Mean Square Velocity Research Articles

Velocity Dispersion of the Open Cluster NGC 2571 by Radial Velocities and Proper Motions

We use a kernel density estimator method to evaluate the stellar velocity dispersion in the open cluster NGC 2571. We derive the 3D velocity dispersion using both proper motions as extracted from Gaia Data Release 3 and single-epoch radial velocities as obtained with the instrument FLAMES at ESO's Very Large Telescope. The mean-square velocity along the line of sight is found to be larger than the one in the tangential direction by a factor of 6–8. We argue that the most likely explanation for such an occurrence is the presence of a significant quantity of unresolved binary and multiple stars in the radial velocity sample. Special attention should be paid to single-line spectroscopic binaries (SB1) since in this case we observe the spectral lines of the primary component only, and therefore the derived radial velocity is not the velocity of the binary system center of mass. To investigate this scenario, we performed numerical experiments varying the fractional abundance of SB1 in the observed sample. These experiments show that the increase of the mean-square radial velocity depends on the fractional abundance of SB1 to a power in the range [0.39, 0.45]. We used the 3D velocity dispersion obtained by the dispersions in the tangential directions and the assumption that the radial velocity dispersion is the same as a tangential one to estimate the virial cluster mass and the cluster mass, taking into account the gravitational field of the Galaxy and the nonstationarity of the cluster. These estimates are 650 ± 30 M ⊙ and 310 ± 80 M ⊙, respectively, in substantial agreement with the photometric cluster mass.

Addition of the Local Volume sample of galaxies from the FAST HI survey

We report the discovery of 20 new dwarf galaxies in the Local Volume identified as optical counterparts to the Five-hundred-meter Aperture Spherical radio Telescope (FAST) All Sky HI Survey (FASHI) sources. The galaxies have a median stellar mass of 7.8 × 106 M⊙ and a median HI mass of 1.0 × 107 M⊙. Most of them are field galaxies, while three are probable members of the M 101 and M 106 groups. We also found seven FASHI radio sources to be probable dark HI clouds in nearby groups. Together with four other known HI clouds in the local groups, their mean-square radial velocity difference of 49 km s−1 with respect to the host galaxies yields an average total mass of (2.7 ± 1.0)×1011 M⊙ for these groups on the projected scale of 90 kpc.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties.

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Extremely persistent dense active fluids.

We study the dynamics of dense three-dimensional systems of active particles for large persistence times τp at constant average self-propulsion force f. These systems are fluid counterparts of previously investigated extremely persistent systems, which in the large persistence time limit relax only on the time scale of τp. We find that many dynamic properties of the systems we study, such as the mean-squared velocity, the self-intermediate scattering function, and the shear-stress correlation function, become τp-independent in the large persistence time limit. In addition, the large τp limits of many dynamic properties, such as the mean-square velocity and the relaxation times of the scattering function, and the shear-stress correlation function, depend on f as power laws with non-trivial exponents. We conjecture that these systems constitute a new class of extremely persistent active systems.

Made-to-measure modelling of globular clusters

ABSTRACT We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the system evolves forward in time via a gravitational N-body code until the model cluster is able to reproduce select properties of an observed cluster. The method is first applied to observations of mock isotropic and anisotropic clusters while fitting against the cluster’s 3D or projected density profile, density weighted mean-squared velocity profile, or its density profile with individual mean-squared velocity profiles assuming $10 {{\ \rm per\ cent}}$ uncertainty in each of these observables. We find that a cluster’s 3D density profile can easily be reproduced by the made-to-measure method, with minor discrepancies in the outer regions if fitting against a cluster’s projected surface density or projected kinematic properties. If an observed cluster is anisotropic, only fitting against the cluster’s density profile and individual mean-squared velocity profiles will fully recover the full degree of anisotropy. Partial anisotropy can be recovered as long as two kinematic properties are included in the fit. We further apply the method to observations of the Galactic globular cluster M4 and generate a complete 6D representation of the cluster that reproduces observations of its surface density profile, mean-squared proper motion velocity profile, and mean-squared line of sight velocity profile. The M2M method predicts M4 is primarily isotropic with a mass of $9.2\pm 0.4\times 10^4\, \mathrm{ M}_{\odot }$ and a half-mass radius of 3.7 ± 0.1 pc.

