monitoring the motion of charged particles in a storage ring. Theangular velocity of the charged particles is continually adjustable by changing the initial energy of particles and thestrength of the magnetic field. This feature is very useful for finding the gravitational waves with different frequencies.     

卷云冰晶粒子散射相函数的展开系数研究

冰晶粒子散射相函数的多项式展开可以应用于卷云条件下大气辐射传输模式的计算。本文利用广义球函数对表面严重粗糙的冰晶粒子相函数进行展开,并对表面严重粗糙的实心棱柱模型、实心棱柱聚合物模型和一般种类混合模型3种冰晶粒子的展开系数特性进行分析研究,数值计算结果表明了广义球函数对表面严重粗糙的冰晶粒子多项式展开的有效性。     

基于不规则衍射理论的冰晶粒子的光散射研究(英文)

在不规则衍射理论的基础上,分析了从可见光到近红外波段冰晶粒子的光散射特性。计算了粒子尺度为20μm,50μm,80μm的五种典型冰晶粒子的消光效率因子和吸收效率因子。最后,为了评估不规则衍射理论的精确性,与有限时域差分法和几何光学法进行了比较。     

Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.     

非定常粒子输运蒙特卡罗散射源分层抽样方法

定常粒子输运蒙特卡罗并行计算是成功的,因为粒子游动是独立的,可以把模拟的粒子数等分到每个处理器去.然而,对非定常问题,由于每个时间步涉及散射源和几何网格的通讯,它严重的制约了并行规模,导致并行不可扩展.研究了两种算法,采用自适应分配处理器,提高了加速比和处理器的利用率;采用蒙特卡罗分层抽样大大降低了处理器之间散射源的通讯量,并行可扩展性显著改善,取得了理想的加速比.     

Scattering Theory for Open Quantum Systems with Finite Rank Coupling

Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A _D in a Hilbert space \({\mathfrak H}\) is used to describe an open quantum system. In this case the minimal self-adjoint dilation \(\widetilde K\) of A _D can be regarded as the Hamiltonian of a closed system which contains the open system \(\{A_{\!D},{\mathfrak H}\}\), but since \(\widetilde K\) is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm–Liouville operators arising in dissipative and quantum transmitting Schrödinger–Poisson systems.     

双层散射介质的单次后向散射光谱分析

从上皮组织的结构特点出发,基于米氏(Mie)散射理论,建立了双层散射介质的单次后向散射光谱的理论模型,该模型通过偏振门屏蔽来自下层的噪声背景,只保留来自上层的单次散射光。计算分析了粒子的形态学参量如平均尺寸及其分布、相对折射率变化时,单次散射光谱的特征。并用傅里叶波形分析法研究了这些参量对单次后向散射光谱曲线形状及其谐波幅值的影响。结果表明,这些只经历了表层粒子单次散射的光谱信号对表层粒子的平均尺寸及其分布、相对折射率具有灵敏性。对光谱曲线波纹结构的幅值、频率,散射强度,光谱谐波的幅值有直接的影响。研究结果对早期癌症的散射光谱特征识别及其特征提取有重要的实用价值。     

An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.     

米氏理论的近似及在粒度测量中的应用

将夫琅禾费衍射理论与几何散射 (包括折射和反射 )相结合 ,给出平行光入射下圆形颗粒在前向大角度范围内的散射光强分布近似算法。由于考虑了衍射、折射和反射相互间的干涉效应和颗粒对光的吸收性 ,对于正常或非正常衍射状态下无因次参量α≥ 40的耗散颗粒 ,在前向 0°～ 60°散射之内 ,该方法对散射光强计算结果与米氏理论结果是吻合的。由于计算速度比米氏理论快 ,有效角度范围比夫琅禾费衍射理论宽 ,因而适合于大颗粒的前向光强计算。将这一计算方法应用到大角度采光时的激光粒度测量实验中 ,收到了良好的效果     

基于AgI2-缔合微粒共振散射效应测定阳离子表面活性剂

在pH 3.5 NaAc-HCl介质中,Ag 与过量的I-形成可溶性AgOI2-;当十六烷基三甲基溴化铵(CT-MAB)与AgI2-共存时形成粒径为700 nm的(CTMA-AgI2)n缔合微粒,在360 nm处产生一个共振散射峰,在470 m处产生一同步散射峰.CTMAB浓度cCTMAB在2.0～50.0×10-7mol·L-1范围内与散射光强度I360nm呈线性关系,回归方程为I360nm=2.03×107 cCTMAB 0.48,相关系数r为0.998 5,检出限为8.0×10-8mol·L-1.据此建立了一个测定阳离子表面活性剂含量的共振散射光谱法,用于水样分析,结果满意.共振散射光谱和激光散射研究表明,CTMAB 与AgI2-可通过静电力形成疏水性的CTMA-AgI2缔合物分子,该缔合物分子自动聚集形成稳定的(CTMA-AgI2)n缔合微粒.由于该缔合微粒仅在360 nm处产生共振散射效应,故体系呈乳白色.     

A Theory for the Quantitative Estimation of Bed Load Transport Using Radioisotopes

In this paper an attempt has been made to develop a simple theory for the application of radiotracer techniques to estimate the quantum of bed material transported in rivers, estuaries, etc. The emphasis is mainly on the physical concepts involved. Certain assumptyions made in the theory are later verified experimentally.     

Normal Transport Properties in a Metastable Stationary State for a Classical Particle Coupled to a Non-Ohmic Bath

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility μ over macroscopic time scales of order exp (c/F), during which it finds itself in a metastable stationary state. The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties.     

非球形大气粒子对任意波束的电磁散射特性

研究大气中变形球状的气象粒子对电磁波以及激光的散射特性,采用广义米氏(Mie)理论,精确地求解在任意波束中大气粒子的散射强度,数值计算激光束腰位置对散射强度分布的影响,分析彩虹强度和散射角与变形球状粒子偏心率的关系,研究随着长短轴比例增加,彩虹强度峰值的偏移。计算结果表明雨滴在下降过程中,它在各个方向的光散射强度逐步减弱,即随着雨滴偏心率的增大,散射强度减少,彩虹角变大。对于激光入射,当粒子距离波束中心位置越远,粒子的散射就越弱,并且随尺寸参量增加,后向散射振荡的频率要大于前向散射,当束腰位置矢径的大小增加时,后向散射和前向散射强度均变小。     

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian.     

Nonsingularity of the Direct Scattering Transform for the KP II Equation with a REal Exponentially Decaying-at-Infinity Potential

We study the direct spectral transform for the heat equation associated with the Kadomtsev-Petviashvili. We show that, for real nonsingular exponentially decaying-at-infinity potential, the directproblem is nonsingular for arbitrarily large potentials. Earlier, thisstatement was proved only for potentials satisfying the small normassumption.