Time-reversal analysis for scatterer characterization

A new application of time-reversal processing of wave scattering data permits characterization of scatterers by analyzing the number and nature of the singular functions (or eigenfunctions) associated with individual scatterers when they have multiple contributions from monopole, dipole, and/or quadrupole scattering terms. We discuss acoustic, elastic, and electromagnetic scattering problems for low frequencies. Specific examples for electromagnetic scattering from one of a number of small conducting spheres show that each sphere can have up to six distinct time-reversal eigenfunctions associated with it.     

Scattering of fermions on the SU(5) colorless magnetic monopole

We discuss the scattering of fermions (d?, u-quarks and e^c) on the SU(5) colorless magnetic monopole. The radial functions of scattering wave are totally separated from the angular parts in the Dirac equations which then reduce to a set of coupled ordinary differential equations. We solve these equations numerically for the d?e^c group with j = 1, and get the result that only the incoming wave of d with j = 1 and j′ = 0 can be scattered into e^c. The cross section is obtained which is intimately connected with the catalysis effect of the monopole for baryon decay.     

Transmission of ultrasound through a single layer of bubbles

We investigate, both experimentally and theoretically, the effect of coupling between resonant scatterers on the transmission coefficient of a model system of isotropic scatterers. The model system consists of a monodisperse layer of bubbles, which exhibit a strong monopole scattering resonance at low ultrasonic frequencies. The layer was a true 2D structure obtained by injecting very monodisperse bubbles (with radius a ∼ 100 μm) into a yield-stress polymer gel. Even for a layer with a low concentration of bubbles (areal fraction, n a ² , of 10-20%, where n is the number of bubbles per unit area), the ultrasonic transmission was found to be significantly reduced by the presence of bubbles (-20 to -50 dB) and showed a sharp minimum at a particular frequency. Interestingly, this frequency did not correspond to the resonance frequency of the individual, isolated bubbles, but depended markedly on the concentration. This frequency shift is an indication of strong coupling between the bubbles. We propose a simple model, based on a self-consistent relation, which takes into account the coupling between the bubbles and gives good agreement with the measured transmission coefficient.     

Time reversal for a single spherical scatterer.

We show that the time reversal operator for a planar time reversal mirror (TRM) can have up to four distinct eigenvalues with a small spherical acoustic scatterer. Each eigenstate represents a resonance between the TRM and an induced scattering moment of the sphere. Their amplitude distributions on the TRM are orthogonal superpositions of the radiation patterns from a monopole and up to three orthogonal dipoles. The induced monopole moment is associated with the compressibility contrast between the sphere and the medium, while the dipole moments are associated with density contrast. The number of eigenstates is related to the number of orthogonal orientations of each induced multipole. For hard spheres (glass, metals) the contribution of the monopole moment to the eigenvalues is much greater than that of the dipole moments, leading to a single dominant eigenvalue. The other eigenvalues are much smaller, making it unlikely multiple eigenvalues could have been observed in previous experiments using hard materials. However, for soft materials such as wood, plastic, or air bubbles the eigenvalues are comparable in magnitude and should be observable. The presence of multiple eigenstates breaks the one-to-one correspondence between eigenstates and distinguishable scatterers discussed previously by Prada and Fink [Wave Motion 20, 151-163 (1994)]. However, eigenfunctions from separate scatterers would have different phases for their eigenfunctions, potentially restoring the ability to distinguish separate scatterers. Since relative magnitudes of the eigenvalues for a single scatterer are governed by the ratio of the compressibility contrast to the density contrast, measurement of the eigenvalue spectrum would provide information on the composition of the scatterer.     

Nucleon polarization and the nuclear charge operator

Effects of nucleon polarization on the nuclear charge operator have been evaluated in a constituent quark model. At momentum transfer q ≈ 4 fm^?1 monopole, dipole and quadrupole excitations are of equal importance. In a harmonic oscillator model for ³He all multipolarities give negative contributions, leading to an overall contribution comparable to the relativistic pair effect. The influence of realistic wave functions, coupling constants and off-shell form factors is discussed.     

气泡线性振动时近海面气泡群的声散射

海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。     

Condensation of interacting bosons in a random potential

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval.     

随钻单极子声波测井模式优化及远探测

针对非均匀性地层地质力学评价和地质导向钻井的需要,研究了随钻单极子声波的方位特性和反射声场特征,并研制了随钻声波测量装置.建立了不同方向速度模型井和反射声场模型,数值模拟了两个模型的单极子声波传播特征,使用单极子声源发射和偏极子接收器接收的测量模式,分别获得了波速周向变化图和反射波的方位特征.模拟结果表明,纵波对地层方...     

Effect of the Pauli exclusion principle and the polarization of nuclei on the potential of their interaction for the example of the 16O+16O system

On the basis of the energy-density method, the effect of simultaneously taking into account the Pauli exclusion principle and the monopole and quadrupole polarizations of interacting nuclei on their interaction potential is considered for the example of the ¹⁶O + ¹⁶O system by using the wave function for the two-center shell model. The calculations performed in the adiabatic approximation reveal that the inclusion of the Pauli exclusion principle and the polarization of interacting nuclei, especially their quadrupole polarization, has a substantial effect on the potential of the nucleus-nucleus interaction.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

