Tube-wave propagation in a fluid-filled borehole generated by a single point force applied to the surrounding formation

Propagation of tube waves in an infinite fluid-filled borehole, generated by a single-force point source placed in the elastic surrounding formation, is analyzed in the long-wave approximation. Integral representations of the precise solution are obtained both for fast and slow formations. An asymptotic analysis of tube-wave propagation in the fluid-filled borehole is performed on the basis of these two integral representations. The complete asymptotic wave field in the borehole fluid for a fast formation consists of P and SV phases and the lowest eigenmode of the Stoneley wave (tube wave). For a slow formation the conical Stoneley wave (Mach wave) is generated. It appears only behind the critical angle defined by the ratio of the S wave velocity in the formation to the low-frequency Stoneley wave velocity and decays weakly with an offset. Asymptotic wave forms are in good agreement with wave forms obtained by straightforward calculations.     

Rayleigh wave attenuation due to the scattering by two-dimensional irregularities of the walls of an empty borehole

Attenuation of the Rayleigh waves propagating along an irregular surface of an empty borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular boundary of a half-space. The technique used to evaluate the attenuation coefficient is based on the perturbation method and the mean field method. As a result, an expression is obtained that relates the partial attenuation coefficients of the surface Rayleigh wave to the scattering by the irregular surface of an empty borehole into the bulk longitudinal and transverse waves (the R → P and R → S processes) and into the surface Rayleigh waves (the R → R processes). The frequency-dependent behavior of the partial attenuation coefficients is analyzed for different correlation functions of irregularities.     

Formation of an energy cascade in a system of vortices on the surface of water

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pumping. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pumping can be described by a power-law function of the wave vector E(k) ～ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm^?1 is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.     

Magnetostriction domain structure in a periodic system of magnetoelastic and elastic nonmagnetic layers

The spectrum of magnetoelastic waves in a periodic structure of alternating ferromagnetic and nonmagnetic layers was studied. In the case of ferromagnetic layers with easy magnetization axes parallel to the layer surfaces, an orientational phase transition induced by an external tangential magnetic field H_e was considered. The formation of an inhomogeneous phase with a spatially modulated order parameter, which is caused by the magnetization being coupled through magnetostriction to lattice strains near the interfaces separating the magnetoelastic from elastic media, is predicted. It is shown that at a certain critical field in excess of the orientational phase transition field in the system without magnetostriction, a magnetoelastic wave propagating in a direction parallel to the in-plane magnetization vector M becomes unstable at finite values of the wave vector and condenses into a magnetostriction domain structure. A phase diagram in the (L, T, H_e) coordinates is constructed, and the regions of existence of thermodynamically equilibrium collinear, canted, and domain phases are established (L and T are the thicknesses of the ferromagnetic and nonmagnetic layers, respectively).     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

An exact solution of the Helmholtz equation u _xx + u _yy + u _zz + k²u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.     

Constructal Design Applied to the Geometric Evaluation of an Oscillating Water Column Wave Energy Converter Considering Different Real Scale Wave Periods

The present work presents numerical study of the influence of geometry on the performance of an oscillating water column (OWC) wave energy converter by means of a constructal design. The main purpose is to maximize the root mean square hydrodynamic power of device, (P_hyd)_RMS, subject to several real scale waves with different periods. The problem has two constraints: hydropneumatic chamber volume (V _HC ) and total OWC volume (V _T ), and two degrees of freedom: H₁/L (ratio of height to length of the hydropneumatic chamber) and H₃ (OWC submergence). For the numerical solution it was used a computational fluid dynamic (CFD) code, based on the finite volume method (FVM). The multiphasic volume of fluid (VOF) model is applied to tackle with the water–air interaction. The results led to important theoretical recommendations about the design of OWC device. For instance, the best shape for OWC chamber, which maximizes the (P_hyd)_RMS, was achieved when the ratio (H₁/L) was four times higher than the ratio of height to length of incident wave (H/λ), (H₁/L) _o = 4(H/λ). Moreover, the optimal submergence (H₃) was achieved as a function of wave height (H) and water depth (h), more precisely given by the following relation: h ? (3H/4) ≤ (H₃) _o ≤ h.     

Oscillations and Waves in a Nonlinear System with the 1/<Emphasis Type="Italic">f</Emphasis> Spectrum

Numerical methods are used to study a spatially distributed system of two nonlinear stochastic equations that simulate interacting phase transitions. Conditions for self-oscillations and waves are determined. The 1/f and 1/k spectra of extreme fluctuations are formed when waves emerge and move under the action of white noise. The distribution of the extreme fluctuations corresponds to the maximum entropy, which is proven by the stability of the 1/f and 1/k spectra. The formation and motion of waves under external periodic perturbation are accompanied by spatiotemporal chaotic resonance in which the domain of periodic pulsations is extended under the action of white noise.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Der Einfluß von Plasmawellen auf das Reflexionsvermögen von Metallen (I)