Effects of mobility matrices completeness on component-based transfer path analysis methods with and without substructuring applied to aircraft-like components

Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method’s robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.

Low-frequency enhancement of acoustic black holes via negative stiffness supporting

Acoustic black holes (ABHs) attract increasing attention in the field of vibration suppression, sound radiation control and energy harvesting. Though the ABH effect usually works well in the mid-high frequency range, it cannot be triggered below the cut-on frequency. Thus, enhancing the vibration reduction at low frequencies is an urgent task. Inspired by the impressive low-frequency performance of the negative stiffness, we propose a novel idea that combines an ABH beam with a negative stiffness element (NS-ABH beam). To characterize such a system, a semi-analytical model is developed based on the Gaussian expansion method (GEM) in the framework of the Rayleigh–Ritz method. The modal loss factors (MLFs) and mean square velocity (MSV) are calculated to estimate the damping performance. The results show that the proposed NS-ABH beam can achieve remarkable vibration reduction below the cut-on frequency without sacrificing the ABH effect at higher frequency. The coupling mechanism between negative stiffness and ABH beam and the reduction mechanism behind are studied based on the modal projection method to better understand the observed phenomena. Finally, experiments have been implemented to validate the theoretical model and the NS-ABH performance.

Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness.

Stochastic resetting causes kinetic phase transitions, whereas its underlying physical mechanism remains to be elucidated. We here investigate the anomalous transport of a particle moving in a chaotic system with a stochastic resetting and a rough potential and focus on how the stochastic resetting, roughness, and nonequilibrium noise affect the transports of the particle. We uncover the physical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system: The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics. From the view of the energy landscape, the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state. This resetting can lead to a kinetic phase transition between no transport and a finite net transport or between negative mobility and positive mobility. The roughness and noise also lead to the transition. Based on the mechanism, the transport of the particle can be tuned by these parameters. For example, the combination of the stochastic resetting, roughness, and noise can enhance the transport and tune negative mobility, the enhanced stability of the system, and the resonant-like activity. We analyze these results through variances (e.g., mean-squared velocity, etc.) and correlation functions (i.e., velocity autocorrelation function, position-velocity correlation function, etc.). Our results can be extensively applied in the biology, physics, and chemistry, even social system.

Onset of turbulence in channel flows with scale-invariant roughness

Using 3D direct numerical simulations of the Navier--Stokes equations, we study the effect of a self-affine wall roughness on the onset of turbulence in channel flow. We quantify the dependence of the turbulent intensity (proportional to the mean-squared velocity fluctuations) on the Reynolds number $\mathrm{Re}$ for different roughness amplitudes $A$. We find that for sufficiently high amplitudes, $A>{A}_{b}$, the transition changes its nature from being subcritical (as is known at $A=0$) to supercritical, i.e., the boundary roughness renders the flow unstable for $\mathrm{Re}>{\mathrm{Re}}_{l}$, where the critical ${\mathrm{Re}}_{l}$ decays nontrivially with increasing $A$. The dependence of the friction factor on $\mathrm{Re}$ is found to follow a generalized Forchheimer law, which interpolates between the laminar and inertial asymptotes. The transition between these two asymptotes occurs at a second critical ${\mathrm{Re}}_{\text{c}}$ which is comparable in magnitude to ${\mathrm{Re}}_{l}$. This implies that transitional flow is an integral part of flow in open fractures when $\mathrm{Re}$ is sufficiently high, and should be accounted for in effective modeling approaches.

