Gaussian Velocity Distribution Research Articles

Detection of atomic vortex beam using the near-field diffraction method

We theoretically introduce the method for detecting the atomic vortex (AV) of a helium atomic beam. The AV detection is based on near-field diffraction. The simulations relied on the Feynman path integral. The Gaussian beam and velocity distribution of helium atoms are taken into account. Gravitational field is also included in this study. This research can be useful in the field of matter-wave optics.

Comparative study of the single and double specularity coefficients on two-fluid modeling of a pseudo-2D gas–solid fluidized bed

The specularity coefficient is an unmeasurable parameter in the most popular wall boundary model during the two-fluid modeling of dense gas–solid flows. Using multiphaseEulerFoam solver, the influence of different specularity coefficient setting strategies on the gas–solid flow inside a pseudo-2D fluidized bed has been explored. It is found that the single specularity coefficient plays a regulatory role in the quantitative prediction. Increasing the specularity coefficient would cause a fluidization transition from freely bubbling to slugging, and the bed characteristics such as pressure drop and bed expansion present monotonic nonlinear changes. The double specularity coefficients approach is shown to significantly improve the predictive accuracy through verifying with the measured particle velocities, bubble diameter and rise velocity. In addition, the lognormal bubble size distribution and Gaussian bubble rise velocity distribution are observed. The specularity coefficient for walls in thickness direction is crucial and its different effects are unignorable. Overall, the present study provides a practical strategy of double specularity coefficients for the solid wall boundary conditions during two-fluid modeling.

Kinematic Structure of the Large Magellanic Cloud Globular Cluster System from Gaia eDR3 and Hubble Space Telescope Proper Motions

We have determined bulk proper motions (PMs) for 31 LMC GCs from Gaia eDR3 and Hubble Space Telescope data using multiple independent analysis techniques. Combined with literature values for distances, line-of-sight velocities, and existing bulk PMs, we extract full 6D phase-space information for 32 clusters, allowing us to examine the kinematics of the LMC GC system in detail. Except for two GCs (NGC 2159 and NGC 2210) whose high velocities suggest they are not long-term members of the LMC system, the data are consistent with a flattened configuration that rotates like the stellar disk. The one-dimensional velocity dispersions are on the order of 30 km s−1, similar to that of old stellar populations in the LMC disk. Similarly to the case for Milky Way disk clusters, the velocity anisotropy is such that the dispersion is smallest in the azimuthal direction; however, alternative anisotropies cannot be ruled out, due to distance uncertainties. The data are consistent with a single multidimensional Gaussian velocity distribution. Given the non-collisional nature of the LMC disk, this suggests that most, if not all, of the LMC GCs are formed by a single formation mechanism in the stellar disk, despite a significant spread in age and metallicity. Any accreted halo GC population is absent or far smaller in the LMC compared to the Milky Way.

Mg-mamposst: a code to test modifications of gravity with internal kinematics and lensing analyses of galaxy clusters

ABSTRACT We present an upgraded version of mg-mamposst, an extension of the mamposst (Modelling Anisotropy and Mass Profile of Spherical Observed Systems) algorithm that performs Bayesian fits of models of mass and velocity anisotropy profiles to the distribution of tracers in projected phase space, to handle modified gravity models and constrain their parameters. The new version implements two distinct types of gravity modifications, namely general chameleon and Vainshtein screening, and is further equipped with a Monte Carlo Markov chain module for an efficient parameter space exploration. The programme is complemented by the clustergen code, capable of producing mock galaxy clusters under the assumption of spherical symmetry, dynamical equilibrium, and Gaussian local velocity distribution functions as in mamposst. We demonstrate the potential of the method by analysing a set of synthetic, isolated spherically symmetric dark matter haloes, focusing on the statistical degeneracies between model parameters. Assuming the availability of additional lensing-like information, we forecast the constraints on the modified gravity parameters for the two models presented, as expected from joint lensing + internal kinematics analyses, in view of upcoming galaxy cluster surveys. In Vainshtein screening, we forecast the weak lensing effect through the estimation of the full convergence-shear profile. For chameleon screening, we constrain the allowed region in the space of the two free parameters of the model, further focusing on the $\displaystyle f(\mathcal {R})$ subclass to obtain realistic bounds on the background field $\displaystyle |f_{\mathcal {R}0}|$. Our analysis demonstrates the complementarity of internal kinematics and lensing probes for constraining modified gravity theories, and how the bounds on Vainshtein-screened theories improve through the combination of the two probes.

