Velocity Probability Distribution Research Articles

Probability distributions of initial rotation velocities and core-boundary mixing efficiencies of γ Doradus stars

Context. The theory of rotational and chemical evolution is incomplete, thereby limiting the accuracy of model-dependent stellar mass and age determinations. The γ Doradus (γ Dor) pulsators are excellent points of calibration for the current state-of-the-art stellar evolution models, as their gravity modes probe the physical conditions in the deep stellar interior. Yet, individual asteroseismic modelling of these stars is not always possible because of insufficient observed oscillation modes. Aims. This paper presents a novel method to derive distributions of the stellar mass, age, core-boundary mixing efficiency, and initial rotation rates for γ Dor stars. Methods. We computed a grid of rotating stellar evolution models covering the entire γ Dor instability strip. We then used the observed distributions of the luminosity, effective temperature, buoyancy travel time, and near-core rotation frequency of a sample of 539 stars to assign a statistical weight to each of our models. This weight is a measure of how likely the combination of a specific model is. We then computed weighted histograms to derive the most likely distributions of the fundamental stellar properties. Results. We find that the rotation frequency at zero-age main sequence follows a normal distribution, peaking at around 25% of the critical Keplerian rotation frequency. The probability-density function for extent of the core-boundary mixing zone, given by a factor of fCBM times the local pressure scale height (assuming an exponentially decaying parameterisation), decreases linearly with increasing fCBM. Conclusions. Converting the distribution of fractions of critical rotation at the zero-age main sequence to units of d−1, we find most F-type stars start the main sequence with a rotation frequency between 0.5 d−1 and 2 d−1. Regarding the core-boundary mixing efficiency, we find that it is generally weak in this mass regime.

Kinematic characteristics of elbow joint range of motion in elite Chinese freestyle swimmers with elbow pain during dry-land simulations of swimming strokes

ABSTRACT The aim of this study was to obtain quantitative data on elbow joint ROM in elite freestyle swimmers with EP in China. Of the 50 elite freestyle swimmers recruited, 41 completed all measurements during dry-land swimming stroke simulations. Elbow joint angle, velocity, and acceleration were measured using inertial measurement units. The RMSE/D was calculated to determine the elbow joint ROM deviation. Joint angle (3.33 ∘ –42.96 ∘ ), angular velocity (−364.15 to 245.69 ∘ / s ), and angular acceleration (−7051.80 to 1465.35 ∘ / s 2 ) were significantly different between the critical pain and healthy. The probability distributions of joint angle (15.47 ∘ ±14.54 ∘ ), angular velocity (2.41 ∘ ±111.06 ∘ / s ), and angular acceleration (1.93 ± 2222.6 ∘ / s 2 ) in the slight pain group were significantly different betweenhealthy and critical pain. The RMSE/D distributions of angular velocity (28.3%) and acceleration (21.48%) in the critical pain deviated from the healthy. The peak value-RMSE/D matrix model obtained proved that elbow ROM significantly differed between the elite freestyle swimmers with EP and the healthy. Angular velocity and acceleration indicate the weakness and negative influence of kinematics on patients with EP. Thus, Potential solutions are to constantly optimise freestyle swimming techniques and strengthen the arm muscles.

Optimization Scheme for Energy Storage Capacity of Large Grid Connected with Wind Farm in New Power System

In this study, our foremost focus was on mitigating the significant impacts on system frequency due to power output variations from large-scale wind farms integrated into the grid. We conducted in-depth simulations using Matlab to meticulously analyze the relationship between the output power of wind turbines and wind speed. Taking into account the power features of wind turbines and the probability distribution of wind velocities, we proposed an innovative calculation method to determine the energy storage requirements to maintain consistent and stable output from wind energy systems over long durations. By rigorously testing with real wind farm data, the feasibility of this method was validated, highlighting its pivotal role as a reference in future wind power project designs.

In situ plasma and neutral gas observation time windows during a comet flyby: Application to the Comet Interceptor mission

