Theoretical Density Distribution Research Articles

Naturalistic study of vehicle-bicycle lateral passing distance on high-speed rural two-lane roadways with paved shoulders

In the United States, 91.4 cm (3.0 ft) has been considered a safe lateral distance when passing bicyclists; however, this threshold may be more suitable to urban environments where most bicycle safety research has originated—limited research is available on rural roadways. In this study, a road bicycle was instrumented to collect naturalistic data and analyze vehicle-bicycle lateral passing distances (LPD) on high-speed rural two-lane roadways with paved shoulders. The bicycle was ridden in the center of the shoulder. Overall, 2,119 observations of vehicles passing the instrumented bicycle were obtained from a study segment. The impacts of different variables on distributions of vehicle-bicycle LPD measurements were analyzed. Passing vehicles with opposing traffic passed the bicyclist significantly closer than passing vehicles without opposing traffic. More predominant with opposing traffic, heavy vehicles passed the bicyclist closer than passenger vehicles. Similarly, following vehicles passed the bicyclist closer than leading vehicles. The study segment was repaved during the data collection period, so data before and after the roadway improvement was available. Vehicles with old pavement/marking passed the bicyclist closer than vehicles with new pavement/marking conditions. Distribution of LPD measurements was skewed to the left towards smaller values and had a long tail to the right towards larger values. Through maximum likelihood estimation, the Log-normal distribution was found to best fit the data distribution. Using empirical and theoretical density distributions, LPD was formally specified as a function of opposing traffic with a theoretical mixture distribution and generalized to estimate the probability of vehicles passing bicyclists below a certain threshold.

Anomaly detection and prediction evaluation for discrete nonlinear dynamical systems

Anomalies in dynamical systems mostly occur as deviations between measurement and prediction. Current anomaly detection methods in multivariate time series often require prior clustering, training data, or cannot distinguish local and global anomalies. Furthermore, no generalized metric exists to evaluate and compare different prediction functions regarding their amount of anomalous behavior. We propose a novel methodology to detect local and global anomalies in time series data of dynamical systems. For this purpose, a theoretical density distribution is derived assuming that only noise conceals the time series. If the theoretical and the empirical density distribution yield significantly different entropies, an anomaly is assumed. For a local anomaly detection, the Mahalanobis distance using the theoretical noise distribution’s covariance is applied to evaluate sequences of predictions and measurements. In addition, the Wasserstein metric enables a comparison of predictions using the distance between the noise and empirical distribution as a measure for selecting the best prediction function. The proposed method performs well on nonlinear time series such as logistic growth and enables a useful selection of a prediction model for satellite orbits. Thus, the proposed method improves anomaly detection in time series and model selection for nonlinear systems.

Halo heating from fluctuating gas in a model dwarf

ABSTRACTThe cold dark matter (CDM) structure formation scenario faces challenges on (sub)galactic scales, central among them being the ‘cusp-core’ problem. A known remedy, driving CDM out of Galactic Centres, invokes interactions with baryons, through fluctuations in the gravitational potential arising from feedback or orbiting clumps of gas or stars. Here, we interpret core formation in a hydrodynamic simulation in terms of a theoretical formulation, which may be considered a generalization of Chandrasekhar’s theory of two body relaxation to the case when the density fluctuations do not arise from white noise; it presents a simple characterization of the effects of complex hydrodynamics and ‘subgrid physics’. The power spectrum of gaseous fluctuations is found to follow a power law over a range of scales, appropriate for a fully turbulent compressible medium. The potential fluctuations leading to core formation are nearly normally distributed, which allows for the energy transfer leading to core formation to be described as a standard diffusion process, initially increasing the velocity dispersion of test particles as in Chandrasekhar’s theory. We calculate the energy transfer from the fluctuating gas to the halo and find it consistent with theoretical expectations. We also examine how the initial kinetic energy input to halo particles is redistributed to form a core. The temporal mass decrease inside the forming core may be fit by an exponential form; a simple prescription based on our model associates the characteristic time-scale with an energy relaxation time. We compare the resulting theoretical density distribution with that in the simulation.

Shape evolution and scaling analysis of soluble cylinders in dissolutive flow

The evolution of solid shapes in dissolutive flows is studied using molecular dynamics simulations. The final self-similar structures of the solid are distinct under the convection- and diffusion-dominated conditions. Introducing a dimensionless number, Ds, allows characterizing the relative influence of convection and diffusion on the final structure. When convection dominates, the convergent shape of the solid is approximately triangular, while the solid is more likely to be sculptured into a cylinder when diffusion dominates. There is a critical value of Ds that controls the transition between convection- and diffusion-dominated cases. However, the convergent shapes are insensitive to their initial states due to the solid assembly at the nanoscale. Furthermore, we discuss the influences of solid dissolution and assembly on the liquid density along different directions and provide fitting curves for the theoretical density distribution as explained from the Smoluchowski equation. Finally, the scaling laws are constructed to quantify the solid evolution, which can analytically forecast the shape evolution under different dominant factors. We believe that these findings provide theoretical support for structure optimization and industrial applications.