Microscopic analysis of the breathing mode in 40Ca and 58Ni

Recent experimental studies of the giant electric resonance region in ⁵⁸Ni and ⁴⁰Ca with inelastically scattered α-particles of energy E_α= 240 MeV are analyzed within a microscopic nuclear structure model. The model includes the continuum RPA and more complex 1p1h⊗phonon configurations. By superimposing the contributions of different multipoles up to L = 4 we obtain good agreement with the newest (reanalyzed) data for the isoscalar monopole strength and for the total (α,α′) cross section in ⁵⁸Ni. Agreement with experiment for the isoscalar monopole resonance in ⁴⁰Ca is obtained too. We emphasize the necessity of using microscopic transition densities and discuss consequences for the analyses of such experiments in light and medium mass nuclei. It is shown that the gross structure of the isoscalar monopole resonance in ⁴⁰Ca is caused by the 1p1h⊗phonon configurations. Received: 23 December 1999 / Revised version: 28 February 2000     

Fragmentation of giant multipole resonances in deformed nuclei

The fragmentation of the giant monopole resonance in deformed nuclei is first studied by coupling the monopole oscillation with the quadrupole oscillation by means of the variational procedure for resonance frequencies. It is shown that, for non-axial symmetry, the monopole oscillation couples with both m = 0 and 2 modes of the quadrupole oscillation and the giant monopole resonance is split into three components, whereas for axial symmetry, the fragmentation is given by E₀(1 + 0.86δ² ± 1.25δ³) and E₀(0.74 ± 0.22δ ? 0.21δ² ± 0.57δ³), where E₀ is the g monopole resonance energy for spherical nuclei, δ is the deformation parameter, and the upper and lower signs stand for prolate and oblate deformations, respectively. The initial fragmentation of the giant quadrupole resonance is seen to be little modified by the coupling, except for the m = 0 mode which is split into two components. The variational method is extended to general multipoles for an ellipsoid and the fragmentation of giant multipole resonances in deformed nuclei is investigated for both axial and non-axial symmetries. A brief discussion is also made about the meaning of the energy eigenvalue involved in the model wave equation in terms of multipole sum rules. The giant dipole resonance for the static octupole deformation is shortly considered. The giant E0 and E3 resonances for largely deformed nuclei are finally examined by solving the spheroidal eigenvalue equation and they are compared with the results of the giant dipole and quadrupole resonances.     

Three-body continuum structure and response functions of halo nuclei (I): 6He

Three-body scattering states of the Borromean two-neutron halo nuclei are explored in a core + n + n model using the method of hyperspherical harmonics. We analyse the continuum structure (the properties of the continuum wave functions) separately from the continuum response (the magnitudes of one-step transitions from the ground state to the continuum). Predictions are made for the positions and strengths of the isoscalar monopole, electric dipole and quadrupole excitations, as well as for nuclear inelastic and charge-exchange response functions, for the ⁶He nucleus. The known 2⁺ resonance in ⁶He is reproduced. We find 1⁻ strength concentrations at lower energies in the proximity of the three-body threshold, and predict new 2⁺, 1⁺ (and possibly 0⁺) resonances at slightly higher energies in ⁶He.     

Field fluctuation spectroscopy in a reverberant cavity with moving scatterers

We report a study of transient ultrasonic waves inside a reverberant cavity containing moving scatterers. We show that the elastic mean free path and the dynamics of the scatterers govern the evolution of the autocorrelation of acoustic wave field. A parallel is established between these results and a closely related technique, diffusing acoustic wave spectroscopy. Excellent agreement is found between experiment and theory for a moving stainless steel ball in a water tank, thereby elucidating the underlying physics, and a potential application, fish monitoring inside aquariums, is demonstrated.     

On appropriate equivalent monopole sets for rigid body scattering problems

The present paper investigates properties of the solutions obtained with the equivalent sources method in scattering problems with the aim of identifying suitable monopole arrangements. Simple geometry scatterers--parallelepipeds with different aspect ratios--are considered and easy-to-implement source supports are tested: linear, circular, elliptical, and a "double linear" one. It was found that the supports providing best solutions differ according to the body geometry and the incidence angle of the impinging wave. Moreover, in the situations in which the other supports fail, it is shown that the double linear one provides satisfactory solutions with a minimum number of monopoles. Rules that furnish appropriate numbers of sources to use as well as their positioning are given for the different cases. A simple procedure based on these rules is proposed for scatterers with a more complex geometry, guaranteeing, still with a low number of monopoles, solutions with satisfactory accuracy.     

Generator coordinate calculations of monopole and quadrupole vibrations with Skyrme's interaction

Skyrme's interaction is shown to lead to significant simplifications in generator coordinate calculations. As an illustration monopole and quadrupole modes are calculated in ⁴He, ¹⁶O and ⁴⁰Ca using pure oscillator wave functions.     

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure–time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.     

A successive scattering methodology with application to two cylinders in the Fresnel region of each other

We present an efficient approach to compute the second-order scattering of an electromagnetic wave by two discrete scatterers in proximity to each other. Such a two-body system represents the simplest canonical arrangement to address near-field volume scattering phenomena in microwave remote sensing models of vegetation. Using an analytical wave-based approach, a successive scattering methodology is employed to derive the first interaction term in multiple scattering by two arbitrary scatterers in terms of their transition operators. The general formulation is applied to find the second-order bistatic scattering amplitude for a pair of finite length thin cylinders at arbitrary interaction distances using the exact Green's function. To improve computational efficiency, the solution is then specialized to the Fresnel region. These second-order bistatic scattering amplitude results are in agreement with the exact Green's function model when the scatterers are in the Fresnel region of each other. Additionally, it is demonstrated that using the far field approximation in the Fresnel region can yield significant deviations from the exact results. The Fresnel model, unlike the far field approximation, accurately predicts the scattering amplitude peak values and null locations, and is suited to fast solutions in realistic canopy simulations.