Sound speed in air-filled sand and marine shallow-layer sandy sediments

Based on the author＇s theory for acoustic propagation in granular media and by employing the extinction theorem, the sound speed formulae in these media were derived. The numerical computations of sound speed in marine sediments and air-filled sand were carried out, and the results demonstrated that under the normal atmosphere the sound speed in airfilled sand is lower than the sound speed in the air. The numerical results also indicated that the influence of scattering interaction between the grains upon the sound speed in the marine shallow-layer sandy sediments has to be taken into account; however, the influence of the viscous-wave interaction can be neglected. The theoretical results obtained from the rigid- granular model seem to match the measured data better than from the elastic-granular model,even the latter model fits better for the real situation, indicating further measurements are necessary in order to gain an insight into this problem thoroughly. Through an analysis of experimental data published in journals a conclusion can be drawn that the theory of granular media is suited to deal with the problems of the sound propagation in air-filled sand better than the theory of porous media.     

Resonance modes in optical fibres

The weakly nonlinear boundary value problem of wave propagation in an optical fibere(for the transverse electric mode,for example)is formulated and a modified linear solution is obained.It is shown that a self-consistent theory of fibre optics should be weakly nonlinear,The mode of critical refraction that does not exist in the linear theory is obtained,showing that it is a mode consisting of resonance modes,It is shown that the signal carriers in a long fibre are of resonance modes,not normal modes,Some experimental data are given for comparison with the theoretical predictions and the agreement seems satisfactory.     

THEORY OF NONLINEAR INTERACTION OF FINITE AMPLITUDE RANDOM SOUND WAVES

In this paper a theory of nonlinear interaction for finite amplitude random sound waves is devel-oped.On the basis of the assumption that the velocity amplitude of source of sound should obeyRayleigh distribution,the authors successfully extend Fenlon's theory to the case of random soundwaves.A series of interesting formulas expressed in the form of the spectral dlstribution are derived(for example,the formulas for the nonlinear distortion of random sound waves,the suppression of theweak random sound wave by the intense regular sound wave,the parametric process of random soundwaves,etc.).In this paper it is also pointed out that some important results of statisitical phenomenaof nonlinear acoustics obtained by O.V.Rudenko can be easily derived from the present theory.     

Theory of sound field in a room

In the normal-mode theory of Morse, it gives a series of normal modes as the solution of forced vibration in a room. But actually there is always the direct radiation besides the normal modes which represent the reverbrant sound field only. The reason is that the normal modes were assumed only in the source, and naturally normal modes only are obtained in the solution. A theory of double source is proposed, that the sound source is both the source of the direct radiation as if in free space before the boundary surfaces were reached by the direct radiation, and after the first reflection from the boundary surfaces, the source of the reflected wavelets, randomly distributed both in space an in time on the boundary surfaces that build up the normal modes after further reflections. The wave equation is formed accordingly, and the solution of the wave equation, the sound field in a room, contains explicitly both the direct radiation and the reverberant sound formed of normal modes. The approximate mean square sound pressure is found to be the dircet sound determined by the sound power of the source,and reverberant sound determined by the sound power reduced by a factor of π/2, different slightly from the result obtained from energy consideration, if the source is pure tone. There is essentially no difference for a source of band noise.     

On study of the theory and algorithm of the three dimensional coupled mode － parabolic equation

A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes in vertical direction and the coupled mode amplitude coefficients in horizontal directions. By using the WKBZ theory and the BDRM theory, the local normal mode analysis can be processed efficiently. A PE-based algorithm, which was implemented in model FOR3D by Lee D et al [“Numerical Ocean Acoustic Propagation in Three Dimensions“, World Scientific, Singapore, 1995] is also adopted to solve the coupled mode amplitude coefficients. Numerical simulations indicate that the efficiency has been greatly improved by using CMPE3D instead of the PE approximations.     