A comet flyby, like the one planned for ESA’s Comet Interceptor mission, places stringent requirements on spacecraft resources. To plan the time line of in situ plasma and neutral gas observations during the flyby, the size of the comet magnetosphere and neutral coma must be estimated well. For given solar irradiance and solar wind conditions, comet composition, and neutral gas expansion speed, the size of gas coma and magnetosphere during the flyby can be estimated from the gas production rate and the flyby geometry. Combined with flyby velocity, the time spent in these regions can be inferred and a data acquisition plan can be elaborated for each instrument, compatible with the limited data storage capacity. The sizes of magnetosphere and gas coma are found from a statistical analysis based on the probability distributions of gas production rate, flyby velocity, and solar wind conditions. The size of the magnetosphere as measured by bow shock standoff distance is 105–106km near 1au in the unlikely case of a Halley-type target comet, down to a nonexistent bow shock for targets with low activity. This translates into durations up to 103–104 seconds. These estimates can be narrowed down when a target is identified far from the Sun, and even more so as its activity can be predicted more reliably closer to the Sun. Plasma and neutral gas instruments on the Comet Interceptor main spacecraft can monitor the entire flyby by using an adaptive data acquisition strategy in the context of a record-and-playback scenario. For probes released from the main spacecraft, the inter-satellite communication link limits the data return. For a slow flyby of an active comet, the probes may not yet be released during the inbound bow shock crossing.

Diffusion of active Brownian particles under quenched disorder.

The motion of a single active particle in one dimension with quenched disorder under the external force is investigated. Within the tailored parameter range, anomalous diffusion that displays weak ergodicity breaking is observed, i.e., non-ergodic subdiffusion and non-ergodic superdiffusion. This non-ergodic anomalous diffusion is analyzed through the time-dependent probability distributions of the particle's velocities and positions. Its origin is attributed to the relative weights of the locked state (predominant in the subdiffusion state) and running state (predominant in the superdiffusion state). These results may contribute to understanding the dynamical behavior of self-propelled particles in nature and the extraordinary response of nonlinear dynamics to the externally biased force.

A Cold Lid on a Warm Ocean: Indian Ocean Surface Rain Layers and Their Feedbacks to the Atmosphere

AbstractOcean surface rain layers (RLs) form when relatively colder, fresher, less dense rain water stably stratifies the upper ocean. RLs cool sea surface temperature (SST) by confining surface evaporative cooling to a thin near‐surface layer, and generate sharp SST gradients between the cool RL and the surrounding ocean. In this study, ocean‐atmosphere coupled simulations of the November 2011 Madden‐Julian Oscillation (MJO) event are conducted with and without RLs to evaluate two pathways for RLs to influence the atmosphere. The first, termed the “SST gradient effect,” arises from the hydrostatic adjustment of the boundary layer to RL‐enhanced SST gradients. The second, termed the “SST effect,” arises from RL‐induced SST reductions impeding the development of deep atmospheric convection. RLs are found to sharpen SST gradients throughout the MJO suppressed and suppressed‐to‐enhanced convection transition phases, but their effect on convection is only detected during the MJO suppressed phase when RL‐induced SST gradients enhance low‐level convergence/divergence and broaden the atmospheric vertical velocity probability distribution below 5 km. The SST effect is more evident than the SST gradient effect during the MJO transition phase, as RLs reduce domain average SST by 0.03 K and narrow vertical velocity distribution, thus delaying onset of deep convection. A delayed SST effect is also identified, wherein frequent RLs during the MJO transition phase isolate accumulated subsurface ocean heat from the atmosphere. The arrival of strong winds at the onset of the MJO active phase erodes RLs and releases subsurface ocean heat to the atmosphere, supporting the development of deep convection.

Describing geophysical turbulence with a Schrödinger–Coriolis equation in velocity space

In this paper, we examine the predictions of the scale-relativity approach for a turbulent fluid in rotation. We first show that the time derivative of the governing Navier–Stokes equation in the usual x-space can be transformed into a Schrödinger-like equation in velocity space with an external vectorial field to account for the rotation, together with a local velocity harmonic oscillator (VHO) potential in the v-space. The coefficients of this VHO are given by the second order x-derivatives of the pressure. We can then give formulas for the velocity and acceleration probability distribution functions (PDF). Using a simple model of anisotropic harmonic oscillator, we compare our predictions with relevant data from both direct numerical simulations (DNS) and oceanic drifter velocity measurements. We find a good agreement of the predicted acceleration PDF with that observed from drifters and some possible support in DNS for the existence of gaps in the local velocity PDF, expected in the presence of a Coriolis force.

Experimental investigation on droplet evolutions in co-flow around the bluff body

Annular mist flow widely exists in natural gas and other engineering fields. Vortex flowmeter has gradually become an effective means of wet gas measurement. However, the droplets in the flow field will influence the stability of the vortex. In this paper, the interaction between droplets and vortex was studied by experiments. A novel in-focus criterion was proposed to improve the accuracy of droplet measurement. Simultaneous acquisition of droplet size, velocity, and concentration was achieved. The spatial evolution of droplet parameters was obtained to determine the position where the droplets were evenly distributed. The bidirectional coupling mechanism between droplets and vortex was studied. Firstly, the influence of the vortex flow field on droplets was reflected by the characteristics of droplet distribution around the bluff body. Secondly, the effect of droplets on the vortex signal in the flow field was analyzed based on Stokes number Stp and liquid-phase load φl. When φl < 0.03, the probability distribution of droplet velocity downstream of the bluff body presents double peaks. The exchange momentum between the small droplets and the vortex is stronger, and vice versa for the larger droplets. Finally, the quality factor of vortex signals decreases from -2.09 to -2.18 with the increase in the volume concentration of droplets. It is further demonstrated that the increase in volume concentration of droplets will destroy the vortex structure and degrade the quality of the vortex signal.