Role of wavefront and velocity distribution with magnetic lens on matter-wave diffraction in near-field regime

Near-field diffraction has been widely studied and applied in many research fields including optics, quantum mechanics and sensor technology. High accuracy sensors, for instance, have been developed based on the Talbot effect, i.e., the self-imaging effect, due to the high sensitivity of the near-field diffraction pattern. Since the visibility of the diffraction pattern depends intensively on velocity distribution and wavefront of the incoming wave, the Talbot-Lau effect is generally used to improve the spatial coherence of the incident wave and hence a better fringe contrast. This research aims to investigate the influences of the wavefront spreading out radially involving the Gaussian velocity distribution on the diffraction pattern of a matter-wave which are key points in design optimization and development of tools for improving fringe quality. The probability density to find the particles in the Talbot-Lau interference pattern can be obtained by employing Feynman path integrals. The theoretical simulation results show that the alteration of wavefront leads to changes in fringe contrast and the width of fringe peaks, whereas the velocity distribution affects only the fringe visibility.

Breaking beta: a comparison of mass modelling methods for spherical systems

ABSTRACT We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, either using line-of-sight velocity data only or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95 per cent confidence intervals over the radial range 0.25 < R/R1/2 < 4, where R1/2 is the half-light radius. However, radially anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy, β, to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase-space distribution function, by using higher order ‘virial shape parameters’ or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles.

A Review on Numerical Development of Tidal Stream Turbine Performance and Wake Prediction

Recently, the output of Computational Fluid Dynamic (CFD) prediction on tidal stream turbine systems has been receiving great attention owing to the vast and untapped tidal stream potential. For several years, many publications have documented the accuracy of CFD methods for steady flows, but not for unsteady flows. A challenging area persisting in the computational field is its dependence on large computing resources, and the unsteady nature of usual tidal streams. To overcome this problem, researchers have proposed modelling simpler, representative devices or combined CFD with alternative predictive methods. Nevertheless, the turbulent modelling has been a critical issue in the CFD methods and great effort has been devoted to the study of turbulence and wave effect on the wake and functioning of the turbine. The present paper is a review of CFD application on tidal stream turbine performance in both steady and unsteady flows. The performance of the turbine predicted by actuator and blade resolved methods, has been in accordance with laboratory observations. Findings of the wake have been both consistent and inconsistent with measurements, arising from interpretation of the blade force, fluid-solving method and onset flow model, and downstream range distance. With regards to arrays, preliminary work shows turbine arrangement can have profound effects in the onset flow, and in consequence, the performance of adjacent turbine rows. The results reported appear to support the wind similarity assumption, such as wake Gaussian velocity distributions and fluctuating turbine output in unsteady flows. Under the influence of surface waves, the wake recovers faster than steady flow condition due to the flow's convective acceleration, but the mean performance stays almost equal. The findings in this paper give a critical review and insight of important implications for future turbine research, such as experimental validation of the turbine prediction output in small and large arrays.

‘Observing’ unrelaxed clusters in dark matter simulations

ABSTRACT We present a detailed study of relaxed and unrelaxed galaxy clusters in a large dark matter only simulation. Recent work has demonstrated clear differences between the galaxy populations in clusters that have Gaussian velocity distributions (relaxed) compared to those that do not (unrelaxed). To directly compare with observations, we identify unrelaxed clusters in the simulations using one-dimensional velocity distributions. We show that non-Gaussian clusters have had recent major mergers and enhanced rates of galaxy infall relative to systems with Gaussian velocity profiles. Furthermore, we find that the fraction of non-Gaussian clusters increases strongly with cluster mass and modestly with redshift. For comparison, we also make use of three-dimensional information available in the simulations to explore the impact of projection on observational measurements. Differences between Gaussian and non-Gaussian clusters are much stronger when three-dimensional information is considered, which demonstrates that the strength of oberserved trends with cluster dynamics are diluted because observed velocity information is limited to one line-of-sight.

The halo’s ancient metal-rich progenitor revealed with BHB stars

Using the data from the Sloan Digital Sky Survey and the Gaia satellite, we assemble a pure sample of $\sim$3000 Blue Horizontal Branch (BHB) stars with 7-D information, including positions, velocities and metallicities. We demonstrate that, as traced with BHBs, the Milky Way's stellar halo is largely unmixed and can not be well represented with a conventional Gaussian velocity distribution. A single-component model fails because the inner portions of the halo are swamped with metal-rich tidal debris from an ancient, head-on collision, known as the "Gaia Sausage". Motivated by the data, we build a flexible mixture model which allows us to track the evolution of the halo make-up across a wide range of radii. It is built from two components, one representing the radially anisotropic Sausage stars with their lobed velocity distribution, the other representing a more metal-poor and more isotropic component built up from minor mergers. We show that inside 25 kpc the "Sausage" contributes at least 50 % of the Galactic halo. The fraction of "Sausage" stars diminishes sharply beyond 30 kpc, which is the long-established break radius of the classical stellar halo.

