Non-zero Relative Velocity Research Articles

A contact force calculation approach for collision analysis with zero or non-zero initial relative velocity

A contact force calculation approach for collision analysis with zero or non-zero initial relative velocity

Oxygen isotope exchange between molten silicate spherules and ambient water vapor with nonzero relative velocity: Implication for chondrule formation environment

Oxygen isotope compositions of chondrules reflect the environment of chondrule formation and its spatial and temporal variations. Here, we present a theoretical model of oxygen isotope exchange reaction between molten silicate spherules and ambient water vapor with finite relative velocity. We found a new phenomenon, that is, mass-dependent fractionation caused by isotope exchange with ambient vapor moving with nonzero relative velocity. We also discussed the plausible condition for chondrule formation from the point of view of oxygen isotope compositions. Our findings indicate that the relative velocity between chondrules and ambient vapor would be lower than several 100ms−1 when chondrules crystallized.

First-order velocity memory effect from compact binary coalescing sources

It has long been known that gravitational waves from compact binary coalescing sources are responsible for a first-order displacement memory effect experienced by a pair of freely falling test masses. This constant displacement is sourced from the non-vanishing final gravitational-wave strain present in the wave's after-zone, often referred to as the non-linear memory effect, and is of the same order of magnitude as the strain from the outgoing quadrupole radiation. Hence, this prediction of general relativity is verifiable experimentally by measurement of the final relative separation between test masses that comprise gravitational-wave detectors. In a separate context, independent calculations have demonstrated that exact, sandwich, plane wave spacetimes exhibit a velocity memory effect: a non-zero relative velocity, gained by a pair of test masses in free fall, after the passage of a gravitational wave. In this paper, we find that in addition to the known constant displacement memory effect test masses experience, a velocity memory effect at leading order arises due to the non-linear nature of gravitational waves from compact binary sources. We discuss the magnitude of the first-order velocity memory effect in the context of observing gravitational-wave radiation from super massive binary black hole mergers in LISA.

Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum

One of the cornerstones of general relativity is the equivalence principle. However, the validity of the equivalence principle has only been established on solar system scales for standard matter fields; this result cannot be assumed to hold for the non-standard matter fields that dominate the gravitational dynamics on cosmological scales. Here we show how the equivalence principle may be tested on cosmological scales for non-standard matter fields using the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes use of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating general relativistic deformations of the past-light cone, and assumes that galaxies can be treated as test particles that are made of baryons and cold dark matter. This assumption leads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold between baryons and dark matter. We show that the relative velocity can be constrained to be less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity mapping/Hα galaxy survey and the bispectrum of the Hα galaxy survey.

Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence.

Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi-two-dimensional system exhibiting a split cascade, is observed. The findings of this work could motivate new experimental settings to study quasi-two-dimensional superfluid turbulence in the bulk of three-dimensional experiments. They might also find applications beyond superfluids in systems described by more than one fluid component.

The generalized spin-orbit interaction: A microscopic origin of the Ørsted magnetic field

This work introduces a generalization of the form of the spin-orbit interaction, the generalized spin-orbit interaction (GSOI). It expresses the magnetic field induced by two charged particles moving with a non-zero relative velocity as a field defined at all points in space, and exists in the reference frames of both particles. This is in contrast to spin-orbit interaction theory, in which the generated magnetic field is defined at only one point in space, and exists in the reference frame of one of the two particles. At the macroscopic scale, it is shown that the GSOI theory implies the same form of the Ørsted magnetic field produced by a current-carrying wire. However, the theory is incompatible with the microscopic form of the Biot-Savart equation that implies that a charged particle induces a magnetic field by having a non-zero velocity. The implications of the GSOI theory on properties of the Ørsted magnetic field in current-carrying atomically thin two-dimensional materials, such as graphene, are discussed. The framework established in this paper aims at re-imagining classical physical concepts in light of an advanced microscopic understanding.

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.

Simulated Analogs of Merging Galaxy Clusters Constrain the Viewing Angle

Abstract A key uncertainty in interpreting observations of bimodal merging galaxy clusters is the unknown angle between the subcluster separation vector and the plane of the sky. We present a new method for constraining this key parameter. We find analogs of observed systems in cosmological n-body simulations, and quantify their likelihood of matching the observed projected separation and relative radial velocities between subclusters, as a function of viewing angle. We derive constraints on the viewing angle of many observed bimodal mergers including the Bullet Cluster (1E 0657-558) and El Gordo (ACT-CL J0102-4915). We also present more generic constraints as a function of projected separation and relative radial velocity, which can be used to assess additional clusters as information about them becomes available. The constraints from these two observables alone are weak (typically ≳70°–75° at 68% confidence and ≳55°–60° at 95% confidence), but they incorporate much more cosmological context than the classical timing argument, marginalizing over many realizations of substructure, peculiar velocities, and so on. Compared with the MCMAC code, which implements the timing argument on NFW halos, our constraints generally predict subcluster separation vectors closer to the plane of the sky. This is because in realistic mergers, the subcluster velocity vectors are not entirely parallel to the separation vector (i.e., the mergers are not perfectly head-on). As a result, observation of a non-zero relative radial velocity does not exclude a separation vector in the plane of the sky, as it does in the head-on timing argument employed by MCMAC.

