Showing papers on "Group velocity published in 2014"

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

Abstract: We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.

Photons that travel in free space slower than the speed of light

Abstract: That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.

An extended traffic flow model on a gradient highway with the consideration of the relative velocity

Abstract: In this paper, an extended traffic flow model on a single-lane gradient highway is proposed with the consideration of the relative velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow on the gradient varies with the slope and the coefficient of the relative velocity: when the slope is constant, the stable regions increase with the increase of the coefficient of the relative velocity; when the coefficient of the relative velocity is constant, the stable regions increase with the decrease of the slope in downhill and increase with the increase of the slope in uphill. The Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations are derived to describe the triangular shock waves, soliton waves, and kink-antikink waves in the stable, metastable, and unstable region, respectively. The numerical simulation shows a good agreement with the analytical result, which shows that the traffic congestion can be suppressed by introducing the relative velocity.

Modal Stability TheoryLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013

Abstract: This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spati ...

Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory

Abstract: The propagation characteristics of the longitudinal wave in a piezoelectric nanoplate were investigated in this study. The nonlocal elasticity theory was used and the surface effects were taken into account. In addition, the group velocity and phase velocity were derived and investigated, respectively. The dispersion relation was analyzed with different scale coefficients, wavenumbers, and voltages. The results showed that the dispersion degree can be strengthened by increasing the wavenumber and scale coefficient.

Scattering of Low-Mode Internal Waves at Finite Isolated Topography

Abstract: A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h0/H0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h0/H0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h0/H0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefor...

A Transverse Oscillation Approach for Estimation of Three-Dimensional Velocity Vectors, Part II: Experimental Validation

Abstract: The 3-D transverse oscillation method is investi- gated by estimating 3-D velocities in an experimental flow-rig system. Measurements of the synthesized transverse oscillating fields are presented as well. The method employs a 2-D trans- ducer; decouples the velocity estimation; and estimates the axi- al, transverse, and elevation velocity components simultaneous- ly. Data are acquired using a research ultrasound scanner. The velocity measurements are conducted with steady flow in six- teen different directions. For a specific flow direction with (α, β) = (45, 15)°, the mean estimated velocity vector at the center of the vessel is (vx, vy, vz) = (33.8, 34.5, 15.2) ± (4.6, 5.0, 0.6) cm/s where the expected velocity is (34.2, 34.2, 13.0) cm/s. The ve- locity magnitude is 50.6 ± 5.2 cm/s with a bias of 0.7 cm/s. The flow angles α and β are estimated as 45.6 ± 4.9° and 17.6 ± 1.0°. Subsequently, the precision and accuracy are calculated over the entire velocity profiles. On average for all direction, the relative mean bias of the velocity magnitude is −0.08%. For α and β, the mean bias is −0.2° and −1.5°. The relative standard deviations of the velocity magnitude ranges from 8 to 16%. For the flow angles, the ranges of the mean angular deviations are 5° to 16° and 0.7° and 8°.

The Effects of Spatial Dispersion on Power Flow Along a Printed-Circuit Tensor Impedance Surface

Abstract: In this communication, expressions for the group velocity and the direction of power flow along an idealized tensor impedance boundary condition (TIBC) and a printed-circuit tensor impedance surface (PCTIS), are found. A PCTIS consists of a patterned metallic cladding over a grounded dielectric substrate. The patterned metallic cladding is modeled by a tensor impedance sheet. Expressions for the surface impedance of a TIBC and a PCTIS are reviewed. From these expressions, the group velocity and direction of power flow are derived as a function of transverse wave vector. A PCTIS exhibits spatial dispersion due to the electrical thickness of its substrate while a TIBC does not. As a result of this spatial dispersion, a PCTIS can have the same surface impedance as a TIBC for a given transverse wave vector, but a different direction of power flow. The expressions for direction of power flow along a TIBC and a PCTIS are verified with a full-wave electromagnetic solver.

Velocity profiles in strongly turbulent Taylor-Couette flow

Abstract: We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio η between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the qualitative trends are the same – down-bending for large wall distances and the (properly shifted and non-dimensionalized) angular velocity profile ω+(r) being close...