The influence of the dynamic state of galaxy clusters on segregation phenomena and velocity dispersion profiles

Abstract In this work we investigate the influence of the dynamic state of galaxy clusters on segregation effects and velocity dispersion profiles (VDPs) for a sample of 111 clusters extracted from SDSS-DR7. We find that 73 clusters have Gaussian (G) velocity distribution and 38 clusters have a complex or non-Gaussian (NG) velocity distribution. We also split the G and NG samples into ‘active’ and ‘passive’ galaxies, according to their specific star formation rates and stellar masses. Our results indicate a strong spatial segregation between active and passive galaxies both in G and NG systems, with passive galaxies being more central. We also found that the passive population in G systems is the only family with lower velocity dispersions for the brightest galaxies (Mr ≲ −22.75), thus presenting velocity segregation with luminosity. The similarity found between the VDPs of the galaxy populations in NG systems indicates that these sets probably share a similar mix of orbits. We also found a clear evolutionary trend for G systems, with brighter galaxies in massive clusters having flatter VDPs. The scenario emerging from this study suggests a direct relationship between segregation effects, VDPs, and the dynamic state of clusters.

The metal-rich abundance pattern – spectroscopic properties and abundances for 107 main-sequence stars

We report results from the high resolution spectral analysis of the 107 metal rich (mostly [Fe/H]$\ge$7.67 dex) target stars from the Calan-Hertfordshire Extrasolar Planet Search program observed with HARPS. Using our procedure of finding the best fit to the absorption line profiles in the observed spectra, we measure the abundances of Na, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, Ni, Cu, and Zn, and we then compare them with known results from different authors. Most of our abundances agree with these works at the level of $\pm$0.05 dex or better for the stars we have in common. However, we do find systematic differences that make direct inferences difficult. Our analysis suggests that the selection of line lists and atomic line data along with the adopted continuum level influence these differences the most. At the same time, we confirm the positive trends of abundances versus metallicity for Na, Mn, Ni, and to a lesser degree, Al. A slight negative trend is observed for Ca, whereas Si and Cr tend to follow iron. Our analysis allows us to determine the positively skewed normal distribution of projected rotational velocities with a maximum peaking at 3 km s$^{-1}$. Finally, we obtained a Gaussian distribution of microturbulent velocities that has a maximum at 1.2 km s$^{-1}$ and a full width at half maximum $\Delta v_{1/2}=$0.35 km s$^{-1}$, indicating that metal rich dwarfs and subgiants in our sample have a very restricted range in microturbulent velocity.

Generation of a cold pulsed beam of Rb atoms by transfer from a 3D magneto-optic trap

We demonstrate a technique for producing a cold pulsed beam of atoms by transferring a cloud of atoms trapped in a three dimensional magneto-optic trap (MOT). The MOT is loaded by heating a getter source of Rb atoms. We show that it is advantageous to transfer with two beams (with a small angle between them) compared to a single beam, because the atoms stop interacting with the beams in the two-beam technique, which results in a Gaussian velocity distribution. The atoms are further cooled in optical molasses by turning off the MOT magnetic field before the transfer beams are turned on.

Dynamical analysis of the cluster pair: A3407 + A3408

We carried out a dynamical study of the galaxy cluster pair A3407 \& A3408 based on a spectroscopic survey obtained with the 4 meter Blanco telescope at the CTIO, plus 6dF data, and ROSAT All-Sky-Survey. The sample consists of 122 member galaxies brighter than $m_R=20$. Our main goal is to probe the galaxy dynamics in this field and verify if the sample constitutes a single galaxy system or corresponds to an ongoing merging process. Statistical tests were applied to clusters members showing that both the composite system A3407 + A3408 as well as each individual cluster have Gaussian velocity distribution. A velocity gradient of $\sim 847\pm 114$ $\rm km\;s^{-1}$ was identified around the principal axis of the projected distribution of galaxies, indicating that the global field may be rotating. Applying the KMM algorithm to the distribution of galaxies we found that the solution with two clusters is better than the single unit solution at the 99\% c.l. This is consistent with the X-ray distribution around this field, which shows no common X-ray halo involving A3407 and A3408. We also estimated virial masses and applied a two-body model to probe the dynamics of the pair. The more likely scenario is that in which the pair is gravitationally bound and probably experiences a collapse phase, with the cluster cores crossing in less than $\sim$1 $h^{-1}$ Gyr, a pre-merger scenario. The complex X-ray morphology, the gas temperature, and some signs of galaxy evolution in A3408 suggests a post-merger scenario, with cores having crossed each other $\sim 1.65 h^{-1}$Gyr ago, as an alternative solution.