Investigating the magnetic field of the quiet Sun internetwork

Abstract We analyze the magnetism of the quiet Sun internetwork (IN) using high-spatial-resolution data obtained by the spectropolarimeter (SP) of the Solar Optical Telescope aboard the Hinode satellite near the disk center of the Sun. The SP data were inverted using the Stokes Inversion based on Response functions (SIR) inversion code with a single-component atmosphere with depth dependent in the solar photosphere, assuming gradients in physical parameters along the line of sight (LOS). To avoid the effect of noise, only pixels with Stokes U and/or Q signals above 4.5 times the noise level are considered. The inversion results show that the magnetic field of the IN has mainly hG field strength and the inclination distribution is quasi-isotropic at the solar surface. The field strength decreases with height and becomes predominantly horizontal at the upper layers. At the mid photosphere, the distributions of field strength and inclination are consistent with those derived by Milne–Eddington inversion. The mean transverse and longitudinal flux densities are 66 Mx cm−2 and 13 Mx cm−2 at log τ = −1.0; we also study the ratio between the transverse and longitudinal components in the IN region as a function of depth in the photosphere, finding that the ratio is almost 2.7 in the deep layer, increasing to 5.1 in the upper layer. The mean field strength is greater than 100 G in the upper photosphere, which is consistent with the results based on the Hanle effect. We present the LOS velocity probability distribution function for IN at different optical depths, where its distribution is mainly associated with upflow velocities of VLOS = 1.2 and 0.6 km s−1 in the deeper and upper layers, respectively. In addition, there exists a reliable inversion analysis, which is obvious from the comparison between the observed and calculated area asymmetries in both Fe i lines of Hinode SP data.

Role of translational noise on current reversals of active particles on ratchet

In this study, we explore using Langevin dynamics simulations, the role of thermal fluctuations on the rectification of non-interacting inertial active (self-propelled) particles in a rocking ratchet setup in the absence and in the presence of the external time periodic drive. The system is first studied in the absence of the external drive. It is found that the average velocity is always positive and a peaked function of the translational noise, indicating that the asymmetry effects dominate at intermediate values of the strength of the thermal noise. In the second part of this work, we study the effect of the external drive on the dynamics of the system by exploring a phase diagram in the parameter space of translational noise and driving frequency for two different strengths of rotational diffusion. For a given constant amplitude of the active force and amplitude of external drive less than the maximum force due to the potential, the average velocity magnitude as well as the direction (+ {hat{x}}/- {hat{x}}) is found to depend on the rotational diffusion, frequency of the external drive and the strength of the translational noise. We discover certain critical parameters in the phase space at which current reversals happen. It is found that when the average particle energy is lower than the potential energy of the barrier, symmetry breaking dominates and the currents are in the ‘easy’ direction of the ratchet. On the other hand, when the energy available per particle crosses the potential energy of the barrier, the competition between inertial effects and diffusion effects decides the direction of currents. We explain our findings by constructing phase difference datum, velocity probability distribution, and current probability analyses. Our results provide a novel method for controlling the direction of transport of inertial active particles.

Measuring the hot ICM velocity structure function using XMM–Newton observations

ABSTRACT It has been shown that the gas velocities within the intracluster medium (ICM) can be measured by applying the novel XMM–Newton EPIC-pn energy scale calibration, which uses instrumental Cu Kα as reference for the line emission. Using this technique, we have measured the velocity distribution of the ICM for clusters involving AGN feedback and sloshing of the plasma within the gravitational well (Virgo and Centaurus) and a relaxed one (Ophiuchus). We present a detailed study of the kinematics of the hot ICM for these systems. First, we compute the velocity probability distribution functions (PDFs) from the velocity maps. We find that for all sources, the PDF follows a normal distribution, with a hint of a multimodal distribution in the case of Ophiuchus. Then, we compute the velocity structure function (VSF) for all sources in order to study the variation with scale as well as the nature of turbulence in the ICM. We measure a turbulence driving scale of ∼10–20 kpc for the Virgo cluster, while the Ophiuchus cluster VSF reflects the absence of strong interaction between the ICM and a powerful Active Galactic Nucleus (AGN) at such spatial scales. For the former, we compute a dissipation time larger than the jet activity cycle, thus indicating that a more efficient heating process than turbulence is required to reach equilibrium. This is the first time that the VSF of the hot ICM has been computed using direct velocity measurements from X-ray astronomical observations.