Time-lapse seismic noise correlation tomography at Valhall

Abstract: We show that a reliable and statistically significant group velocity time-lapse difference between 2004 and 2010 can be retrieved from ambient seismic noise in an offshore hydrocarbon exploitation setting. We performed a direct comparison of Scholte wave group velocity images obtained using regularized tomography. We characterize the expected variation in group velocity images from the 2004 or 2010 recordings that result from fluctuations in the cross correlations by looking at cross correlations of portions of the recordings. We prove that the time-lapse difference is statistically significant. The time-lapse group velocity image from ambient noise data shows strong similarities with a time-lapse phase velocity map obtained from controlled source data. The most striking features are a northern and a southern group velocity increase due to compaction and subsidence as a result of reservoir production.

Achromatic THz wave plate composed of stacked parallel metal plates

Abstract: We propose a simple achromatic terahertz wave plate composed of stacked parallel metal plates with a hole array. It consists of an ensemble of designed parallel plate waveguides; the high and low propagation speeds of waves in TE and TM waveguide modes with the same group velocity cause a constant phase difference over a wide frequency region. Using that wave plate, we obtained intense single- and multi-cycle THz pulses with circular polarization.

Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators

Abstract: We present experimental results demonstrating the phenomenon of acoustic transparency with a significant slowdown of sound propagation realized with a series of paired detuned acoustic resonators (DAR) side-attached to a waveguide. The phenomenon mimics the electromagnetically induced transparency in atomic physics. By arranging four identical DAR pairs along the waveguide with an equal subwavelength separation between adjacent pairs, we show that this arrangement features unique properties of narrow-band transmission and strong dispersion. In particular, we demonstrate side-lobe suppression of more than 20 dB on both sides of the transparency window, and we quantify directly (using a pulse propagation) the acoustic slowdown effect, resulting in the sound group velocity of \ensuremath{\sim}9.8 m/s (i.e. in the group refractive index of 35). We find very similar values of the group refractive index by using measurements of the phase of the transmitted wave. It is also shown that a direct coupling exists between the DAR in each pair, which cannot be explained by the interference of waves radiated from those resonators. This detrimental coupling becomes noticeable for small values of detuning and also if the cross-sectional area of the neck of the resonators is increased.

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Abstract: We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scalefilaments with a free parameter—the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

Electromagnetically induced transparency in a two-dimensional quantum dot: Effects of impurity, external fields, hydrostatic pressure and temperature

Abstract: In this paper effects of external electric and magnetic fields, hydrostatic pressure and temperature on the electromagnetically induced transparency of a two-dimensional quantum dot are investigated. To do this, absorption as well as refractive index and the group velocity of the probe light pulse in the presence of external electric and magnetic fields are discussed. The results show that the electromagnetically induced transparency occurs in the system and its frequency, transparency window and group velocity of the probe field are strongly affected by the confinement potential, external fields, hydrostatic pressure and temperature. It is found that, in comparison with the atomic systems, electromagnetically induced transparency and the group velocity of light can be controlled via the confinement potential and external perturbations.

New statistical analysis of the horizontal phase velocity distribution of gravity waves observed by airglow imaging

Abstract: We have developed a new analysis method for obtaining the power spectrum in the horizontal phase velocity domain from airglow intensity image data to study atmospheric gravity waves. This method can deal with extensive amounts of imaging data obtained on different years and at various observation sites without bias caused by different event extraction criteria for the person processing the data. The new method was applied to sodium airglow data obtained in 2011 at Syowa Station (69°S, 40°E), Antarctica. The results were compared with those obtained from a conventional event analysis in which the phase fronts were traced manually in order to estimate horizontal characteristics, such as wavelengths, phase velocities, and wave periods. The horizontal phase velocity of each wave event in the airglow images corresponded closely to a peak in the spectrum. The statistical results of spectral analysis showed an eastward offset of the horizontal phase velocity distribution. This could be interpreted as the existence of wave sources around the stratospheric eastward jet. Similar zonal anisotropy was also seen in the horizontal phase velocity distribution of the gravity waves by the event analysis. Both methods produce similar statistical results about directionality of atmospheric gravity waves. Galactic contamination of the spectrum was examined by calculating the apparent velocity of the stars and found to be limited for phase speeds lower than 30 m/s. In conclusion, our new method is suitable for deriving the horizontal phase velocity characteristics of atmospheric gravity waves from an extensive amount of imaging data.

