Resonant acoustic scattering by a finite linear grating of elastic shells

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.     

激光等离子体受激散射的线性理论研究

利用包含两种阻尼(Landau阻尼和碰撞阻尼)成分的受激拉曼散射(SRS)、受激布里渊散射线性分析程序LIP,在给定的等离子体状态下分析了阻尼成分、激光强度以及等离子体组分对点火尺度等离子体中受激散射不稳定性发展的影响.详细评估了碰撞阻尼的效应,发现碰撞阻尼在接近1/4临界密度处能有效抑制受激散射的增长,从而造成SRS光谱上的"缝"现象.同时,电子温度的升高会在特定的密度区域促进SRS的发展.研究结果可为点火实验的设计提供参考.     

Approximation methods in viscoelasticity theory

According to Volterra’s principle, the solution of the quasistatic problem in linear elasticity theory for an isotropic medium can be obtained from a solution of the corresponding problem of elasticity theory by substituting an integral operator with respect to time for the Poisson ratio and the subsequent interpretation of the constitutive operator function. The method of approximation uses an expansion of constitutive functions into a sum of rational operators. An evaluation is made for the accuracy of the solution, which is related to the quality of approximation. For an anisotropic medium, the constitutive function depends on several integral operators. In this case, a special method of approximation of the constitutive function is suggested which uses the introduction of “canonical” operators. A priori and a posteriori evaluations of the solution are given. Generalizations to nonhomogeneous (composite) media and nonlinear cases are indicated.     

Iteration method for solving linear viscoelasticity problems

Substantiation is given for a new iteration method that makes it possible to solve, with prescribed accuracy, boundary-value problems of quasistatics of a linearly viscoelastic body. A theorem is proved about the convergence of the iteration processes introduced. An approximate correspondence principle, making it possible to construct a solution for viscoelastic problems from known elastic problems, is obtained as a consequence of the theorem. Examples are given of an approximate determination of the connected-creep function, in terms of which numerous analytical solutions to viscoelasticity problems can be expressed.Deceased.Scientific-Research Institute of Applied Mathematics and Mechanics at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 129–136, April, 1993.     

Mesoscopic theory of the viscoelasticity of polymers

We have advanced our previous static theory of polymer entanglement involving an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go beyond the Gaussian approximation, to the one-loop level, to compute the frequency dependent storage and loss moduli of the system. The four parameters in our theory are obtained by fitting to available experimental data on polystyrene melts of various chain lengths. This provides a physical representation of the parameters in terms of the chain length of the system. It is shown that the parameters chosen describe the crossover from an unentangled to an entangled state. The crossover is characterized by a dramatic increase in a time scale appearing in the theory, analogous to critical slowing down in phase transition theory. This result should stimulate more detailed experiments in this regime to test this concept.     

An exploration in acoustic radiation force experienced by cylindrical shells via resonance scattering theory

In nonlinear acoustic regime, a body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force (RF). This force is a second-order quantity of the velocity potential function of the ambient medium. Exploiting the sufficiency of linear solution representation of potential function in RF formulation, and following the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of the resonant field and a background (non-resonant) component, we will show that the radiation force is a composition of three components: background part, resonant part and their interaction. Due to the nonlinearity effects, each part contains the contribution of pure partial waves in addition to their mutual interaction. The numerical results propose the residue component (i.e., subtraction of the background component from the RF) as a good indicator of the contribution of circumferential surface waves in RF. Defining the modal series of radiation force function and its components, it will be shown that within each partial wave, the resonance contribution can be synthesized as the Breit-Wigner form for adequately none-close resonant frequencies. The proposed formulation may be helpful essentially due to its inherent value as a canonical subject in physical acoustics. Furthermore, it may make a tunnel through the circumferential resonance reducing effects on radiation forces.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.     

Stretched backgrounds for acoustic scattering models

For the computational solution of the acoustic scattering problem, new domain integral equations are proposed. These domain integral equations describe the acoustic wave propagation in some chosen inhomogeneous background, whereas the influence of the scattering object is viewed as a superposition of contrast sources. A stretching procedure of the inhomogeneous background to a homogeneous one leads to a domain integral equation in a stretched space, where the Green function has the same simple functionality as the one of the non-stretched homogeneous background. This leads to improved efficiency in the computation of the scattering problem at hand.     

General three-particle scattering theory

A unified treatment of three-particle scattering theory with a three-body force in addition to the usual pair interactions is developed. The relationship of the generalized AGS and Faddeev formalisms to each other as well as distinct versions of each corresponding to the two most natural techniques for handling the three-body potential are established. It is found, just as in the case without the three-particle force, that the AGS formalism appears to be more practical for considering elastic and rearrangement scattering in two-body channels. On the other hand, for scattering amplitudes with at least one three-body channel (breakup and the 3-to-3) the Faddeev version of the theory is preferable. Other advantages of each formalism depending upon the treatment of the three-body interaction are noted.     

Commutators and scattering theory

We use commutators to find classes of operators which are smooth with respect to the HamiltonianH for a system of quantum mechanical particles which repel each other. It follows thatH is absolutely continuous, the wave operators are complete in many cases when they exist and limits of momentum observables as time approaches ± exist even in cases where the long range of the interaction precludes existence of the wave operators.     

Combined variable-phase-off-shell scattering theory

We develop a first order linear differential equation for the fully off-shell scattering amplitude in terms of the cut-off radius of the local two-body interaction. The on- and half-off-shell equation of Calogero and of Sobel are derived as special cases. The input of our equation involves interpolating half off-shellT matrices parametrized by well known phase and quasiphase functions.     

Hybrid linear and matrix acoustic arrays

This work describes a new technique for constructing both linear and matrix array transducers. It used completely separated piezoelectric elements whose vibration modes have been studied experimentally. Each piezoelectric element has a $\text{λ}\text{4}$ matching plate and backing, and so it forms a separate transducer. The array is formed by an assembly of these transducers.The technique shows some interesting features such as the possibility of reducing the dispersion of the electroacoustic characteristics of the single elements to the required value, mechanical strength, and the possibility of periodical maintenance.     

Operating principles of linear acoustic tomograph

An enhanced linear acoustic tomograph is designed for the early medical diagnosis of pathological neoplasms of soft biological tissues. Problems associated with additional prospects for tomographic imaging are discussed.     

Methods of investigation of boundary value problems in viscoelasticity theory

The present paper is devoted to some classical and modern methods of solving boundary value problems of viscoelasticity theory, including the Volterra principle, Il’yushin’s approximation method, Pobedrya’s method of numerical realization of an elastic solution, the method of Laplace (Laplace-Carson) transform and Z-transform, the method of time steps, the usage of viscoelastic models with fractional time derivatives (fractal models), and methods using a new representation of constitutive relations of nonlinear viscoelasticity To Boris Efimovich Pobedria on the occasion of his 70th birthday     

Irregular scattering of acoustic rays by vortices

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.     

Enhanced scattering of acoustic waves at interfaces

We propose a general method to realize a total scattering of an incident acoustic wave at interfaces between different media while allowing the flow of air, fluids and/or particles. This originates from the enlargement of the equivalent acoustic scattering cross section of an embedded object coated with acoustic metamaterials, which causes the coated object to behave as a scatterer bigger than its physical size. We theoretically design a model circular cylindrical object coated with such metamaterials whose properties are determined according to two different, but identical, methods. The desired function is confirmed for both far-field and near-field cases with full wave simulations based on the finite element method. This work reveals a promising way to achieve noise shielding and naval camouflage.     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.