Bispectral analysis in inverse nonlinear acoustics problems

Using the spectral solution to the evolutionary Burgers equation, we have numerically simulated the propagation of intense random acoustic waves in a nondisperse medium. We have solved the problem of reconstructing the initial signal spectrum using the measured spectral and bispectral characteristics of the received signal on short tracks.     

水下目标回波特性计算的图形声学方法

根据Kirchhoff近似公式建立了一种水下目标回波特性实时工程预报的新方法-可视化图形声学计算方法GRACO (Graphical Acoustics Computing)。该方法利用三维图形处理系统,采用建模软件对水下复杂目标进行几何建模,并基于OpenGL技术把几何模型转化为屏幕上目标的可视化像素图形,获取像素中包含的目标表面法向量和空间距离信息,最后通过把回波特性预报中的面积分转化为屏幕上可视化图形的像素求和计算,完成水下目标回波特性预报。计算结果表明图形声学方法有较高的精度,计算速度比板块元方法快9~10倍。     

On spectral methods for solving nonlinear acoustics equations

Two very efficient methods for obtaining approximate solutions to nonlinear acoustics equations are discussed. I proposed these methods earlier, but they are still little known. The first method is based on expanding an unknown function into a Taylor series with respect to the coordinate (evolution variable) and on approximate summation of the terms of this series in all orders up to the infinite order. This series can be summed completely only in particular cases, e.g., for a simple wave. It has been noted that the partial summation technique is implemented more easily if all the terms of the series are represented as corresponding topological diagrams. The second method is based on introducing a “nonlinear” phase delay (proportional to the wave amplitude) for the temporal variable in linear solutions of the problem. The application technique of these methods is illustrated by obtaining approximate solutions of the Burgers equation.     

Classical problems of nonlinear acoustics and wave theory

Focusing of a vibration field in finite sized elastic systems using time reversal of signals from a point’s wideband source is theoretically analyzed. It is shown that the result of space and time focusing for a classical reversal algorithm in limited systems with small losses depends of the positional relationship of the source and the signal receiver. A focusing algorithm eliminating this dependence and increasing the efficiency of the focusing of the vibration field is proposed. Theoretical estimates are confirmed with the results of numerical experiments with the models of elastic bodies.     

Black hole acoustics in the minimal geometric deformation of a de Laval nozzle

The correspondence between sound waves, in a de Laval propelling nozzle, and quasinormal modes emitted by brane-world black holes deformed by a 5D bulk Weyl fluid are here explored and scrutinized. The analysis of sound waves patterns in a de Laval nozzle in the laboratory, reciprocally, is here shown to provide relevant data about the 5D bulk Weyl fluid and its on-brane projection, comprised by the minimal geometrically deformed compact stellar distribution on the brane. Acoustic perturbations of the gas fluid flow in the de Laval nozzle are proved to coincide with the quasinormal modes of black holes solutions deformed by the 5D Weyl fluid, in the geometric deformation procedure. Hence, in a phenomenological Eötvös–Friedmann fluid brane-world model, the realistic shape of a de Laval nozzle is derived and its consequences studied.     

Extended molecules and geometric scattering resonances in optical lattices

We develop a theory describing neutral atom scattering at low energies in an optical lattice. We show that, for a repulsive interaction, as the microscopic scattering length increases the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.     

Hemodynamics and nonlinear acoustics: General approaches and solutions

Related problems of nonlinear acoustics and hemodynamics are discussed. Equations describing the propagation of pulse waves in elastic tubes taking into account the dependence of the cross-section, linear and nonlinear elasticity on the distance along the axis are obtained. It is shown that in narrowing tubes with their elasticity increasing shock fronts may be formed with the peak pressure increasing, and the peak speed decreasing. The analogous behavior was observed in experiments. The expression of the nonlinearity coefficient as a sum of the “geometrical” and “physical” nonlinearities having different signs is obtained. It is supposed that in a normally functioning system these nonlinearities compensate each other. The formation of the shock waves is the evidence of vascular pathology. It is shown that it is possible to restore the local heterogeneity of a vessel (the change of the cross-section or rigidity) on the basis of measurements of the reflected or transmitted wave. The principle of the action of the acoustic pump not containing mechanically moving parts is described.     

The geometric phase in nonlinear frequency conversion

The geometric phase of light has been demonstrated in various platforms of the linear optical regime, raising interest both for fundamental science as well as applications, such as flat optical elements. Recently, the concept of geometric phases has been extended to nonlinear optics, following advances in engineering both bulk nonlinear photonic crystals and nonlinear metasurfaces. These new technologies offer a great promise of applications for nonlinear manipulation of light. In this review, we cover the recent theoretical and experimental advances in the field of geometric phases accompanying nonlinear frequency conversion. We first consider the case of bulk nonlinear photonic crystals, in which the interaction between propagating waves is quasi-phase-matched, with an engineerable geometric phase accumulated by the light. Nonlinear photonic crystals can offer efficient and robust frequency conversion in both the linearized and fully-nonlinear regimes of interaction, and allow for several applications including adiabatic mode conversion, electromagnetic nonreciprocity and novel topological effects for light. We then cover the rapidly-growing field of nonlinear Pancharatnam-Berry metasurfaces, which allow the simultaneous nonlinear generation and shaping of light by using ultrathin optical elements with subwavelength phase and amplitude resolution. We discuss the macroscopic selection rules that depend on the rotational symmetry of the constituent meta-atoms, the order of the harmonic generations, and the change in circular polarization. Continuous geometric phase gradients allow the steering of light beams and shaping of their spatial modes. More complex designs perform nonlinear imaging and multiplex nonlinear holograms, where the functionality is varied according to the generated harmonic order and polarization. Recent advancements in the fabrication of three dimensional nonlinear photonic crystals, as well as the pursuit of quantum light sources based on nonlinear metasurfaces, offer exciting new possibilities for novel nonlinear optical applications based on geometric phases.     

