Acoustic Wave Propagation in an Underwater Sound Channel 1. Qualitative Theory

We give a qualitative study of wave propagation in an inhomogeneousmedium principally by geometrical optics and ray theory. Theinhomogeneity is represented by a sound-speed profile whichis dependent upon one coordinate, namely the depth; and we discussthe general characteristics of wave propagation which resultfrom a source placed on the sound channel axis. We show thatour mathematical model of the sound-speed in the ocean actuallypredicts some of the behaviour of the observed physical phenomenain the underwater sound channel. Using ray theoretic techniqueswe investigate the implications of our profile on the followingcharacteristics of SOFAR propagation: (i) the sound energy travellingfurther away from the axis takes less time to travel from sourceto receiver than sound energy travelling closer to the axis,(ii) the focusing of sound energy in the sound channel at certainranges, (iii) the overall ray picture in the sound channel.     

Approach for Adaptive Sound Power Minimization of Elemental Sources in Theory and Experiments

Low frequency noise is a major issue in future aircraft with counter rotating open rotor engines. Passive noise treatments are bulky and heavy at these low frequencies. That is why active approaches are considered. The well known concept of destructive interference is used by state of the art active noise cancellation methods. The active systems are located closely to the noise source to cancel it. The microphones used for pressure minimization are in the near sound field of the noise source where active and reactive sound intensity are present. The pressure based concept is minimizing just the potential part of the acoustic energy. A new approach is proposed in this paper. It minimizes directly the net flow of acoustic energy that is transmitted into an interior. Simulation results showed that a proper estimation of acoustic power output is achieved by measuring sound intensity at a single point directly on the central axis of each secondary source. The innovative energy based active control approach (TASPM) has also successfully been validated in a laboratory environment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of phonon branch of the Bose spectrum of a superfluid Fermi system for large momenta

The phonon branch of Bose spectrum of a superfluid Fermi system (Bogolyubov sound) is investigated atT=0. It is shown that a Bogolyubov sound quantum (with arbitrary momentum) is stable and cannot decay into several excitations with lower energy.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 114–117, 1983.     

Nonequilibrium Statistical Thermodynamics of Two Dissipative Processes in Solids: Energy Losses of Channeled Particles at Low Velocities and Ultrasound Absorption by Conduction Electrons

We use methods of nonequilibrium statistical thermodynamics to investigate two dissipative processes in solids. We find the electron energy losses of a particle moving in a planar channeling regime and the sound absorption coefficient in metals under electron impurity scattering. The oscillator model is used to analyze the contribution from the effect of electron entrainment by a moving scattering center to the total dissipated energy. We investigate the frequency and temperature dependence of energy losses and also the dependence of the absorption coefficient on the sound wave vector.     

Hydrodynamic Theory of Sound Wave Propagation

We formulate the limits of applicability of the hydrodynamic equations and prove the necessity of introducing a correction to the potential energy transfer in the heat conductivity equation, which allows developing the hydrodynamic theory of the propagation of sound waves with small amplitudes. We show that this correction affects almost all predictions of the standard hydrodynamic theory. In particular, this correction allows extending the applicability domain of the hydrodynamic theory to the case of an arbitrarily viscous liquid. Moreover, in total accordance with the experimental data, the theory predicts that the sound speed and the damping rate remain finite at all frequencies up to frequencies of the order of 10^-12 sec^-1, while the hydrodynamic equations make no sense at higher frequencies and sound wave propagation in the medium consequently becomes impossible. We show that the dimensionless dispersion equation contains only one material parameter. We predict the existence of the highly damped second sound.     

Aerodynamic noise from wave-turbulence interaction

In order to estimate the acoustic energy scattered when a unit volume of free turbulence, such as in free jets, interacts with a plane steady sound wave, theoretical expressions are derived for two simple models of turbulence: eddy model and isotropic model. The effect of convection by mean motion of the energy-bearing eddies on the incident sound wave and on the sound generated from wave-turbulence interaction is taken into account. Finally, by means of a representative calculation, the directionality pattern and Mach number dependence of the noise so generated is discussed.     