Retrieval of Peak Thunderstorm Wind Velocities Using WSR-88D Weather Radars

Abstract The current study develops a variant of the VAD method to retrieve thunderstorm peak event velocities using low-elevation WSR-88D radar scans. The main challenge pertains to the localized nature of thunderstorm winds, which complicates single-Doppler retrievals as it dictates the use of a limited spatial scale. Since VAD methods assume constant velocity in the fitted section, it is important that retrieved sections do not contain background flow. Accordingly, the current study proposes an image processing method to partition scans into regions, representing events and the background flows, that can be retrieved independently. The study compares the retrieved peak velocities to retrievals using another VAD method. The proposed technique is found to estimate peak event velocities that are closer to measured ASOS readings, making it more suitable for historical analysis. The study also compares the results of retrievals from over 2600 thunderstorm events from 19 radar–ASOS station combinations that are less than 10 km away from the radar. Comparisons of probability distributions of peak event velocities for ASOS readings and radar retrievals showed good agreement for stations within 4 km from the radar while more distant stations had a higher bias toward retrieved velocities compared to ASOS velocities. The mean absolute error for velocity magnitude increases with height ranging between 1.5 and 4.5 m s−1. A proposed correction based on the exponential trend of mean errors was shown to improve the probability distribution comparisons, especially for higher velocity magnitudes.

Comparison of quantized transfers of a given volume of gas through a pipe under its temporal and velocity probability distributions

The paper considers the quantization of gas volume transfers along a hypothetical pipe. The volume of gas is represented by two probability distributions in temporal and velocity form. The known model of optimal in the sense of filling information quantization is applied to quantization of material objects. There is a constant size gap between quanta. Technological aspects of formation of quanta are not considered. On the basis of the carried out minimum cost study the advantage of velocity quantization over time quantization for a number of selected quanta is determined. A normal probability distribution is taken as the initial distribution of the gas volume. The results of the article can be applied to any material and information processes. The main purpose in future research is recommended for any complex network processes, analysis and synthesis of their quality.

Statistical characteristics, probability distribution, and power potential of sea water velocity in Turkey

Sea currents have the potential to supply electricity from a renewable energy source to coastal regions. The assessment of the potential energy that could be generated is the first step toward developing this resource. In this study, the data was collected at 5 m and 35 m depths below the sea surface level, including sea current velocity and direction. A detailed field measurement, of the probability of sea water velocity at three stations (Antalya, Silivri, Istanbul) for 5 months is carried out. The sea current power density values in these stations were 10.41, 4.92, and 7.91 W/m2 at 5 m depth, respectively. Besides, average sea current power density values were seen to be closely arranged with 11.44, 4.07, and 9.06 W/m2 at 35 depths, respectively. In addition, statistical analysis applying Weibull and Rayleigh models is also presented. It is shown that the use of a Weibull probability distribution facilitates the analysis of sea velocity conditions and is also able to predict the power density with a high degree of accuracy. The results of this study are useful for the understanding of marine hydrodynamics of these areas, where sea current power projects may be started in Turkey.

Statistical analysis of flow velocity field inside random packed beds

Immersed boundary method is used for simulation of fluid flow through random packed beds of various particles (cylinders and rings) obtained in a separate numerical simulation of the packing process. Due to complexities of the random packing structure the flow velocity is also highly complex despite the laminar regime. The statistical characteristics of the flow field are examined in detail and compared between various packings - not only probability distribution of flow velocity but also novel statistical measures that provide useful information about the flow applicable to simplified models of flow in similar structures. The measures are based on the statistics of the flow deflection angle i.e. the angle between the local flow velocity vector and the inlet velocity direction. The proposed two-dimensional map allows for assessment of the probability distribution of the flow deflection angle for different values of the velocity magnitude.

Active particles driven by competing spatially dependent self-propulsion and external force

We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim-velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. We thus show that the interplay of two relatively simple physical fields can be employed to generate complex emerging behavior.

