Dipole Velocity Research Articles

Generating intrinsic dipole anisotropy in the large scale structures

There have been recent reports of unexpectedly large velocity dipole in the NRAO VLA Sky Survey (NVSS) data. We investigate whether the excess in the NVSS dipole reported can be of cosmological origin. We assume a long wavelength inhomogeneous scalar perturbation of the form $\ensuremath{\alpha}\mathrm{sin}(\ensuremath{\kappa}z)$ and study its effects on the matter density contrasts. Assuming an ideal fluid model, we calculate, in the linear regime, the contribution of the inhomogeneous mode to the density contrast. We calculate the expected dipole in the large scale structure (LSS) for two cases, first assuming that the mode is still superhorizon everywhere, and second assuming the mode is subhorizon but has crossed the horizon deep in matter domination and is subhorizon everywhere in the region of the survey (NVSS). In both cases, we find that such an inhomogeneous scalar perturbation is sufficient to generate the reported values of dipole anisotropy in LSS. For the superhorizon modes, we find values which are consistent with both cosmic microwave background and NVSS results. We also predict signatures for the model which can be tested by future observations.

On the determination of the diagonal components of the optical activity tensor in chiral molecules

It is shown that the diagonal components of the mixed electric-magnetic dipole polarizability tensor, used to rationalize the optical rotatory power of chiral molecules, are origin independent, if they are referred to the coordinate system defined by the eigenvectors of the dynamic electric dipole polarizability, for a given value ω of the frequency of a monochromatic wave impinging on an ordered sample. Within this reference frame, the individual diagonal components of the mixed electric-magnetic dipole polarizability are separately measurable properties. The theoretical method is applied via a test calculation to the cyclic 1,2-M enantiomer of the dioxin molecule, using a large Gaussian basis set to estimate near Hartree-Fock values within a series of dipole length, velocity, and acceleration representations.

Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4C seismic data

A central component of imaging methods is receiver-side wavefield backpropagation or extrapolation in which the wavefield from a physical source scattered at any point in the subsurface is estimated from data recorded by receivers located near or at the Earth’s surface. Elastic reverse-time migration usually accomplishes wavefield extrapolation by simultaneous reversed-time ‘injection’ of the particle displacements (or velocities) recorded at each receiver location into a wavefield modeling code. Here, we formulate an exact integral expression based on reciprocity theory that uses a combination of velocity-stress recordings and quadrupole-dipole backpropagating sources, rather than the commonly used approximate formula involving only particle velocity data and dipole backpropagating sources. The latter approximation results in two types of nonphysical waves in the scattered wavefield estimate: First, each arrival contained in the data is injected upward and downward rather than unidirectionally as in the true time-reversed experiment; second, all injected energy emits compressional and shear propagating modes in the model simulation (e.g., if a recorded P-wave is injected, both P and S propagating waves result). These artifacts vanish if the exact wavefield extrapolation integral is used. Finally, we show that such a formula is suitable for extrapolation of ocean-bottom 4C data: Due to the fluid-solid boundary conditions at the seabed, the data recorded in standard surveys are sufficient to perform backpropagation using the exact equations. Synthetic examples provide numerical evidence of the importance of correcting such errors.

Atomic harmonic generation in time-dependentR-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390 nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.

Invalidity of the Ehrenfest theorem in the computation of high-order-harmonic generation within the strong-field approximation

It is known that the strong-field approximations commonly used in models for computing high-order-harmonic generation invalidate the Ehrenfest theorem. Therefore, the time derivative of the atomic dipole or of the dipole velocity does not correspond to the dipole acceleration. We study the consequences of this invalidation for the quantitative evaluation of high-order-harmonic spectra in hydrogen at different wavelengths and intensities. As a main result, we propose a form for the time derivative of the kinetic momentum that allows a quantitatively accurate computation of the acceleration spectra using the dipole-velocity matrix elements.

Ice cover perturbation by a dipole in motion within a liquid

The two-dimensional problem of ice cover perturbation by a dipole starting to move uniformly, rectilinearly, and horizontally in a liquid initially at rest is considered. It is shown that stationary waves of two different types can be established on the liquid/ice interface, depending on the ice thickness and the dipole velocity. Examples of the numerical investigation of these waves are presented.