Entropy and Mass Distribution in Disc Galaxies

The relaxed motion of stars and gas in galactic discs is well approximated by a rotational velocity that is a function of radial position only, implying that individual components have lost any information about their prior states. Thermodynamically, such an equilibrium state is a microcanonical ensemble with maximum entropy, characterised by a lognormal probability distribution. Assuming this for the surface density distribution yields rotation curves that closely match observational data across a wide range of disc masses and galaxy types and provides a useful tool for modelling the theoretical density distribution in the disc. A universal disc spin parameter emerges from the model, giving a tight virial mass estimator with strong correlation between angular momentum and disc mass, suggesting a mechanism by which the proto-disc developed by dumping excess mass to the core or excess angular momentum to a satellite galaxy. The baryonic-to-dynamic mass ratio for the model approaches unity for high mass galaxies, but is generally <1 for low mass discs, and this discrepancy appears to follow a similar relationship to that shown in recent work on the Radial Acceleration Relation (RAR). Although this may support Modified Newtonian Dynamics (MOND) in preference to a Dark Matter (DM) halo, it does not exclude undetected baryonic mass or a gravitational DM component in the disc.

Understanding and Modeling the Super-spreading Events of the Middle East Respiratory Syndrome Outbreak in Korea

Understanding and Modeling the Super-spreading Events of the Middle East Respiratory Syndrome Outbreak in Korea

The environments of Ly α blobs – I. Wide-field Ly α imaging of TN J1338−1942, a powerful radio galaxy at z ≃ 4.1 associated with a giant Ly α nebula★

We exploit wide-field Ly$alpha$ imaging with Subaru to probe the environment around TN J1338-1942, a powerful radio galaxy with a >100 kpc Ly$\alpha$ halo at z=4.11. We used a sample of Ly$\alpha$ emitters (LAEs) down to $\log(L_{\rm Ly\alpha} [erg\, s^{-1}])\sim 42.8$ to measure the galaxy density around TNJ1338, compared to a control sample from a blank field taken with the same instrument. We found that TNJ1338 resides in a region with a peak overdensity of $\delta_{\rm LAE}=2.8\pm 0.5$ on scales of $8\, h^{-1}\rm Mpc$ (on the sky) and $112\, h^{-1}\rm Mpc$ (line of sight) in comoving coordinates. Adjacent to this overdensity, we found a strong underdensity where virtually no LAEs are detected. We used a semi-analytical model of LAEs derived from the Millennium Simulation to compare our results with theoretical predictions. While the theoretical density distribution is consistent with the blank field, overdense regions such as that around TNJ1338 are very rare, with a number density of $6.4\times 10^{-8}\rm Mpc^{-3}$ (comoving), corresponding to the densest < 0.4 percentile at $z\simeq 4.1$. We also found that the Ly$\alpha$ luminosity function in the TNJ1338 field differs from that in the blank field: the number of bright LAEs ($\log(L_{\rm Ly\alpha}[erg\,s^{-1}]) \gtrsim 43.3$) is enhanced, while the number of fainter LAEs is relatively suppressed. These results suggest that some powerful radio galaxies associated with Ly$\alpha$ nebulae reside in extreme overdensities on $\sim 3$--$6\, \rm Mpc$ scales, where star-formation and AGN activity may be enhanced via frequent galaxy mergers or high rates of gas accretion from the surroundings.

Neutron halo state of13C

Angular distributions for the12C(d, p)13C transfer reactions have been measured at Ed = 11.8 MeV, and compared with those of the DWBA calculations. By means of this comparison, density distributions of the last neutron in the ground state and the first 1/2+ state of13C are extracted. The properties of these states in13C have also been studied in the framework of the nonlinear relativistic mean-field theory with NL-SH parameters. It is found that the first 1/2+ state in13C is a neutron halo state shown by both the experimental and theoretical density distributions of the last neutron.

Calculation of gravity anomalies of 3D sources using drillhole density data

The method whereby the gravity anomaly of three-dimensional sources is calculated using a combination of analytical and numerical integration can be generalized for models where the upper and lower surfaces of the source can vary arbitrarily and its three-dimensional density variation is defined by vertical density polynomes fitted to the measured values of the drillhole samples in the area. This method permits modelling of, for example, folded sources where the density varies arbitrarily in three dimensions in the source region. At the first stage of interpretation, the density distribution between the drillholes is determined as a weighted average of the surrounding drillhole densities. The difference between the measured anomaly and the anomaly calculated from this density model can then be used to calculate new theoretical density distributions for fictitious drillholes in the area between the real drillholes. One can use those points also for guiding the location of future holes, for instance, in ore prospecting or oil drilling. By keeping the upper and lower surfaces constant and by fitting new drillholes in the area, we can perform 'semi-geometric' modelling without making any a priori assumptions concerning the geometry of the source. The method is equally well applicable to magnetic modelling.