All-optical probing of the nonlinear acoustics of a crack

Experiments with an all-optical method for the study of the nonlinear acoustics of cracks in solids are reported. Nonlinear acoustic waves are initiated by the absorption of radiation from a pair of laser beams intensity modulated at two different frequencies. The detection of acoustic waves at mixed frequencies, absent in the frequency spectrum of the heating lasers, by optical interferometry or deflectometry provides unambiguous evidence of the elastic nonlinearity of the crack. The high contrast in crack imaging achieved by remote optical monitoring of the nonlinear acoustic processes is due to the strong dependence of the efficiency of optoacoustic conversion on the state of the crack. The highest acoustic nonlinearity is observed in the transitional state of the crack, which is intermediate between the open and the closed ones.     

A shadowgraph method for ocean acoustics

A knowledge of convection activity in the upper few hundred metres of the ocean is important in establishing ocean-atmosphere heat fluxes and in understanding large-scale water-circulation processes. The usual methods for investigating internal structures in the ocean have certain drawbacks. Lowering probes into the ocean can provide local information only, while towed arrays of sensors are cumbersome and expensive. An alternative acoustic method for revealing internal structures is proposed. It is based on the observed acoustic intensity only and does not rely on phase or travel times. For this reason it is really an acoustic shadowgraph. The method is explained and its successful use in a sea trial is reported.     

Adiabatic geometric phase in the nonlinear coherent coupler

We introduce the concept of geometric phase to the nonlinear coherent coupler. With considering the adiabatic change of the distance-dependent phase mismatch, we calculate the adiabatic geometric phase related to the supermode of the coupler analytically. We find that the phase depends on the input light intensity explicitly. In particular, in the low and high intensity limits, the phase equals half of the area on the Poincare sphere enclosed by the evolution loop of the system. At the critical intensity where different supermodes merge, the phase diverges, which can be considered as the signal of a continuous phase transition.     

Extended geometric Supergravity on Group Manifolds with Spontaneous Fibration

We review and develop geometrical gauging involving the sequence: Lie group/Principal Bundle, for an Internal symmetry group/Soft Group Manifold, for Non-Internal groups. In the Internal case, we rederive the Ghost-fields and the BRS transformations and equations geometrically. In the case of a Soft Group Manifold, we study Spontaneous Fibration, rederive Gravity and Supergravity and then present Extended geometric Supergravity theories.     

复射线法及其在水声技术中的应用

本文介绍复源点射线技术原理,概述各种复射线分析方法,并举例说明这种方法在水声技术中一些可能的应用,包括指向性声场的复射线分析,声辐射器阵列方向性的复射线模拟,近区和远区声场的复射线变换,以及声呐目标强度的复射线理论预估等。     

Relatively undistorted waves and waveforms in nonlinear acoustics: Exact solutions of equations

We demonstrate the physical conditionality and efficiency of using relatively undistorted waves as an anzats for determining exact solutions to equations of nonlinear acoustics.     

A beam tracing method for interactive architectural acoustics

A difficult challenge in geometrical acoustic modeling is computing propagation paths from sound sources to receivers fast enough for interactive applications. This paper describes a beam tracing method that enables interactive updates of propagation paths from a stationary source to a moving receiver in large building interiors. During a precomputation phase, convex polyhedral beams traced from the location of each sound source are stored in a "beam tree" representing the regions of space reachable by potential sequences of transmissions, diffractions, and specular reflections at surfaces of a 3D polygonal model. Then, during an interactive phase, the precomputed beam tree(s) are used to generate propagation paths from the source(s) to any receiver location at interactive rates. The key features of this beam tracing method are (1) it scales to support large building environments, (2) it models propagation due to edge diffraction, (3) it finds all propagation paths up to a given termination criterion without exhaustive search or risk of under-sampling, and (4) it updates propagation paths at interactive rates. The method has been demonstrated to work effectively in interactive acoustic design and virtual walkthrough applications.     

New approach to the normal mode method in underwater acoustics

A new approach to the numerical solution of normal model problems in underwater acoustics is presented,in which the corresponding normal mode problem is transformed to the problem of solving a dynamic system.Three applications are considered:(1)the broad band normal mode problem;(2) the range-dependent problem with perturbation proportional to the range parameter;and (3) the evolution of the normal mode with environmental parameters.A numerical simulation for a broad band problem is performed,and the calculated eigenvalues have good agreement with those obtained by the standard normal mode code KRAKAN.     

Algebraic and geometric space-time analogies in nonlinear optical pulse propagation

We extend recently developed algebraic space-time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian breathers in nonlinear optical fibers.