Localized States of an Excess Electron in an Ionic Cluster

A theory of an electron affinity for an ionic cluster is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanopartiele. A critical size of the cluster regarding in formation of an electron＇s autolocalized state, dependencies of energy and radius of a polaron on a cluster＇s size are obtained by a variational method. It has been found that binding energy of the electron in the cluster depends on a eluster＇s radius but a radius of electron＇s auto-localization does not depend on the cluster＇s radius and it equals to the polaron radius in a corresponding infinity crystal. A bound state of the electron in a cluster is possible only if the duster＇s radius is more than the polaron radius.     

Modified scaling angular spectrum method for numerical simulation in long-distance propagation

The angular method(AS)cannot be used in long-distance propagation because it produces severe numerical errors due to the sampling problem in the transfer function.Two ways can solve this problem in AS for long-distance propagation.One is zero-padding to make sure that the calculation window is wide enough,but it leads to a huge calculation burden.The other is a method called band-limited angular spectrum(BLAS),in which the transfer function is truncated and results in that the calculation accuracy decreases as the propagation distance increases.In this paper,a new method called modified scaling angular spectrum(MSAS)to solve the problem for long-distance propagation is proposed.A scaling factor is introduced in MSAS so that the sampling interval of the input plane can be adjusted arbitrarily unlike AS whose sampling interval is restricted by the detector’s pixel size.The sampling interval of the input plane is larger than the detector’s pixel size so the size of calculation window suitable for long-distance field propagation in the input plane is smaller than the size of the calculation window required by the zero-padding.Therefore,the method reduces the calculation redundancy and improves the calculation speed.The results from simulations and experiments show that MSAS has a good signal-to-noise ratio(SNR),and the calculation accuracy of MSAS is better than BLAS.     

Stability and a fast calculation method of travel speed of pulse peak in convergence zone

A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.     

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.     

Viscoelastic BISQ Model for Low-Permeability Sandstone with Clay

A modified BISQ （Blot/Squirt） model for wave propagation in low-permeability sandstone is developed by introducing the viscoelastic mechanism of a porous skeleton into Dvorkin＇s model. The linear viscoelasticity of the Kelvin Voigt constitutive law is employed to describe the stress-strain relation of a solid frame with clay while the ultrasonic waves propagate through the fluid-saturated sandstone. The phase velocity and attenuation of two p-waves are given based on the present BISQ model. The comparisons between numerical results and experimental data indicate that our viscoelastic model is more realistic and feasible for wave propagation in the low-permeability sandstone, especially with clay, than traditional BISQ models.     

Acoustic performance prediction of Helmholtz resonator with conical neck

There is no accurate analytical approach for the acoustic performance prediction of Helmholtz resonator with conical neck,which has broad band acoustic attenuation performance in the low frequency range.To predict the acoustic performance of the resonator accurately,a general theory model based on the one-dimensional analysis approach with acoustic length corrections is developed.The segmentation method is used to calculate the acoustic parameters for sound propagation in conical tubes.And then,an approximate formula is deduced to give accurate correction lengths for conical tubes with difierent geometries.The deviations of the resonance frequency between the transmission loss results obtained by the general theory with acoustic lengths correction and the results from the finite element method and experiments are less than 2 Hz,which is much better than the results from one-dimensional approach without corrections.The results show that the method of acoustic length correction for the conical neck greatly improved the accuracy of the one-dimensional analysis approach,and it will be quick and accurate to predict the sound attenuation property of Helmholtz resonator with conical neck.     

Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear

The axial-stress dependence of sound wave velocity in granular packing is experimentally investigated with tri-axial and uni-axial devices. Preparing samples by repetitive loadings and unloadings in a range of 20 kPa–1000 kPa, we find that the axial-stress dependence of sound wave velocity approaches the Hertz scaling with an exponent of 1/6 for large axial stresses( 400 kPa). Weak deviation from the Hertz scaling is seen at low stresses. Repetitive axial loadings slightly reduce this deviation, and sound velocities increase nonlinearly approaching some saturated values. Velocities for uni-axial case are found slightly to be bigger than those for tri-axial isotropic compression case. These effects are discussed in the frameworks of granular solid hydrodynamics(GSH) and effective medium theory(EMT), which indicate that they cannot be explained with density nor Janssen ratio only. Dissipation occurring during wave propagation may be a non-negligible factor.     