The Flutter Shutter Code Calculator

The goal of the utter shutter is to make uniform motion blur invertible, by a \uttering shutter that opens and closes on a sequence of well chosen sub-intervals of the exposure time interval. In other words, the photon ux is modulated according to a well chosen sequence called utter shutter code. This article provides a numerical method that computes optimal utter shutter codes in terms of mean square error (MSE). We assume that the observed objects follow a known (or learned) random velocity distribution. In this paper, Gaussian and uniform velocity distributions are considered. Snapshots are also optimized taking the velocity distribution into account. For each velocity distribution, the gain of the optimal utter shutter code with respect to the optimal snapshot in terms of MSE is computed. This symmetric optimization of the utter

Gaussian-inspired auxiliary non-equilibrium thermostat (GIANT) for Dissipative Particle Dynamics simulations

We present in this letter an auxiliary thermostat for non-equilibrium simulations in Dissipative Particle Dynamics based on the Gaussian distribution of particle velocities in the fluid. We demonstrate the ability of the thermostat to maintain the temperature under a wide range of shear rates and dissipative parameters, and to extend the shear rate window accessible by DPD significantly. The effect of proposed method on the viscosity of a DPD fluid is studied which is particularly of interest when the rheological behavior of a complex fluids is subject of DPD simulations. Furthermore, performance of the proposed method is compared to the ones from the well-known Lowe–Andersen scheme in regards to temperature and viscosity measurements.

Alternative Algorithm for Temperature Measurements of Cold Atoms in Cs Fountain Clocks

We report an alternative algorithm to the deconvolution method for obtaining Gaussian velocity distribution for temperature measurements in Cs fountain clocks. We estimate the velocity distribution of the cloud of cold atoms from time-of-flight signals, at different times, by calculating the square speed point by point (PBP). Then, the temperature of the Cs atomic cloud is inferred from the width ( $e^{-1/2}$ ) of the velocity distribution. We have done an exhaustive comparison of the PBP algorithm with the deconvolution method using both theoretical and experimental data for Gaussian velocity distributions. Finally, when comparing the process to obtain the velocity distribution in both the PBP algorithm and the deconvolution method, it is found that our approach is easier to implement and automate.

IN-SYNC. III. THE DYNAMICAL STATE OF IC 348—A SUPER-VIRIAL VELOCITY DISPERSION AND A PUZZLING SIGN OF CONVERGENCE

Most field stars will have encountered the highest stellar density and hence the largest number of interactions in their birth environment. Yet the stellar dynamics during this crucial phase are poorly understood. Here we analyze the radial velocities measured for 152 out of 380 observed stars in the 2?6 Myr old star cluster IC 348 as part of the SDSS-III APOGEE. The radial velocity distribution of these stars is fitted with one or two Gaussians, convolved with the measurement uncertainties including binary orbital motions. Including a second Gaussian improves the fit; the high-velocity outliers that are best fit by this second component may either (1) be contaminants from the nearby Perseus OB2 association, (2) be a halo of ejected or dispersing stars from IC 348, or (3) reflect that IC 348 has not relaxed to a Gaussian velocity distribution. We measure a velocity dispersion for IC 348 of 0.72 ? 0.07 km s?1 (or 0.64 ? 0.08 km s?1 if two Gaussians are fitted), which implies a supervirial state, unless the gas contributes more to the gravitational potential than expected. No evidence is found for a dependence of this velocity dispersion on distance from the cluster center or stellar mass. We also find that stars with lower extinction (in the front of the cloud) tend to be redshifted compared with stars with somewhat higher extinction (toward the back of the cloud). This data suggest that the stars in IC 348 are converging along the line of sight. We show that this correlation between radial velocity and extinction is unlikely to be spuriously caused by the small cluster rotation of 0.024 ? 0.013 km s?1 arcmin?1 or by correlations between the radial velocities of neighboring stars. This signature, if confirmed, will be the first detection of line of sight convergence in a star cluster. Possible scenarios for reconciling this convergence with IC 348's observed supervirial state include: (a) the cluster is fluctuating around a new virial equilibrium after a recent disruption due to gas expulsion or a merger event, or (b) the population we identify as IC 348 results from the chance alignment of two sub-clusters converging along the line of sight. Additional measurements of tangential and radial velocities in IC 348 will be important for clarifying the dynamics of this region and informing models of the formation and evolution of star clusters. The radial velocities analyzed in this paper have been made available online.

