Propagation of finite amplitude sound waves radiated from a pulsating sphere

The propagation of weakly non-linear acoustic waves is studied, which are radiated from a harmonically pulsating sphere in an inviscid perfect gas. A representation of the solution is presented for a far field equation of the first order, which is closely related to the solution obtained by the method of renormalization. The applicability of the method to the present problem is proved within the first order approximation. The asymptotic solution in the far field is obtained up to the second order by using the method of renormalization. A uniformly valid solution is, to the second approximation, constructed by matching the near field solution with the far field solution. Also investigated is the effect of dimensionless parameters and the second order correction on the acoustic shock formation distances and the non-linear distortion of waveforms.     

Propagation of finite amplitude sound waves radiated from an oscillating rigid sphere

The propagation of weakly non-linear acoustic waves radiated from a harmonically oscillating sphere in an inviscid perfect gas is studied. A representation of the exact solution is presented for a far field equation of the first order, governing the radial component of velocity. The tangential component of velocity is readily derived from the result for the radial velocity. The components are then expanded in a Fourier series, with the fundamental frequency being that of the oscillator. A uniformly valid solution is constructed by matching the near field solution with the far field solution. The acoustic shock formation distances are also evaluated, which shows the anisotropic character of the shock formation.     

Magnetization waves in the Landau-Lifshitz model

The solutions of the Landau-Lifshitz equation with finite-gap behaviour at infinity are considered. By means of the inverse scattering method the large-time asymptotics is obtained.     

Magnetization curves of deposited finite spin chains

The European Physical Journal B - Two-dimensional arrays of interacting magnetic nanostructures offer a remarkable playground for simulating, experimentally, lattice spin models. Initially designed...     

New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma

Abstract

The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas–Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.     

Absorption of finite amplitude focused ultrasound

Predictions of the absorption of focused finite amplitude waves based on weak shock theory have been tested experimentally. The characteristics of this absorption are qualitatively different from those associated with small signal losses. Under appropriate conditions, the absorption of finite amplitude ultrasound is determined largely by source amplitude, field geometry, and the nonlinear properties of the medium and is only weakly dependent upon the small signal absorption coefficient of the material. These effects are seen most dramatically in sharply focused sound fields. To emphasize nonlinear absorption in an experimental test of these predictions, measurements of heating were made in agar which has a very small linear absorption coefficient. Under appropriate conditions, nonlinear losses can make the effective absorption coefficient of this poorly absorbing material somewhat greater than the soft tissues of the body.     

Calibration of ultrasonic hydrophone probes up to 100 MHz using time gating frequency analysis and finite amplitude waves

A number of ultrasound imaging systems employs harmonic imaging to optimize the trade off between resolution and penetration depth and center frequencies as high as 15 MHz are now used in clinical practice. However, currently available measurement tools are not fully adequate to characterize the acoustic output of such nonlinear systems primarily due to the limited knowledge of the frequency responses beyond 20 MHz of the available piezoelectric hydrophone probes. In addition, ultrasound hydrophone probes need to be calibrated to eight times the center frequency of the imaging transducer. Time delay spectrometry (TDS) is capable of providing transduction factor of the probes beyond 20 MHz, however its use is in practice limited to 40 MHz. This paper describes a novel approach termed time gating frequency analysis (TGFA) that provides the transduction factor of the hydrophone probes in the frequency domain and significantly extends the quasi-continuous calibration of the probes up to 60 MHz. The verification of the TGFA data was performed using TDS calibration technique (up to 40 MHz) and a nonlinear calibration method (up to 100 MHz). The nonlinear technique was based on a novel wave propagation model capable of predicting the true pressure-time waveforms at virtually any point in the field. The spatial averaging effects introduced by the finite aperture hydrophones were also accounted for. TGFA calibration results were obtained for different PVDF probes, including needle and membrane designs with nominal diameters from 50 to 500 micro m. The results were compared with discrete calibration data obtained from an independent national laboratory and the overall uncertainty was determined to be +/-1.5 dB in the frequency range 40-60 MHz and less than +/-1 dB below 40 MHz.     

Time-reversed sound beams of finite amplitude.

Numerical simulations based on the nonlinear parabolic wave equation are used to investigate time reversal of sound beams radiated by unfocused and focused sources. Emphasis is placed on nonlinear propagation distortion in the time-reversed beam, and specifically its effect on field reconstruction. Distortion of this kind, due to amplification during time reversal, has been observed in recent experiments [A. P. Brysev et al., Acoust. Phys. 44, 641-650 (1998)]. Effects of diffraction introduced by time-reversal mirrors with finite apertures are also considered. It is shown that even in the presence of shock formation, the ability of time reversal to retarget most of the energy on the source or focal region of the incident beam is quite robust.     

Finite amplitude waves in ion-beam plasma systems

Several types of solitary waves can exist in an ion-beam plasma system. Their velocity is determined as a function of the beam velocity and the wave amplitude θ₀. The region of existence is limited for θ₀ → 0 by the linear modes, and for finite θ₀ by the trapping of the beam or background ions.     

Large amplitude spin waves in ultra-cold gases

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. The full position and momentum dependence of the distribution function must then be retained. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves (or internal conversion) in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped ⁸⁷Rb atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence. In two appendices we calculate the Wigner transform of the interaction term in the S matrix method, to first order in gradients; Appendix A.1 treats the case of spin-independent interactions, Appendix A.2 that of spin-dependent interactions.Received: 17 April 2003, Published online: 17 July 2003PACS: 05.30.-d Quantum statistical mechanics - 51.10.+y Kinetic and transport theory of gases - 75.30.Ds Spin waves     

Random combinations of sine waves of equal amplitude

Random combinations of up to ten sine waves have been considered and the distribution of the resultant amplitudes obtained.     

Symmetric waves are traveling waves for a shallow water equation modeling surface waves of moderate amplitude

Following a general principle introduced by Ehrnström, Holden and Raynaud in 2009, we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.     

Bessel beams of finite amplitude in absorbing fluids

Second-harmonic generation in a Bessel beam is investigated analytically, with emphasis on the effect of absorption. It is shown that absorption has a strong influence on the far-field beam profile. Numerical results are presented for higher harmonics and for waveform distortion in a Bessel beam that forms a shock.