Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Capturability analysis of a geometric guidance law in relative velocity space

In this paper, a relative velocity approach is used to analyze the capturability of a geometric guidance law. Point mass models are assumed for both the missile and the target. The speeds of the missile and target are assumed to remain constant throughout the engagement. Lateral acceleration, obtained from the guidance law, is applied to change the path of the missile. The kinematic equations for engagements in the horizontal plane are derived in the relative velocity space. Some analytical results for the capture region are obtained for non-maneuvering and maneuvering targets. For non-maneuvering targets it is enough for the navigation gain to be a constant to intercept the target, while for maneuvering targets a time varying navigation gain is needed for interception. These results are then verified through numerical simulations.

A zero-relative-velocity belt skimmer, Stage II : Confirming tests and prototype design /

Final report, issued May 1977.

Debris perturbed by radiation pressure: relative velocities across circular orbits

In the present work we consider a dynamical system of mum size particles around the Earth subject to the effects of radiation pressure. Our main goal is to study the evolution of its relative velocity with respect to the co-planar circular orbits that it crosses. The particles were initially in a circular geostationary orbit, and the particles size were in the range between 1 and 100 mum. The radiation pressure produces variations in its eccentricity, resulting in a change in its orbital velocity. The results indicated the maximum linear momentum and kinetic energy increases as the particle size increases. For a particle of 1 mum the kinetic energy is approximately 1.56 x 10(-7) J and the momentum is 6.27 x 10(-11) kg m/s and for 100 mum the energy is approximately 1.82 x 10(-4) J and the momentum is 2.14 x 10(-6) kg m/s. (C) 2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

The ecological dynamics of 1v1 sub-phases in association football

This paper analyzes effects of different practice task constraints on heart rate (HR) variability during 4v4 smallsided football games. Participants were sixteen football players divided into two age groups (U13, Mean age: 12.4±0.5 yrs; U15: 14.6±0.5). The task consisted of a 4v4 sub-phase without goalkeepers, on a 25x15 m field, of 15 minutes duration with an active recovery period of 6 minutes between each condition. We recorded players’ heart rates using heart rate monitors (Polar Team System, Polar Electro, Kempele, Finland) as scoring mode was manipulated (line goal: scoring by dribbling past an extended line; double goal: scoring in either of two lateral goals; and central goal: scoring only in one goal). Subsequently, %HR reserve was calculated with the Karvonen formula. We performed a time-series analysis of HR for each individual in each condition. Mean data for intra-participant variability showed that autocorrelation function was associated with more short-range dependence processes in the “line goal” condition, compared to other conditions, demonstrating that the “line goal” constraint induced more randomness in HR response. Relative to inter-individual variability, line goal constraints demonstrated lower %CV and %RMSD (U13: 9% and 19%; U15: 10% and 19%) compared with double goal (U13: 12% and 21%; U15: 12% and 21%) and central goal (U13: 14% and 24%; U15: 13% and 24%) task constraints, respectively. Results suggested that line goal constraints imposed more randomness on cardiovascular stimulation of each individual and lower inter-individual variability than double goal and central goal constraints.

Variables governing the dynamics of attacker-defender systems in team sport

This project was a step forward in the examination and identification of key variables on the perception, decision making and action of team sport athletes through theoretical insights provided by the ecological dynamics perspective. The methodology drew on experiential knowledge of elite coaches to drive further empirical investigation into the specific task, environmental and personal constraints that shape the behaviour of athletes in specific performance contexts. The thesis has provided an effective rationale for further investigation into the emergent perception, decision making and action demanded of athletes in these unpredictable, fluent, fast-paced environments.

Dynamics of attacker–defender dyads in Association Football : parameters influencing decision-making