Calculating the fragmentation process in quadrupole ion traps

The present theoretical study calculates the consequences of an ion dissociating in a quadrupole field, describing both 3D and linear ion traps. The dissociation induces a change in q-stability parameter, resulting in fragment ions abruptly changing their trajectories. This includes a change in oscillation amplitude and mean-square velocity, i.e., effective collisional temperature. While the first one can lead to ions being lost to the electrodes, the latter one can be used to determine how likely fragment ions are to be further excited. During the collisional focusing process, ions can endure internal heating, just like during the injection process. The difference here is that fragment ions start this process with already elevated internal energies. The process is calculated by making use of the well-known phase-space ellipses. It is shown that fragment ions of lower m/z in average decrease their oscillation amplitude and are thus better trapped. Only very light ions close to the LMCO have a high chance of being lost. However, lighter fragment ions in average start with higher mean-square velocities than the precursor was assumed to need to have to induce dissociation, suggesting further collisional heating. Despite the harsh collisional environment m/z ratios close to the LMCO in average have to endure, a small percentage of these ions drastically decrease their oscillation amplitude, not requiring any collisional focusing. Fragment ions of higher m/z in average increase their oscillation amplitudes, however, their low velocities make further internal heating unlikely. The used calculations have been uploaded to Github: https://github.com/NeugebauerT/ion-trap.

Polar vortex crystals: Emergence and structure

Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We show that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale, Lγ=(U/γ)1/3, characterizing the size of the crystal in terms of the mean-square velocity U of the fluid and the polar parameter γ=fp/a2p, with fp the Coriolis parameter at the pole and ap the polar radius of the planet.

Bayesian Inference of Globular Cluster Properties Using Distribution Functions

Abstract We present a Bayesian inference approach to estimating the cumulative mass profile and mean-squared velocity profile of a globular cluster (GC) given the spatial and kinematic information of its stars. Mock GCs with a range of sizes and concentrations are generated from lowered-isothermal dynamical models, from which we test the reliability of the Bayesian method to estimate model parameters through repeated statistical simulation. We find that given unbiased star samples, we are able to reconstruct the cluster parameters used to generate the mock cluster and the cluster’s cumulative mass and mean-squared velocity profiles with good accuracy. We further explore how strongly biased sampling, which could be the result of observing constraints, might affect this approach. Our tests indicate that if we instead have biased samples, then our estimates can be off in certain ways that are dependent on cluster morphology. Overall, our findings motivate obtaining samples of stars that are as unbiased as possible. This may be achieved by combining information from multiple telescopes (e.g., Hubble and Gaia), but will require careful modeling of the measurement uncertainties through a hierarchical model, which we plan to pursue in future work.

Active Ornstein–Uhlenbeck model for self-propelled particles with inertia

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein–Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle’s mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical inertial time, determined by the particle’s mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle’s motion is completely governed by inertial effects as it remains superdiffusive for all times.

Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers

We propose a first minimal theory for boundary layer turbulence that captures very well the profile of the mean-square velocity fluctuations in the streamwise direction and give a quantitative prediction of the Townsend-Perry constants. Our theory is based on connecting all moments of velocity fluctuations as a function of the distance to the wall with the turbulent energy spectrum. A similar spectral theory was proposed in G. Gioia and P. Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] to explain the friction factor and the von K\'arm\'an law in G. Gioia, N. Guttenberg, N. Goldenfeld, and P. Chakraborty [Phys. Rev. Lett. 105, 184501 (2010)]. We generalized it by including fluctuations in the wall-shear stress and the streamwise velocity. The theoretical predictions for the mean velocity and mean-square fluctuations reproduce the shape of the velocity profiles in the buffer and inertial layer obtained from wind tunnel experiments.