On the dipole, velocity and acceleration forms in high-order harmonic generation from a single atom or molecule

We consider high-order harmonic generation from a single atom or molecule and show that the generated harmonic field is proportional to the dipole velocity. We derive this result by solving Maxwell's wave equation for an infinitely thin gas. Hence, the dipole velocity form is the one that relates directly to the harmonic field, and it should be used as a reference when performing calculations with the dipole or acceleration forms.

State-selective detection of velocity-filtered ND3molecules

Translationally cold and slow ND${}_{3}$ is prepared by filtering the slow molecules from a thermal gas-phase sample using a curved electrostatic hexapole guide. This filter, like the curved quadrupole guide introduced by Rangwala et al. [Phys. Rev. A 67, 043406 (2003)] selects molecules by their forward velocity and effective electric dipole moment. Here we describe two main modifications with respect to previous work: (1) A segmented hexapole guide is used that produces a harmonic potential for the linearly Stark-shifted levels of ND${}_{3}$. A curved guide is combined with a straight hexapole guide, and independent high-voltage supplies are employed to allow for bandpass velocity filtering. (2) State-selective laser ionization is used to obtain time- and state-selective detection of the guided molecules. This enables the experimental determination of the rotational state population of the guided molecules.

Comparison between length and velocity gauges in quantum simulations of high-order harmonic generation

We solve the time-dependent Schr\"odinger equation for atomic hydrogen in an intense field using spherical coordinates with a radial grid and a spherical harmonic basis for the angular part. We present the high-order harmonic spectra based on three different forms, the dipole, dipole velocity, and acceleration forms, and two gauges, the length and velocity gauges. The relationships among the harmonic phases obtained from the Fourier transform of the three forms are discussed in detail. Although quantum mechanics is gauge invariant and the length and velocity gauges should give identical results, the two gauges present different computation efficiencies, which reflects the different behavior in terms of characteristics of the physical couplings acting in the two gauges. In order to obtain convergence, more angular momentum states are required in the length gauge, while more grid points are required in the velocity gauge. At lower laser intensity, the calculation in the length gauge is faster than that in the velocity gauge, while at high laser intensity, the calculation in the velocity gauge is more efficient. The velocity gauge is also expected to be more efficient in higher-dimensional calculations.

Consistency of ΛCDM with geometric and dynamical probes

The ΛCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade it remains the simplest model that fits remarkably well (almost) all cosmological observations. In this talk I review the increasingly successful fits provided by ΛCDM on recent geometric probe data of the cosmic expansion. I also briefly discuss some emerging shortcomings of the model in attempting to fit specific classes of data (eg cosmic velocity dipole flows and cluster halo profiles). Finally, I summarize recent results on the theoretically predicted matter overdensity evolution (a dynamical probe of the cosmic expansion), emphasizing its scale and gauge dependence on large cosmological scales in the context of general relativity. A new scale dependent parametrization which describes accurately the growth rate of perturbations even on scales larger than 100h−1 Mpc is shown to be a straightforward generalization of the well known scale independent parametrization f(a) = Ωm(a)γ valid on smaller cosmological scales.

Recollision dynamics of electron wave packets in high-order harmonic generation

We numerically investigate the dynamics of recollision of an electron in high-order harmonic generation (HHG) for an H atom and a molecular ion $\text{H}_{2}{}^{+}$ using a short (ten optical cycles), and intense $({I}_{0}\ensuremath{\ge}{10}^{14}\text{ }\text{W}/{\text{cm}}^{2})$, $z$-polarized linear laser pulse with wavelength 800 nm by accurately solving the three-dimensional time-dependent Schr\odinger equation. A time-frequency analysis obtained via Gabor transforms is employed to identify electron recollision and recombination times responsible for the generation of harmonics. We find that the HHG spectra are mainly attributed to the recollision of an inner electron wave packet with the parent ion in agreement with the classical recollision model. A time delay of the electron recollision occurs between wave packets in inner and outer regions, near to and far from the parent ion, due to different phase of the acceleration (as well as dipole velocity) of the electron. Inner wave packets at recollision contain mainly short and long trajectories whereas outer wave packets contain only single trajectories. Lower-order harmonics are generated mainly by single recollisions near field extrema, i.e., in strong electric fields whereas higher-order harmonics are generated by double trajectories with different intensities. In the case of $\text{H}_{2}{}^{+}$ at a critical nuclear distance for charge resonance enhanced ionization, we also find that HHG mainly comes from contributions of the inner electron wave packet, but with more complex recollision trajectories due to the presence of more than one Coulomb center. Triple recollision trajectories are shown to occur generally for the latter.