On the relation between the speed of sound and the internal energy of polymers

The relation between the speed of sound and the changes of internal energy, entropy, volume, and temperature associated with the deformation of polymers is derived.All-Union Scientific Research and Design-Technological Institute of Asbestos Technical Products, Yaroslavl. Translated from Mekhanika Polimerov, No. 1, pp. 157–159, January–February, 1970.     

A new family of polynomial solutions for charged fluid spheres

We present a new family of relativistic charged fluid spheres described by a space time metric with a prescribed metric potential g₄₄ along with the specific choice of electric field intensity which vanishes at the centre and monotonically increasing towards the pressure free surface. The charged fluid solutions so obtained satisfy all the energy conditions along with the velocity of sound which decreases away from the centre. Also the solutions are utilized to construct the models of super-dense stars.     

Computation of state variables of one-dimensional non-stationary pipe flow at orifices on pipe ends

Boundary conditions of orifices in conjunction with the graphical method of characteristics given in [1] are reformulated and made ready to be used with finite difference methods. Orifice flow to the apparent narrowest cross-section is assumed conserving entropy and energy, thereafter not recovering pressure without exceeding sound speed. These conditions allow to eliminate state variables at the narrowest cross-section. Additional equations stem from mass conservation and a balance of the Riemann variable over the outgoing cross-characteristic and either further energy conservation or a balance of entropy over the outgoing particle path. They permit to determine the state at the boundary of the computational grid for usual finite difference methods. A single nonlinear equation has to be solved only in case of outflow. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The finite-time blowup of the solution of an initial boundary-value problem for the nonlinear equation of ion sound waves

We obtain blowup conditions for the solutions of initial boundary-value problems for the nonlinear equation of ion sound waves in a hydrogen plasma in the approximation of “hot” electrons and “heavy” ions. A specific characteristic of this nonlinear equation is the noncoercive nonlinearity of the form ?_t|?u|², which complicates its study by any energy method. We solve this problem by the Mitidieri–Pohozaev method of nonlinear capacity.     

A low-Mach number method for the numerical simulation of complex flows

A new numerical procedure which considers a modification to the artificial acoustic stiffness correction method (AASCM) is here presented, to perform simulations of low Mach number flows with the compressible Navier–Stokes equations. An extra term is added to the energy fluxes instead of using an energy source correction term as in the original model. This new scheme re-scales the speed of sound to values similar to the flow velocity, enabling the use of larger time steps and leading to a more stable numerical method. The new method is validated performing Large Eddy Simulations on test problems. The effect of a crucial numerical parameter alpha is evaluated as well as the robustness of the method to variations of the Mach number. Numerical results are compared to the existing experimental data showing that the new method achieves good agreement increasing the time-step, and therefore accelerating the computation for low-Mach convective flows.     

Collective excitations in the superconducting phase of the one-band Hubbard model

The method of functional integration is used to investigate the collective excitations in the superconducting state of the one-band two-dimensional Hubbard model with repulsion. The energy spectrum of the Bose modes is obtained. The existence of a branch of Bogolyubov sound is demonstrated. The phase structure and symmetry of the model are also considered.deceasedSt. Petersburg Branch, V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Metematicheskaya Fizika, Vol. 102, No. 3, pp. 457–462, March, 1995.     

Diffraktion eines schwachen Stosses an einer ebenen Platte durch die Grenzschicht

Zusammenfassung Es wird ein schwacher Stoss untersucht, welcher sich entlang einer halbunendlichen ebenen Platte ausbreitet. Es wird das Schallfeld berechnet, welches infolge der instationären Grenzschicht hinter dem Stoss abgestrahlt wird. Potential und Druck lassen sich durch elliptische Integrale darstellen. Mit dem berechneten Druckfeld lässt sich eine Dämpfung angeben.