Universal scaling laws of diffusion in two-dimensional granular liquids.

We find, in a two-dimensional air table granular system, that the reduced diffusion constant D* and excess entropy S(2) follow two distinct scaling laws: D*∼e(S(2)*) for dense liquids and D∼e(3S(2)*) for dilute ones. The scaling for dense liquids is very similar to that for three-dimensional liquids proposed previously [M. Dzugutov, Nature (London) 381, 137 (1996); A. Samanta et al., Phys. Rev. Lett. 92, 145901 (2004)]. In the dilute regime, a power law [Y. Rosenfeld, J. Phys.: Condens. Matter 11, 5415 (1999)] also fits our data reasonably well. In our system, particles experience low air drag dissipation and interact with each others through embedded magnets. These near-conservative many-body interactions are responsible for the measured Gaussian velocity distribution functions and the scaling laws. The dominance of cage relaxations in dense liquids leads to the different scaling laws for dense and dilute regimes.

On the resolution of the phase space density required to obtain a specified accuracy of the solar wind bulk velocity

AbstractPlasma measurements with significantly improved accuracy and time resolution are needed to advance knowledge and understanding of plasma physical process in the magnetosphere and the solar wind. In this study, it is shown how small unresolved features in particle distribution functions can have significant impacts on the measurement of plasma bulk parameters such as the plasma bulk velocity. Errors are caused by the numerical integration scheme used to compute the phase space integrals and by errors or experimental uncertainties in measurements of the phase space distribution. Here the errors in the bulk velocity caused by the numerical integration procedure are investigated for both Gaussian (Maxwellian) velocity distributions and Kappa distributions. The particle distribution functions are perturbed by a small “bump” represented by a relatively small amplitude Gaussian with a thermal width that is much smaller than the thermal width of the unperturbed distribution. The goal is to find the grid spacing Δv in phase space required to obtain a specified accuracy of the mean flow velocity . For parameters encountered in the solar wind near the orbit of the Earth, it is shown that to determine the radial component of the solar wind bulk velocity with an accuracy less than 0.1 km/s requires a grid spacing less than Δv/v = 0.8% or, equivalently, an energy spacing less than ΔE/E = 1.6%. To accurately resolve the velocity components transverse to the heliocentric radial direction, it is found that the spacing of the angle bins must be less than Δθ = 0.4∘. The required spacing of the energy and angle bins are approximately 1 order of magnitude less than those of any solar wind ion instrument ever flown in space.

The statistical behaviour of attached eddies

Townsend’s attached eddy hypothesis forms the basis of an established model of the logarithmic layer in wall-bounded turbulent flows in which this inertially dominated region is characterised by a hierarchy of geometrically self-similar eddying motions that scale with their distance to the wall. The hypothesis has gained considerable support from high Reynolds number measurements of the second-order moments of the fluctuating velocities. Recently, Meneveau and Marusic [“Generalized logarithmic law for high-order moments in turbulent boundary layers,” J. Fluid Mech. 719, R1 (2013)] presented experimental evidence that all even-ordered moments of the streamwise velocity will exhibit a logarithmic dependence on the distance from the wall. They demonstrated that this was consistent with the attached eddy hypothesis, so long as the velocity distribution is assumed to be Gaussian (which allows the use of the central limit theorem). In this paper, we derive this result from the attached eddy model without assuming a Gaussian velocity distribution, and find that such logarithmic behaviours are valid in the large Reynolds number limit. We also revisit the physical and mathematical basis of the attached eddy hypothesis, in order to increase rigour and minimise the assumptions required to apply the hypothesis. To this end, we have extended the proof of Campbell’s theorem to apply to the velocity field corresponding to a forest of variously sized eddies that are randomly placed on the wall. This enables us to derive all moments of the velocity in the logarithmic region, including cross-correlations between different components of the velocity. By contrast, previous studies of the attached eddy hypothesis have considered only the mean velocity and its second order moments. From this, we obtain qualitatively correct skewnesses and flatnesses for the spanwise and wall-normal fluctuations. The issue of the Reynolds number dependence of von Kármán’s constant is also addressed.