Temporal soliton excitation in an ε-near-zero plasmonic metamaterial

Abstract: The excitation of temporal solitons in a metamaterial formed by an array of e-near-zero (ENZ) plasmonic channels loaded with a material possessing a cubic (χ(3)) nonlinearity are theoretically explored. The unique interplay between the peculiar dispersion properties of ENZ channels and their enhanced effective nonlinearity conspires to yield low threshold intensities for the formation of slow group velocity solitons.

Source location in plates based on the multiple sensors array method and wavelet analysis

Abstract: A new method for impact source localization in a plate is proposed based on the multiple signal classification (MUSIC) and wavelet analysis. For source localization, the direction of arrival of the wave caused by an impact on a plate and the distance between impact position and sensor should be estimated. The direction of arrival can be estimated accurately using MUSIC method. The distance can be obtained by using the time delay of arrival and the group velocity of the Lamb wave in a plate. Time delay is experimentally estimated using the continuous wavelet transform for the wave. The elastodynamic theory is used for the group velocity estimation.

Flying radio frequency undulator

Abstract: A concept for the room-temperature rf undulator, designed to produce coherent X-ray radiation by means of a relatively low-energy electron beam and pulsed mm-wavelength radiation, is proposed. The “flying” undulator is a high-power short rf pulse co-propagating together with a relativistic electron bunch in a helically corrugated waveguide. The electrons wiggle in the rf field of the −1st spatial harmonic with the phase velocity directed in the opposite direction in respect to the bunch velocity, so that particles can irradiate high-frequency Compton's photons. A high group velocity (close to the speed of light) ensures long cooperative motion of the particles and the co-propagating rf pulse.

Stability of Bragg Grating Solitons in a Semilinear Dual Core System With Dispersive Reflectivity

Abstract: The existence and stability of quiescent Bragg grating solitons in a linearly coupled dual core system, where one core has the Kerr nonlinearity and is equipped with a Bragg grating with dispersive reflectivity and the other core is a linear uniform waveguide, are investigated. When the group velocity in the linear core is zero, the linear spectrum of the system possesses two genuine bandgaps. It is found that soliton solutions exist throughout the bandgaps. When the group velocity in the linear core is nonzero, the linear spectrum contains three gaps, a genuine central gap and an upper and lower gaps that overlap with one branch of continuous spectrum. It is found that solitons do not exist in the central gap. On the other hand, the lower and upper gaps are completely filled with soliton solutions. It is also found that above a certain value of dispersive reflectivity parameter, sidelobes appear in the soliton's profile. We have found exact analytical expressions for the tails of solitons that agree very well with the numerical solutions. The stability of solitons have been analyzed by means of systematic numerical stability analysis. we have considered the effects and interplay of coupling coefficient, group velocity in the linear core and dispersive reflectivity on the stability of solitons. Vast stable regions have been found in the upper and lower gaps. A key finding is that stronger coupling coefficient tends to enhance the stabilizing effect of dispersive reflectivity. In the vicinity of the stability border, unstable solitons initially radiate some energy and subsequently evolve to a single moving soliton. In some cases, when the group velocity in the linear core is nonzero, the unstable soliton breaks up into two moving solitons. These results demonstrate that stable moving solitons exist in this model.

Non-Hermitian-transport effects in coupled-resonator optical waveguides

Abstract: Coupled-resonator optical waveguides are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise- and counterclockwise-propagating waves, which, in combination with the losses, induces nonorthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-Hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-Hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., non-Hermitian degeneracies at which not only the frequencies and decay rates but also the eigenmodes themselves coalesce. The non-Hermitian corrections to the group velocity are largest in the regions around the exceptional points.

Optically controllable switch for light propagation based on triple coupled quantum dots.

Abstract: A switch is proposed for controlling the subluminal and superluminal light propagation through the triple coupled quantum dots system. The steady-state and transient behavior of the absorption and the dispersion of a probe pulse through a triple quantum dots molecule are investigated. We demonstrate that the group velocity of a light pulse can be controlled from subluminal to superluminal or vice versa by controlling the rates of incoherent pumping and tunneling between electronic levels. Switching time is calculated by discussing the dependency of optical transient properties on the incoherent pumping and inter-dot tunneling rates. We introduce three controlling parameters that make it possible to control the wave propagation electrically or even optically in such coupled quantum dot systems.