Effect of Source＇s Height on Air-to-Water Sound Transmission with a Small-Scale Rough Sea Surface

A self-consistent perturbation approach is presented/or analyzing the effect of theairborne source＇s height on the air-to-water sound transmission in shallow water with a randomly rough sea surface. It is shown in early researches that, in shallow water with a smooth sea surface, the airborne source＇s height mostly affects the phase of the sound field and barely influences the amplitude. However, in shallow water with a rough sea surface, few researches about such a problem have been published. In this work, the sound fields in shallow water with a randomly rough sea surface induced by an airborne source at different heights are calculated by a seff-consistent perturbation approach. The numerical simulation results show that the fluctuation of the scattered field decreases as the source＇s height increases, in contrast, the averaged energy of the total field is hardly influenced by the source＇s height in the statistical sense.     

On study of the theory and algorithm of the three dimensional coupled mode-parabolic equation

A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes     

Steady-state sound field in enclosures

The classical normal-mode theory expresses the steady-state soundfield in an enclosure produced by a sound source as a series of normal modes ofvibration.Experimental facts are not often explained by this theory,and it wasconjectured that the normal-mode expression is not the complete solution ofthe wave equation in the enclosure,but only the reverberant part of it,and thereshould be an additional term representing the direct spherical radiation to makethe solution complete.The problem is examined by critically reviewing the de-rivation of the normal-mode expression,and by theoretical analysis of thesteady-state sound field in the room and experimental measurements therein.The conjecture is thus confirmed,and it is definitely shown that the sound fieldshould contain the direct wave as well as the standing waves(normal modes)formed by the confinement of the boundary surfaces.Relevant mathematicalexpressions are derived.     

PROPAGATION OF SOUND IN HIGHLY CONCENTRATED SUSPENSIONS

In this papet,an improved theory about propagation of sound in highly concentrated suspensionsis elaborated.The effects of multiple scattering among suspended particles are taken into accountnot only for compressional wave but also for thermal wave and Viscosity wave.Supposing that thewavelength of scattered compressional wave is much larger than the diameter of suspended particles,we have found out the sound field near a particular particle produced by the thermal wave and viscouswave scattered from other particles by introducing proper statistical hypotheses.Hence,the rigoroussolutions can be obtained by means of the boundary conditions of the particle.The formulas forcalculating the effective density and effective bulk modulus of suspensions are derived in the paper.For two typical concentrated suspensions,namely,coal slurry and soil slurry,numerical results arecalculated and discussed.     

Numerical prediction of envelope line-spectrum intensity in underwater acoustic waveguides

In order to predict the detectible range and region of passive sonar in underwater channel,the attenuation causes of envelope line-spectrum height during vessel noise propagation are analyzed and an approach of numerical prediction is proposed.In the paper a model for vessel radiated noise is established by a periodically locally stationary random process,two formulae of the envelope line-spectrum height with and without background-noise are deduced, therefore the attenuation rule of the envelope line-spectrum height is obtained.It is shown that the transmission loss of the sound level of the envelope line-spectrum is same as the sound level of the stationary spectrum,but the decrease of envelope line-spectrum height depends on a modified scale of amplitude modulation depth which is variable with the ratio of signal to noise. An approach of numerical prediction for envelope line-spectrum height is as follows:first,the transmission loss of the stationary radiated noise is derived using the numerical approaches of normal modes or wavenumber integration or PE etc.,then the ratio of signal to noise on sound field is calculated,finally the decrease of envelope line-spectrum height is obtained according to the modified scale,and the envelope line-spectrum height in sound field is predicted.The theory and the numerical prediction approach possess certain innovation,practicality,simplicity and suitability for engineering.     

Modeling of Nonlinear Propagation in Multi-layer Biological Tissues for Strong Focused Ultrasound

A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation （SBE） is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals.     

Mechanical properties an undercut evaluated resonance test and of silicon nanobeams with by combining the dynamic finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing, and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice＇s quantum strategy. Whereas in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, Bob＇s payoffs are found symmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob＇s classical strategy remains always dominant against any choice of Alice＇s strategy.