Loop decay in Abelian-Higgs string networks

We study the decay of cosmic string loops in the Abelian-Higgs model. We confirm earlier results that loops formed by intersections of infinite strings formed from random-field initial conditions disappear quickly, with lifetimes proportional to their initial rest-frame length, ${\ensuremath{\ell}}_{\mathrm{init}}$. We study a population with ${\ensuremath{\ell}}_{\mathrm{init}}$ up to 6000 inverse mass units and measure the proportionality constant to be $0.14\ifmmode\pm\else\textpm\fi{}0.04$, independently of the initial lengths. We propose a new method to construct oscillating nonself intersecting loops from initially stationary strings and show that by contrast these loops have lifetimes scaling approximately as ${\ensuremath{\ell}}_{\mathrm{init}}^{2}$, in line with previous works on artificially created string configurations. We show that the oscillating strings have a mean-square velocity of ${\overline{v}}^{2}\ensuremath{\simeq}0.500\ifmmode\pm\else\textpm\fi{}0.004$, consistent with the Nambu-Goto value of $1/2$, while the network loops have ${\overline{v}}^{2}\ensuremath{\simeq}0.40\ifmmode\pm\else\textpm\fi{}0.04$. We argue that whatever the mechanism behind the network loop decay is, it is nonlinear, can only be suppressed by careful tuning of initial conditions, and is much stronger than gravitational radiation. An implication is that one cannot use the Nambu-Goto model to derive robust constraints on the tension of field theory strings. We advocate parametrizing the uncertainty as the fraction ${f}_{\mathrm{NG}}$ of Nambu-Goto-like loops surviving to radiate gravitationally. None of the 31 large network loops created survived longer than 0.25 of their initial length, so one can estimate that ${f}_{\mathrm{NG}}<0.1$ at 95% confidence level. If the recently reported NANOgrav signal is due to cosmic strings, ${f}_{\mathrm{NG}}$ must be greater than ${10}^{\ensuremath{-}3}$ in order not to violate bounds from the cosmic microwave background.

Shape- and scale-dependent coupling between spheroids and velocity gradients in turbulence

Rotations of spheroidal particles immersed in turbulent flows reflect the combined effects of fluid strain and vorticity, as well as the time history of these quantities along the particle's trajectory. Conversely, particle rotation statistics in turbulence provide a way to characterise the Lagrangian properties of velocity gradients. Particle rotations are also important for a range of environmental and industrial processes where particles of various shapes and sizes are immersed in a turbulent flow. In this study, we investigate the rotations of inertialess spheroidal particles that follow Lagrangian fluid trajectories. We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence and investigate the dynamics of different particle shapes at different scales in turbulence using a filtering approach. We find that the mean-square particle angular velocity is nearly independent of particle shape across all scales from the Kolmogorov scale to the integral scale. The particle shape does determine the relative split between different modes of rotation (spinning vs tumbling), but this split is also almost independent of the filter scale suggesting a Lagrangian scale-invariance in velocity gradients. We show how the split between spinning and tumbling can be quantitatively related to the particle's alignment with respect to the fluid vorticity.

Probability distributions in quadrupole ion traps

The solution to Mathieu's equation was modified and combined to only one single sine function. In this form, the cumulative probability functions for a fixed RF-phase can be determined as arcsine distributions. The probability of a normalized position u/umax or normalized velocity u˙/u˙max is relative to 1/1−(u/umax)2, u˙/u˙max respectively. This corrects reference descriptions present in the literature, which stated the probability to be proportional to 1−(u/umax)2. Resulting probability plots show that ions that are heavy on the relative mass scale of quadrupole ion traps, are more likely to be found close to the maximum of their oscillation amplitude. Light ions are more likely to be found at the center of their oscillation. The velocity distributions show that the likeliest velocity converges for low q-values to the mean-square velocity but splits into two likely velocity regions with increasing q-value. It is further emphasized, that these distributions describe the probability of a single ion and in order to describe the behavior of an ensemble of ions, it is inevitably needed to define a distribution of oscillation amplitudes umax.