Tetracarbonylchloroethylidynechromium: electron deformation density revisited. Joint multipole model refinement and ab initio CASSCF study

The X-ray diffraction measurements obtained by Goddard and Kruger for Cl(CO) 4 Cr≡C−CH 3 (crystallizing in P2 1 /c; a=6.504 (2) A, b=11.261 (5) A, c=12.756 (6) A, β=105.58 (3)°, Z=4) have been refined by using the multipole model proposed by Hansen and Coppens. Static and dynamic model maps are obtained that provide suitable information concerning the reorganization of the electron density induced by the Cr≡C and Cr−(CO) 4 bonding. The observed alternation of the Cr−C CO bond length does not seem to be the consequence of a delocalized electronic effect originating in the methyl group. The static maps are discussed in connection with a theoretical density distribution obtained from ab initio CASSCF calculations. Both the theoretical and the multipole model maps show the marked covalent character of the Cr≡C π bonds, compared to the π back-donation occurring in the Cr(CO) 4 plane

Application of perturbation theory to the crystal–melt interface

The Abraham–Singh perturbation theory is applied to the case of the interface between an fcc crystal and its melt. The starting point is the density distribution of a hard-sphere liquid near a hard wall. The perturbation theory corrects the hard-sphere fluid density distribution by accounting for the soft repulsive nature of the crystal face with respect to the fluid atoms, this interaction being approximated by its two-dimensional Boltzmann average potential. Account is taken of the thermal motion of the crystalline molecules at the interface. The theoretical density distribution is in good agreement with that obtained from a molecular dynamics experiment, for both (100) and (111) faces.

Can elliptical galaxies be equilibrium systems?

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational+centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes withn=0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in, elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Younget al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical glaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

Determination of the Mean Number of Bonds per snow grain And of the Dependence of the Tensile Strength of Snow on Stereological Parameters

AbstractA theoretical density distribution of the Dumber of bonds per grain as a function of the mean number of bonds per grain is derived from the assumption of randomness and isotropy of grain and grain-bond location and orientation. The knowledge of the theoretical density distribution allows the determination of the effective distribution parameters from section planes or thin sections. The concept of the fundamental unit to describe the strength of snow is introduced. Structural parameters developed on the basis of the fundamental units show improved correlations with the tensile strength.

Determination of the Mean Number of Bonds per snow grain And of the Dependence of the Tensile Strength of Snow on Stereological Parameters

AbstractA theoretical density distribution of the Dumber of bonds per grain as a function of the mean number of bonds per grain is derived from the assumption of randomness and isotropy of grain and grain-bond location and orientation. The knowledge of the theoretical density distribution allows the determination of the effective distribution parameters from section planes or thin sections. The concept of the fundamental unit to describe the strength of snow is introduced. Structural parameters developed on the basis of the fundamental units show improved correlations with the tensile strength.

Theoretical density distribution of plasma streaming around a cylinder

The distribution of plasma density around a metallic cylinder in a collisionfree plasma is determined by the system of Vlassov equations and the Poisson equation. The plasma may have a streaming velocity perpendicular to the cylinder axis producing a wake behind the cylinder. In the region outside a thin double layer at the cylinder surface the problem allows some simplification. Then numerical solutions become possible-even if the streaming velocity is low. Some numerical solutions are presented. A magnetic field produces an asymmetric shape of the wake, if the gyration radius of the ion becomes comparable to the cylinder radius.

3α decay of the 10.84 and 11.83 MeV states of 12C

The theoretical density distributions for the 12C-3α break-up have been compared with those obtained experimentally for the 10.84 and 11.83 MeV states of 12C. The spin and parity assignment of the 11.83 MeV state of 12C has been deduced from the analysis of data.

Electro-optical measurement of longitudinal dispersion in turbulent pipe flow

An attempt was made to correlate light beam absorption with the longitudinal dispersion of ink in turbulent pipe flow. Ink was injected into water flowing in a 2.22 cm ID pipe and the light beam produced by a laser traversed the pipe through transparent sections. Light beam attenuation by the ink pulse was measured with a photodiode and recorded by various means. Attenuation was measured at two locations downstream of the injection point. Since the attenuation was calibrated for ink density, theoretical prediction of the ink density distribution and the resulting light attenuation at the points of laser traverse was produced. The theoretical density distribution was based on only the first order source of longitudinal dispersion: the velocity gradient. The comparison between theory and experiment shows that, over a wide range of turbulence, dispersion was almost entirely due to velocity gradient and can be conveniently measured by the light beam absorption technique.