Extension of the frequency range for experimental determination of dispersion relationship of flexural waves in beams by correlation method

The dispersion relation is the key for studies of wave propagation. The experimental determination of a dispersion relation by measurements of wave properties in different points in space meets the challenge of spatial aliasing, which is further augmented by numerical instability of calculations. This paper presents and discusses a concept aimed to overcome the spatial aliasing problem in measurements of dispersion relation of mechanical waves propagating through beams. The concept is based on the properties of the dispersion relationship and it may be extended to the case of all other waves with monotonous dispersion relationship.

RANDOM GRAVITY WAVES IN TWO-LAYER GIDRODYNAMIC SYSTEM

The article is devoted to the study of the propagation of random gravitational waves in a three-dimensional hydrodynamic system half-space– half-space. An overview of studies on the analysis of the propagation of random waves in different systems is given. Mathematical statement of the problem contains second-order differential equations with respect to velocity potentials, kinematic and dynamic conditions on the contact surface. To study the problem, the field of deviations and the potentials of the wave velocities are presented in the form of expansions in Fourier-Stiltjes integrals. Stochastic amplitudes of the corresponding fields are expressed through the amplitude of the deviation field in the form of recurrent relations. Using the expansion in series in a small parameter for the stochastic field amplitude variations, the dynamic equation in integral form has been received. It should be noted that the use of a small parameter makes it possible to control the contribution of the nonlinearity of the corresponding terms. Subintegral functions of two- and three-wave interaction are obtained in symmetrized form. Based on the obtained equation, a linear dispersion relationship is derived. In the two-dimensional case, it degenerates into the dispersion relationship obtained by A. Naifehfor deterministic wave motions in a two-layer system. Using the equations for the amplitude of the deviation field and the ensemble averaging procedure, the equation for the spectrum of the first harmonics is obtained. The reliability of the obtained results is confirmed by a comparison with previous studies of the problem of propagation of random surface gravitational waves performed in the works of Masuda and others. The obtained results can be used in the study of the propagation of random internal waves in the oceans.

Thermodynamical properties of bosons and fermions for a lattice motivated dispersion relationship

In this paper we calculate the basic thermodynamical quantities for a system of bosonic simple harmonic oscillators (BSHOs) and the corresponding system of fermionic simple harmonic oscillators (FSHOs) using a dispersion relationship similar to cases in general relativity and condensed matter physics. In the FSHO, we see negative temperatures, and in both cases we obtain finally a system of oscillators with only one effective frequency of vibration. Also we see that pressure is less than zero for T[Formula: see text][Formula: see text][Formula: see text]Tc where Tc is the critical temperature for bosons.

Using Complex Orthogonal Decomposition to Extract Dispersion Relationships for Mass Chain

Complex orthogonal decomposition (COD) was used to determine the extracted dispersion relationship of a traveling wave in a mass chain. When COD extracts a wavenumber it will produce M values for each wavenumber, γi, and N values for each frequency, ωi; where M is the number of masses and N is the number of time samples. In this work, least squares and a simple mean of the M-γi’s and N-ωi’s extracted values were used to determine each γi and ωi, respectively. An analytical dispersion relationship for the mass chain is derived in addition to an approximate dispersion relationship. The approximate derivation was found using Lindstedt-Poincaré’s perturbation method. Lastly, the effects of the sampling rate on parameter extraction was studied. COD could accurately extract the wavenumber and frequency of a traveling wave in the mass chain. Using a simple mean provided marginally better results than that of least squares. Sampling at the Nyquist criterion gave accurate results which improved both marginally and asymptotically as the sampling rate increased.

Phonon dispersion relationship and oxygen isotope effect in superconductor LaFeAsO

In this paper, we calculate ab initially the phonon dispersion relationship of the superconductor LaFeAsO and investigate a main property in the superconductor, the oxygen isotope effect. Based on this phonon dispersion relationship, we find the fact that an important reason of the oxygen isotope effect is connected with the phonon. This result agrees well with the experimental data where the power index of the oxygen isotope effect in the superconductor LaFeAsO is small.

Group Line Energy in Phase-Resolved Ocean Surface Wave Orbital Velocity Reconstructions from X-band Doppler Radar Measurements of the Sea Surface

The wavenumber-frequency spectra of many radar measurements of the sea surface contain a linear feature at frequencies lower than the first order dispersion relationship commonly referred to as the “group line”. Plant and Farquharson, showed numerically that the group line is at least partially caused by wave interference-induced breaking of steep short gravity waves. This paper uses two wave retrieval techniques, proper orthogonal decomposition (POD) and FFT-based dispersion curve filtering, to examine two X-band radar datasets, and compare wave orbital velocity reconstructions to ground truth wave buoy measurements within the field of view of the radar. POD allows group line energy to be retained in the reconstruction, while dispersion curve filtering removes all energy not associated with the first order dispersion relationship. Results show that when group line energy is higher or comparable to dispersion curve energy, the inclusion of this group line energy in phase-resolved orbital velocity reconstructions increases the accuracy of the reconstruction. This increased accuracy is demonstrated by higher correlations between POD reconstructed time series with buoy ground truth measurements than dispersion curve filtered reconstructions. When energy lying on the dispersion relationship is much higher than the group line energy, the FFT and POD reconstruction methods perform comparably.

The elastic Rayleigh drop

Soft gel drops exhibit shape oscillations which obey a dispersion relationship that depends upon elastocapillary and compressibility effects, thus extending the classical analysis for the Rayleigh drop to include elasticity.

Methodologies and Technologies to Retrieve Information From Text Sources

A tool which algorithmically traces the effectiveness of the text files would be helpful in determining whether the text file have all the characteristic of important concepts. Every text source is build up on key phrases, and these paramount phrases follow a certain grammatical linguistic pattern widely used. An enormous amount of information can be derived from these key concepts for the further analysis such as their dispersion, relationship among the concepts etc. The relationship among the key concepts can be used to draw a concept graphs. So, this chapter presents a detailed methodologies and technologies which evaluate the effectiveness of the extracted information from text files.