The wellknown derivation ofFresnel's formula for the reflection coefficient of a metal surface in the case of an oblique incident wave polarized parallel to the plane of incidence includes a mistake concerning the boundary conditions and neglecting the possibility of optical excitation of plasma waves. The right formula for this case is derived in the following paper byForstmann. The discussion of an approximate formula obtained by a simplified method leads in the case of vanishing reflectivity forΩ>Ω _p to a real Brewster-angleα _B . ForΩ<Ω _p there exists another solution with a complex Brewster-angle, representing a surface wave in form of a Zenneck-wave. For large wave numbers and for light velocity ? electron velocity the dispersion formula for these surface waves is nearly identical with that obtained byRitchie andWagner, while for small wave numbers there is a great difference between these two formulas. In the middle region the frequenceΩ is nearlyΩ _p /√2.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Density ducts formed by heating the Earth’s ionosphere with high-power HF radio waves

The parameters of plasma disturbances at altitudes 660 and 840 km, measured by the instruments onboard the French DEMETER satellite and the US DMSP satellites passing through the magnetic flux tube footed at the region of intense modification of the F ₂ ionospheric layer by the high-power HF radio waves of the Sura heating facility, are presented. The formation of artificial enhanced-density plasma ducts in the outer ionosphere is observed experimentally. Conditions facilitating the formation of such ducts are pointed out.     

Consecutive Quasi-Phase-Matched Interactions of Light Waves in Periodically Poled Nonlinear Optical Crystals

A new type of quasi-phase-matched interactions of light waves is considered — consecutive interactions of waves with frequencies w, 2w, 3w and w, 2w, 4w. They are shown to be possible in a periodically poled LiNbO₃:Y:Mg crystal for both co- and counterpropagating waves. It is shown that under certain conditions the energy of a high-intensity pump wave in the consecutive three-frequency interactions under consideration can be completely converted to the energy of one of the other two waves.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Collision between two ortho-positronium (Ps) atoms: A four-body Coulomb problem

The elastic collision between two ortho-positronium (e.g. S = 1) atoms is studied using an ab-initio static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment S = 0, i.e., singlet (+) and S = 2, i.e., triplet (?) states are studied. An augmented Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section (σ), the quenching cross-section (σ_q) and ortho-to-para conversion ratio (σ/σ_q). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.     

Ultrasonic attenuation in insulating crystals

A theory for the dampingΓ of ultrasonic waves due to three-phonon processes is developed by using a Green's function method. The imaginary part of the self-energy of the impressed ultrasound phonons interacting with thermal phonons is calculated. In the limits ofω τ very large and very small the known results are rederived, whereω is the frequency of the ultrasonic wave andτ the thermal phonon relaxation time. The intermediate range ofω τ values is discussed in detail for the case of longitudinal phonon attenuation. It is found, that forω τ>1 a Landau-Rumer type law applies also for longitudinal phonons,Γ～ωT ⁴. But it is shown that dispersion effects and large third-order elastic anisotropy can lead to a stronger temperature dependence thanT ⁴ and a weaker dependence on frequency thanω. These results are compared with recent experiments.     

The fourth-order nonlinear Schrödinger equation for the envelope of Stokes waves on the surface of a finite-depth fluid

The method of multiple scales is used to derive the fourth-order nonlinear Schrödinger equation (NSEIV) that describes the amplitude modulations of the fundamental harmonic of Stokes waves on the surface of a medium-and large-depth (compared to the wavelength) fluid layer. The new terms of this equation describe the third-order linear dispersion effect and the nonlinearity dispersion effects. As the nonlinearity and the dispersion decrease, the equation uniformly transforms into the nonlinear Schrödinger equation for Stokes waves on the surface of a finite-depth fluid that was first derived by Hasimoto and Ono. The coefficients of the derived equation are given in an explicit form as functions of kh (h is the fluid depth, and k is the wave number). As kh tends to infinity, these coefficients transform into the coefficients of the NSEIV that was first derived by Dysthe for an infinite depth.     

Exact travelling solutions for some nonlinear physical models by ( <Emphasis Type="Italic">G</Emphasis>′/ <Emphasis Type="Italic">G</Emphasis>)-expansion method

In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (G′/G)-expansion method is used to construct travelling wave solutions of the two-dimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many fields such as, solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The (G′/G)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.     

Fracture localization in space as a cause of variations in the amplitude distribution of acoustic emission signals

The change in the spatial distribution of acoustic emission sources in the course of the deformation and fracture of samples of materials and rocks is accompanied by changes in the amplitude distribution of the received signals because of the geometric spread of the elastic wave front. It is customary to characterize the amplitude distributions of acoustic emission signals in terms of the b value (the slope of the differential amplitude distribution). In particular, the localization of the sources may cause a decrease in the b value, which is usually interpreted as a precursor of macrofracture. A correct interpretation of the decrease in the b value is only possible if the location of the sources in space is accomplished and a correction for the spread and attenuation of elastic waves is introduced.     

Resonant and nonresonant contributions from unphysical regions in dispersion relations

Unphysical regions on the right hand cut in partial wave dispersion relations for a two-particle processA+B→A′+B′ are expressed by measurable quantities, under the assumption that there is only one important 2-particle channel in the unphysical region. The solution is unique, if the phase shiftδ _l for the elastic scattering in the channel responsible for the appearance of the unphysical region takes a value between 0 andπ at the physical threshold forA+B→A′+B′. The difference between non resonant (δ_l≠π/2 in the unphysical region) and resonant contributions is shortly discussed.