An Overview of the Lagrangian Dispersion Modeling of Heavy Particles in Homogeneous Isotropic Turbulence and Considerations on Related LES Simulations

Particle tracking is a competitive technique widely used in two-phase flows and best suited to simulate the dispersion of heavy particles in the atmosphere. Most Lagrangian models in the statistical approach to turbulence are based either on the eddy interaction model (EIM) and the Monte-Carlo method or on random walk models (RWMs) making use of Markov chains and a Langevin equation. In the present work, both discontinuous and continuous random walk techniques are used to model the dispersion of heavy spherical particles in homogeneous isotropic stationary turbulence (HIST). Their efficiency to predict particle long time dispersion, mean-square velocity and Lagrangian integral time scales are discussed. Computation results with zero and no-zero mean drift velocity are reported; they are intended to quantify the inertia, gravity, crossing-trajectory and continuity effects controlling the dispersion. The calculations concern dense monodisperse spheres in air, the particle Stokes number ranging from 0.007 to 4. Due to the weaknesses of such models, a more sophisticated matrix method will also be explored, able to simulate the true fluid turbulence experienced by the particle for long time dispersion studies. Computer evolution and performance since allowed to develop, instead of Reynold-Averaged Navier-Stokes (RANS)-based studies, large eddy simulation (LES) and direct numerical simulation (DNS) of turbulence coupled to Generalized Langevin Models. A short review on the progress of the Lagrangian simulations based on large eddy simulation (LES) will therefore be provided too, highlighting preferential concentration. The theoretical framework for the fluid time correlation functions along the heavy particle path is that suggested by Wang and Stock.

Modeling droplet dispersion in a turbulent tubing flow at a high droplet holdup

Modeling emulsion formation in a turbulent tubing flow is required for different petroleum technology applications, such as surface oil/water separation or evaluation of accuracy of subsurface performance of specific logging equipment. Dispersion of noncoalescing droplets in a turbulent tubing flow at droplet holdups reaching 30% is modeled. An in-house developed engineering code based on the advection-diffusion population balance approach is employed for simulations. A model of droplet breakup, recently proposed and validated for high-dispersed phase volume fractions, is incorporated into the code. This model assumes that the droplet breakup process is driven by droplet fluctuations. According to the model, the mean-square droplet fluctuation velocity is calculated using the kinetic theory of granular media.This developed model is used to study dispersion of water in a turbulent oil flow through a tubing under realistic conditions. One of the important results is an explicit demonstration of a decrease in the droplet size reduction rate with an increase in the water holdup. An evolution of mean droplet sizes along the production tubing under different flow conditions is illustrated. The simulation tool developed is a significant step toward the ultimate goal: an ability to characterize water in oil emulsion prior to multiphase production logging.

Particle Brownian motion due to random classical radiation: superfluid-like behavior in the presence of classical zero-point radiation

Nonrelativistic classical mechanics allows no fundamental transition between low-velocity and high-velocity forms of behavior, nor between low-temperature and high-temperature forms. In contrast, classical electrodynamics, which is a relativistic theory, allows fundamental transitions in velocity. Furthermore, the inclusion within the classical theory of Lorentz-invariant classical zero-point radiation allows classical electrodynamics to distinguish high-temperature and low-temperature forms of behavior. Because electromagnetism is a relativistic theory, it may provide a thermal radiation bath which gives rise to phenomena in Brownian motion which are not included in a model with a thermal bath based upon nonrelativistic particles. Here we explore the Brownian motion of a classical electric-dipole particle in random classical radiation, making use of the calculations of Einstein and Hopf. The Brownian motion as a function of temperature is analyzed in terms of the mean-square velocity and the diffusion constant for four different classical radiation spectra: the Rayleigh–Jeans spectrum, the Planck spectrum without zero-point radiation, the zero-point radiation spectrum, and the Planck spectrum including zero-point radiation. We illustrate how the inclusion of classical electromagnetic zero-point radiation alters Brownian motion behavior between high-temperature and low-temperature forms. For the Planck spectrum with zero-point radiation, the high-temperature Brownian motion agrees with some aspects found from nonrelativistic mechanics, while the low-temperature behavior includes some aspects analogous to superfluid behavior. At sufficiently low temperatures, the Brownian particle has an increasing mean-square velocity and more rapid diffusion with decreasing temperature due to the increasing dominance of the classical electromagnetic zero-point radiation.