Previous work on pattern-forming dynamics of team sports has investigated sub-phases of basketball and rugby union by focussing on one-versus-one (1v1) attacker-defender dyads. This body of work has identified the role of candidate control parameters, interpersonal distance and relative velocity, in predicting the outcomes of team player interactions. These two control parameters have been described as functioning in a nested relationship where relative velocity between players comes to the fore within a critical range of interpersonal distance. The critical influence of constraints on the intentionality of player behaviour has also been identified through the study of 1v1 attacker-defender dyads. This thesis draws from previous work adopting an ecological dynamics approach, which encompasses both Dynamical Systems Theory and Ecological Psychology concepts, to describe attacker-defender interactions in 1v1 dyads in association football. Twelve male youth association football players (average age 15.3 ± 0.5 yrs) performed as both attackers and defenders in 1v1 dyads in three field positions in an experimental manipulation of the proximity to goal and the role of players. Player and ball motion was tracked using TACTO 8.0 software (Fernandes & Caixinha, 2003) to produce two-dimensional (2D) trajectories of players and the ball on the ground. Significant differences were found for player-to-ball interactions depending on proximity to goal manipulations, indicating how key reference points in the environment such as the location of the goal may act as a constraint that shapes decision-making behaviour. Results also revealed that interpersonal distance and relative velocity alone were insufficient for accurately predicting the outcome of a dyad in association football. Instead, combined values of interpersonal distance, ball-to-defender distance, attacker-to-ball distance, attacker-to-ball relative velocity and relative angles were found to indicate the state of dyad outcomes.

Microscopic cooperative traffic based on NGSIM data

The deployment of new emerging technologies, such as cooperative systems, allows the traffic community to foresee relevant improvements in terms of traffic safety and efficiency. Vehicles are able to communicate on the local traffic state in real time, which could result in an automatic and therefore better reaction to the mechanism of traffic jam formation. An upstream single hop radio broadcast network can improve the perception of each cooperative driver within radio range and hence the traffic stability. The impact of a cooperative law on traffic congestion appearance is investigated, analytically and through simulation. Ngsim field data is used to calibrate the Optimal Velocity with Relative Velocity (OVRV) car following model and the MOBIL lane-changing model is implemented. Assuming that congestion can be triggered either by a perturbation in the instability domain or by a critical lane changing behavior, the calibrated car following behavior is used to assess the impact of a microscopic cooperative law on abnormal lane changing behavior. The cooperative law helps reduce and delay traffic congestion as it increases traffic flow stability.

Structure and dynamics of two-dimensional sheared granular flows

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

A Triggering Mechanism for Enhanced Star-Formation in Colliding Galaxies

We propose a physical mechanism to explain the origin of the intense burst of massive-star formation seen in colliding/merging, gas-rich, field spiral galaxies. We explicitly take account of the different parameters for the two main mass components, H-2 and H I, of the interstellar medium within a galaxy and follow their consequent different evolution during a collision between two galaxies. We also note that, in a typical spiral galaxy-like our galaxy, the Giant Molecular Clouds (GMCs) are in a near-virial equilibrium and form the current sites of massive-star formation, but have a low star formation rate. We show that this star formation rate is increased following a collision between galaxies. During a typical collision between two field spiral galaxies, the H I clouds from the two galaxies undergo collisions at a relative velocity of approximately 300 km s-1. However, the GMCs, with their smaller volume filling factor, do not collide. The collisions among the H I clouds from the two galaxies lead to the formation of a hot, ionized, high-pressure remnant gas. The over-pressure due to this hot gas causes a radiative shock compression of the outer layers of a preexisting GMC in the overlapping wedge region. This makes these layers gravitationally unstable, thus triggering a burst of massive-star formation in the initially barely stable GMCs.The resulting value of the typical IR luminosity from the young, massive stars from a pair of colliding galaxies is estimated to be approximately 2 x 10(11) L., in agreement with the observed values. In our model, the massive-star formation occurs in situ in the overlapping regions of a pair of colliding galaxies. We can thus explain the origin of enhanced star formation over an extended, central area approximately several kiloparsecs in size, as seen in typical colliding galaxies, and also the origin of starbursts in extranuclear regions of disk overlap as seen in Arp 299 (NGC 3690/IC 694) and in Arp 244 (NGC 4038/39). Whether the IR emission from the central region or that from the surrounding extranuclear galactic disk dominates depends on the geometry and the epoch of the collision and on the initial radial gas distribution in the two galaxies. In general, the central starburst would be stronger than that in the disks, due to the higher preexisting gas densities in the central region. The burst of star formation is expected to last over a galactic gas disk crossing time approximately 4 x 10(7) yr. We can also explain the simultaneous existence of nearly normal CO galaxy luminosities and shocked H-2 gas, as seen in colliding field galaxies.This is a minimal model, in that the only necessary condition for it to work is that there should be a sufficient overlap between the spatial gas distributions of the colliding galaxy pair.

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (eta) of the missile commanded latax. However, for certain values of N and eta, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law, the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Persistent passive hopping and juggling is possible even with plastic collisions

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.