988 resultados para Matter wave statistics


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Exact N-wave solutions for the generalized Burgers equation u(t) + u(n)u(x) + (j/2t + alpha) u + (beta + gamma/x) u(n+1) = delta/2u(xx),where j, alpha, beta, and gamma are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.

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In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.

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Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

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Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

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A simple equivalent circuit model for the analysis of dispersion and interaction impedance characteristics of serpentine folded-waveguide slow-wave structure was developed by considering the straight and curved portions of structure supporting the dominant TE10-mode of the rectangular waveguide. Expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam-hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was simple yet accurate in predicting the dispersion and interaction impedance behaviour at millimeter-wave frequencies. The analysis was benchmarked against measurement as well as with 3D electromagnetic modeling using MAFIA for two typical slow-wave structures (one at the Ka-band and the other at the W-band) and close agreement observed.

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An analysis of rectangular folded-waveguide slow-wave structure was developed using conformal mapping technique through Schwarz's polygon transformation and closed form expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures, one operating in Ka-band and the other operating in Q-band, against measurement and 3D electromagnetic modeling using MAFIA.

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In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.

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In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

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Submarine groundwater discharge (SGD) is an integral part of the hydrological cycle and represents an important aspect of land-ocean interactions. We used a numerical model to simulate flow and salt transport in a nearshore groundwater aquifer under varying wave conditions based on yearlong random wave data sets, including storm surge events. The results showed significant flow asymmetry with rapid response of influxes and retarded response of effluxes across the seabed to the irregular wave conditions. While a storm surge immediately intensified seawater influx to the aquifer, the subsequent return of intruded seawater to the sea, as part of an increased SGD, was gradual. Using functional data analysis, we revealed and quantified retarded, cumulative effects of past wave conditions on SGD including the fresh groundwater and recirculating seawater discharge components. The retardation was characterized well by a gamma distribution function regardless of wave conditions. The relationships between discharge rates and wave parameters were quantifiable by a regression model in a functional form independent of the actual irregular wave conditions. This statistical model provides a useful method for analyzing and predicting SGD from nearshore unconfined aquifers affected by random waves

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With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

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Subsampling is a common method for estimating the abundance of species in trawl catches. However, the accuracy of subsampling in representing the total catch has not been assessed. To estimate one possible source of bias due to subsampling, we tested whether the position on trawler sorting trays from which subsamples were taken affected their ability to represent species in catches. This was done by sorting catches into 10 kg subsamples and comparing subsamples taken from different positions on the sorting tray. Comparisons were made after species were grouped into three categories of abundance, either 'rare', 'common' or 'abundant'. A generalised linear model analysis showed that taking subsamples from different positions on the sorting tray had no major effect on estimating the total numbers or weights of fish or invertebrates, or the total number of fish or invertebrate taxa, recorded in each position. Some individual taxa showed differences between positions on the sorting tray (11.5% of taxa ina three-position design; 25% in a five-position design). But consistent and meaningful patterns in the position of these taxa on the sorting tray could only be seen for the pony fish Leiognathus moretoniensis and the saucer scallop Amusium pleuronectes. Because most bycatch laxa are well mixed throughout the catch, subsamples can be taken from any position on trawler sorting trays without introducing bias.

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This paper analyses the performance of particular wave-energy converter that uses the gyroscopic effects of a large rotating fly-wheel in combination with a controlled power-take-off device. Controlled gyroscopic forces have been used successfully in the past to reduce the motion of marine structures. With appropriately designed power-take-off elements, gyroscopic forces can be controlled to optimise the extracted energy from the motion of marine structures.

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Based on a simple picture of speckle phenomena in optical interferometry it is shown that the recent signal-to-noise ratio estimate for the so called bispectrum, due to Wirnitzer (1985), does not possess the right limit when photon statistics is unimportant. In this wave-limit, which is true for bright sources, his calculations over-estimate the signal-to-noise ratio for the bispectrum by a factor of the order of the square root of the number of speckles.

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The atomic hydrogen gas (H I) disk in the outer region (beyond similar to 10 kpc from the center) of Milky Way can provide valuable information about the structure of the dark matter halo. The recent three-dimensional thickness map of the outer H I disk from the all sky 21 cm line Leiden/Argentine/Bonn survey, gives us a unique opportunity to investigate the structure of the dark matter halo of Milky Way in great detail. A striking feature of this new survey is the north-south (N-S) asymmetry in the thickness map of the atomic hydrogen gas. Assuming vertical hydrostatic equilibrium under the total potential of the Galaxy, we derive the model thickness map of the H I gas. We show that simple axisymmetric halo models, such as softened isothermal halo (producing a flat rotation curve with V-c similar to 220 km s(-1)) or any halo with density falling faster than the isothermal one, are not able to explain the observed radial variation of the gas thickness. We also show that such axisymmetric halos along with different H I velocity dispersion in the two halves, cannot explain the observed asymmetry in the thickness map. Amongst the nonaxisymmetric models, it is shown that a purely lopsided (m = 1, first harmonic) dark matter halo with reasonable H I velocity dispersion fails to explain the N-S asymmetry satisfactorily. However, we show that by superposing a second harmonic (m = 2) out of phase onto a purely lopsided halo, e. g., our best fit and more acceptable model A (with parameters epsilon(1)(h) = 0.2, epsilon(2)(h) = 0.18, and sigma(H I) = 8.5 km s(-1)) can provide an excellent fit to the observation and reproduce the N-S asymmetry naturally. The emerging picture of the asymmetric dark matter halo is supported by the. cold dark matter halos formed in the cosmological N-body simulation.