---

If a weak shock wave is moving parallel to a half-infinite plane wall, an instationary boundary layer is formed. The sound field radiated by the boundary layer is calculated. Potential and pressure can be expressed in terms of elliptic integrals. With the calculated pressure an energy absorption can be derived.

     

Asymptotic behavior of second sound thermoelasticity with internal time-varying delay

In this paper, we consider a thermoelastic system of second sound with internal time-varying delay. Under suitable assumption on the weight of the delay, we prove, using the energy method, that the damping effect through heat conduction given by Cattaneo’s law is still strong enough to uniformly stabilize the system even in the presence of time delay.     

Coupling Boundary Elements to a Raytracing Procedure using the Singular Indirect Method

The coupling of Boundary Elements and a raytracing procedure is presented here. Such a hybrid method is best suited to the study of realistic outdoor sound propagation problems: The noise often acts in a domain where many objects like buildings or sound insulation walls scatter the sound. Thus, diffraction has to be taken into account. BEM is well suited. To study the effects of this noise on a sound receiver far away, raytracing may be preferable for such application, because refraction can be implemented more easily. Hence, a Boundary Element Analysis is performed in noisy nearfield regions, a raytracing procedure at a larger distance from the sound sources. First, the direct Boundary Element algorithm is applied to determine the sound pressure at interface points. Second, a singular indirect Boundary Element formulation is used to find intensities of point sources on the same interface which produce the previously determined sound pressure. Finally, these sound intensities are the input data for the raytracing procedure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface

This paper is concerned with a nonlinear model which describes the interaction of sound and elastic waves in a two‐dimensional acoustic chamber in which one flat ‘wall’, the interface, is flexible. The composite dynamics of the structural acoustic model is described by the linearized equations for a gas defined on the interior of the chamber and the nonlinear Timoshenko beam equations on the interface. Uniform stability of the energy associated with the interactive system of partial differential equations is achieved by incorporating a nonlinear feedback boundary damping scheme in the equations for the gas and the beam. Copyright © 2006 John Wiley & Sons, Ltd.     

Micro-Perforated Panels – Assessing the Sound Absorption

Nowadays micro-perforated panels (MPP) are continuously gaining interest in terms of the efficient design, simulation and the acoustic energy absorption capacity. The MPP construction and functionality is based on the Helmholtz resonator. The present article presents and discusses a couple sets of MPPs made of plastic and wood of different design. The analyzed MPP samples have different geometrical parameters such as the microperforation diameter, the panel thickness and the distance between holes. The MPP structure is coupled with sound-absorbing materials of different thicknesses which are partially or completely filling the air between the perforated plate and the backing rigid surface. A series of measurements performed by using the impedance tube, in order to determine the sound absorption coefficient are mentioned. The mathematical modeling approaches are presented with references to the Maa theory and experimental models like the one developed by Delany and Bazley. The coupling effort for design, mathematical modelling and experimental validation will ends into conclusions and preferred absorbing structure proposals for the highest sound absorption effciency and for the widest frequency band. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering by a perfect conductor in a waveguide: energy-preserving schemes for integral equations

^** Email: darkovolkov{at}yahoo.ca, darko{at}wpi.edu The scattering matrix for a perfectly conducting electricalcylinder (or a sound hard obstacle) in a waveguide is unitary.This is a well-known result which is a consequence of the conservationof power. When a numerical method is employed to approximatethe reflection and transmission coefficients of the cylinder,an approximate scattering matrix can be constructed. An integralequation of the second kind for an unknown density can be solved,and the density can then be used for computing the entries ofthe approximate scattering matrix. We show that this approximatematrix is unitary for cylinders of symmetric cross-section,regardless of the order of the approximation. In the nonsymmetriccase, the approximate scattering matrix still satisfies a conservationof energy condition, albeit in an unfamiliar form. As the orderof the approximation is increased, conservation of energy isalso satisfied in the more familiar form to machine accuracy.     

Global existence and exponential stability of solutions to the quasilinear thermo-diffusion equations with second sound

This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.     

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND

This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.