The dynamics of a viscous vortex dipole

The structure of a two-dimensional viscous dipole is accurately analyzed using both numerical simulations and theoretical analyses. First, a model is proposed, which computes the dipole velocity and the vortex ellipticity based on a heuristic relation between a vortex patch and a vortex with distributed vorticity profile. Second, during the stage where vortices are close to each other, a generalized self-similar solution is postulated to describe the vorticity profiles observed during the viscous spreading of the dipole. Numerical as well as theoretical considerations are given, which demonstrate the adequacy of such a hypothesis. Finally the structure of the tail that is generated behind the dipole is given in an analytical form, which favorably compares to numerical results.

Multiconfigurational time-dependent Hartree-Fock calculation of vertical excitation energies and transition moments of O2

Excitation energies and oscillator strengths in the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approximation are presented for the O2 molecule. Variations of excitation energies with respect to the diffuse character of the basis set are examined. The equivalence between oscillator strengths calculated in the dipole length and dipole velocity approximation in the MCTDHF approximation is investigated.

On the agreement between dipole length and dipole velocity calculated oscillator strengths

On the agreement between dipole length and dipole velocity calculated oscillator strengths

Polarization directions of electronic transitions in large conjugated molecules of low symmetry

Advances in experimental techniques for determination of transition moment directions in large molecules call for evaluation of the reliability of angles calculated using the semiempirical SCF-CI PPP method. Two disturbing features are considered: first, the large difference between oscillator strengths calculated by the dipole length and dipole velocity methods; second, the considerable effect of more highly excited configurations on the calculated transition moments and gradients. The two problems can be handled simultaneously if matrix elements of the linear momentum operator are obtained from the resonance integrals, since then the two operators give identical answers using wave functions derived from complete configuration interaction (CI). Numerical investigation on model systems is made of the extent of CI needed for such convergence. For strong transitions, results for polarization directions already reach their limiting values when very limited CI is performed.

DETECTING THE COSMIC DIPOLE ANISOTROPY IN LARGE-SCALE RADIO SURVEYS

The detection of a dipole anisotropy in the sky distribution of sources in large-scale radio surveys can be used to constrain the magnitude and direction of our local motion with respect to an isotropically distributed extragalactic radio source population. Such a population is predicted to be present at cosmological redshifts in an isotropically expanding universe. The extragalactic radio source population is observed to have a median redshift of z ~ 1, a much later epoch than the cosmic microwave background (z ~ 1100). I consider the detectability of a velocity dipole anisotropy in radio surveys having a finite number of source counts. The statistical significance of a velocity dipole detection from radio source counts is also discussed in detail. I find that existing large-scale radio survey catalogs do not have a sufficient number of sources to detect the expected velocity dipole with statistical significance, even if survey masking and flux calibration complications can be completely eliminated (i.e., if both the surveys and observing instruments are perfect). However, a dipole anisotropy should be easily detectable in future radio surveys planned with next-generation radio facilities, such as the Low Frequency Array and the Square Kilometer Array; tight constraints on the dipole magnitude and direction should be possible if flux calibration problems can be sufficiently minimized or corrected and contamination from local sources eliminated.