Aerosol–stratocumulus interactions: towards a better process understanding using closures between observations and large eddy simulations

Abstract. We carried out a closure study of aerosol–cloud interactions during stratocumulus formation using a large eddy simulation model UCLALES–SALSA (University of California Los Angeles large eddy simulation model–sectional aerosol module for large applications) and observations from the 2020 cloud sampling campaign at Puijo SMEAR IV (Station for Measuring Ecosystem–Atmosphere Relations) in Kuopio, Finland. The unique observational setup combining in situ and cloud remote sensing measurements allowed a closer look into the aerosol size–composition dependence of droplet activation and droplet growth in turbulent boundary layer driven by surface forcing and radiative cooling. UCLALES–SALSA uses spectral bin microphysics for aerosols and hydrometeors, and incorporates a full description of their interactions into the turbulent-convective radiation-dynamical model of stratocumulus. Based on our results, the model successfully described the probability distribution of updraught velocities and consequently the size dependency of aerosol activation into cloud droplets, and further recreated the size distributions for both interstitial aerosol and cloud droplets. This is the first time such a detailed closure is achieved not only accounting for activation of cloud droplets in different updraughts, but also accounting for processes evaporating droplets and drizzle production through coagulation–coalescence. We studied two cases of cloud formation, one diurnal (24 September 2020) and one nocturnal (31 October 2020), with high and low aerosol loadings, respectively. Aerosol number concentrations differ more than 1 order of magnitude between cases and therefore, lead to cloud droplet number concentration (CDNC) values which range from less than 100 cm−3 up to 1000 cm−3. Different aerosol loadings affected supersaturation at the cloud base, and thus the size of aerosol particles activating to cloud droplets. Due to higher CDNC, the mean size of cloud droplets in the diurnal high aerosol case was lower. Thus, droplet evaporation in downdraughts affected more the observed CDNC at Puijo altitude compared to the low aerosol case. In addition, in the low aerosol case, the presence of large aerosol particles in the accumulation mode played a significant role in the droplet spectrum evolution as it promoted the drizzle formation through collision and coalescence processes. Also, during the event, the formation of ice particles was observed due to subzero temperature at the cloud top. Although the modelled number concentration of ice hydrometeors was too low to be directly measured, the retrieval of hydrometeor sedimentation velocities with cloud radar allowed us to assess the realism of modelled ice particles. The studied cases are presented in detail and can be further used by the cloud modellers to test and validate their models in a well-characterized modelling setup. We also provide recommendations on how increasing amount of information on aerosol properties could improve the understanding of processes affecting cloud droplet number and liquid water content in stratiform clouds.

Augmenting the Double-Gaussian Representation of Atmospheric Turbulence and Convection via a Coupled Stochastic Multi-Plume Mass-Flux Scheme

Abstract Modern general circulation models continue to require parameterizations of subgrid transport due to planetary boundary layer (PBL) turbulence and convection. Some schemes that unify these processes rely on assumed joint probability distributions of vertical velocity and moist conserved thermodynamic variables to predict the subgrid-scale contribution to the mean state of the atmosphere. The multivariate double-Gaussian mixture has been proposed as an appropriate model for PBL turbulence and shallow convection, but it is unable to reproduce important features of shallow cumulus convection. In this study, a novel unified PBL turbulence–convection–cloud macrophysics scheme is presented based on the eddy-diffusivity/mass-flux framework. The new scheme augments the double-Gaussian representation of subgrid variability with multiple stochastic mass-flux plumes at minimal added computational cost. Improved results for steady-state maritime and transient continental shallow convection from a single-column model implementation of the new scheme are shown with respect to reference large-eddy simulations. Improvements are seen in the cloud layer due to mass-flux plumes occupying the extreme moist, low liquid-water potential temperature tail of the joint temperature–moisture distribution. Significance Statement Computer models of the atmosphere used to predict future climate are unable to directly represent air motion at small spatial scales because it would take too long to run the model over the entire planet. Instead, models typically use coarse model grid spacing and a simplified statistical representation of the physical processes that cause small-scale motions. This paper improves a particular simplified representation by adding a mechanism to represent statistically rare events of strong small-scale air motion that coherently transport air from near the surface to higher in the atmosphere. This increased transport also improves the representation of clouds, a particularly difficult phenomenon to simulate in models.

Dynamics of active particles with space-dependent swim velocity.

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

A seemingly universal particle kinetic distribution in porous media

We study many-particle transport in randomly jammed packing of spheres at different particle Péclet numbers (Pe*). We demonstrate that a modified Nakagami-m function describes particle velocity probability distributions when particle deposition occurs. We assess the universality of said function through comparison against Lagrangian simulations of various particle types as well as experimental data from the literature. We construe the function's physical meaning as its ability to explain particle deposition in terms of Pe* and the competition between distributions of energy barriers for particle release and particles' diffusive energy.