Quantum simulation of high-order harmonic spectra of the hydrogen atom

Three alternative forms of spectra, based on the dipole moment, dipole velocity, and dipole acceleration, are compared by a numerical solution of the Schrodinger equation for a hydrogen atom interact- ing with a linearly polarized laser pulse, whose electric field is given by Et = E0ftcos0t + with Gaussian carrier envelope ft = expt 2 / 2 . The carrier frequency 0 is fixed to correspond to a wavelength of 800 nm. Spectra for a selection of pulses, for which the intensity I0 = c0E 0 , duration T, and carrier-envelope phase are systematically varied, show that, depending on , all three forms are in good agreement for pulses with I0 Ib, the over-barrier ionization threshold, but that marked differences among the three appear as the pulse becomes shorter and stronger I0 Ib. Except for scalings by powers of the frequency, the three forms differ from one another only by proportional to the expectation values of the dipole moment ztf or dipole velocity ztf at the end tf of the pulse. For long, weak pulses the limit contributions are negligible, whereas for short, strong ones they are not. In the short, strong limit, where ztf 0 and therefore zt may increase without bound i.e., the atom may ionize, depending on ,a n based on the acceleration form provides a convenient computational pathway to the corresponding infinite-time dipole-velocity spectrum, which is related directly to the experimentally measured harmonic photon number spectrum HPNS. For short, intense pulses the HPNS is quite sensitive to and exhibits not only the usual odd harmonics but also even ones. The analysis also reveals that most of the photons are emitted during the passage of the pulse. Because of the divergence of zt the dipole- moment form does not provide a numerically reliable route to the for very short few- cycle, very intense laser pulses.

Migration of air channels: An instability of air flow in mobile saturated porous media

A set of two-dimensional laboratory visualization experiments reveals a previously unrecognized gas-flow instability in a porous medium saturated with a glycerine–water solution. The medium is a non-fixed vertically placed packing of grains of crushed fused silica glass. The interaction of the injected air flow and the medium structure leads to mobilization of the medium and an instability, which causes the air channel to migrate. This instability is dominated by a dimensionless number α , which can be interpreted as a normalization of a critical velocity with a dipole velocity for saturated conditions. The channel migration appears as a sequence of previous channels collapsing and new channels opening. The channel migration comes to a stop after some time, leaving one thin and stable channel. The process is studied by calculating the cumulated lateral movement distance of a channel and the lateral width of the area affected by the migration, both scaled by α with an empirical power of 0.25. Another dimensionless number f is defined to qualify the migration under different grain size, height of bed, and air flow rate.

Influence of measurement errors and deviations from Tully‐Fisher relationship on multipole structure of bulk galaxy motion

AbstractThe velocity field of large‐scale non‐Hubble galaxy motion recovered from peculiar velocities of spiral galaxies is distorted due to measurement errors and deviations from Tully‐Fisher relationship. To figure out how this affects the multipole structure we use the Monte‐Carlo approach and simulate errors and deviations. We use the galaxies from the Revised Flat Galaxy Catalogue subsample and the generalized Tully‐Fisher relationship in the ‘H I line width–angular diameter’ version. The analysis of the multipole structure has shown that the dipole velocity component (bulk motion) is underestimated, and the characteristic values of the quadrupole component are overestimated. The directions of the quadrupole component's eigenvectors can be determined precisely enough. Typical deviation angles of bulk motion apices lie between 17 and 40.. The main input is caused by errors in the measurement of the angular diameter. The probability of the quadrupole component being incidental can be estimated at the 4 per cent level. For the octopole component, it can be estimated at the 7–10 per cent level. This is essentially higher than the estimations less than 1 per cent due to the Fisher test. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Harmonic generation: Quantum-electrodynamical theory of the harmonic photon-number spectrum

Simulations of harmonic generation in the single-atom limit usually describe the harmonic radiation as proportional to the squared magnitude of the Fourier transform (FT) of the expectation value of either the dipole moment or the dipole acceleration. However, no derivation of an explicit single-atom representation of the typical experimental measurement (i.e., the number of harmonic photons produced versus the frequency of the harmonic) has been given. By means of the first principles of quantum electrodynamics a formula for this ``harmonic photon-number spectrum'' is derived, which is proportional to the double FT of the time-autocorrelation function of the dipole velocity of the whole system. Within the long-wavelength approximation the time-correlation function can be recast as the FT of the squared magnitude of the expectation value of the dipole velocity of a single representative atom.