Andreev–Bashkin effect in superfluid cold gases mixtures

We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.

Transport in superfluid mixtures

We present a general method for constructing effective field theories for non-relativistic superfluids, generalizing the previous approaches of Greiter, Witten, and Wilczek, and Son and Wingate to the case of several superfluids in solution. We investigate transport in mixtures with broken parity and find a parity odd "Hall drag" in the presence of independent motion as well as a pinning of mass, charge, and energy to sites of nonzero relative velocity. Both effects have a simple geometric interpretation in terms of the signed volumes and directed areas of various sub-complexes of a "velocity polyhedron": the convex hull formed by the endpoints of the velocity vectors of a superfluid mixture. We also provide a simple quasi-one-dimensional model that exhibits non-zero Hall drag.

Planar multi-body model of iceberg free drift and towing in broken ice

There are no full-scale data on iceberg towing in ice. However, there is a great interest in such an operation. Simulating the interaction between icebergs and surrounding ice floes during towing may help with choosing iceberg management strategies and design criteria for icebreakers and tug vessels. Broken ice has a discontinuous nature; therefore, it is proposed to model the interaction using a discrete element method (DEM) and known approximations of wind and water drag, wave, and Coriolis forces. The DEM is used to simulate the contacts between rigid, polygon-shaped ice floes. The floes are prevented from interpenetration by applying contact impulses tending to separate the bodies. Depending on the relative velocity of the contacting bodies, the contacts can be classified into two categories: collisions at non-zero relative velocity and resting contacts where the contacting bodies have the same velocity. Converting the calculated impulses into contact forces is straightforward for resting contacts but not for collisions. First, the applied impulses for collisions depend on the choice of restitution coefficient. Second, the collision duration must be estimated in order to convert collision impulses into forces. This paper discusses the choice of the restitution coefficient for ice and proposes an approach to estimate the collision force using the collision duration, which appears to be roughly proportional to the square root of the reduced mass. Additionally, the paper presents an innovative method to generate the ice field through which the iceberg is towed. The field is represented by a domain filled with randomly shaped rigid ice floes. The algorithm is capable of creating an ice field of given concentration and size distribution of the ice floes. The power law size distribution, obtained from aerial and satellite image analysis, is reproduced with high accuracy. The new approach to estimate the collision forces is subjected to a simple test on isolated floe impacts showing a good agreement with experimental and full-scale data. Finally, the simulation of iceberg towing is demonstrated and compared to experimental data. The results of the simulation were found to be in satisfactory agreement with the experiment.

On the dynamic efficiency of internal shocks in magnetized relativistic outflows

We study the dynamic efficiency of conversion of kinetic-to-thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We model internal shocks as being caused by collisions of shells of plasma with the same energy flux and a non-zero relative velocity. The contact surface, where the interaction between the shells takes place, can break up either into two oppositely moving shocks (in the frame where the contact surface is at rest), or into a reverse shock and a forward rarefaction. We find that for moderately magnetized shocks (magnetization $\sigma\simeq 0.1$), the dynamic efficiency in a single two-shell interaction can be as large as 40%. Thus, the dynamic efficiency of moderately magnetized shocks is larger than in the corresponding unmagnetized two-shell interaction. If the slower shell propagates with a sufficiently large velocity, the efficiency is only weakly dependent on its Lorentz factor. Consequently, the dynamic efficiency of shell interactions in the magnetized flow of blazars and gamma-ray bursts is effectively the same. These results are quantitatively rather independent on the equation of state of the plasma. The radiative efficiency of the process is expected to be a fraction $f_r<1$ of the estimated dynamic one, the exact value of $f_r$ depending on the particularities of the emission processes which radiate away the thermal or magnetic energy of the shocked states.

Postcapture Dynamics of a Spacecraft-Manipulator-Payload System

Space manipulators will play an increasingly signie cant role in future space operations. They will handle payloadsofvarying geometricorphysicalpropertiesdependingontheirmissions.Intheidealcase,themanipulator should approach the payload in such a manner that, at the time of capture, the relative velocity between the endeffector and the payload grapple point is zero. Then the capture will be without impact and a smooth one. In practice, however, this is not likely, and there will be a nonzero relative velocity between the end effector and the payload grapple point, leading to an impact. In this paper we study the dynamics of the manipulator, the mother spacecraft, and the payload after such a capture with an impact. The dynamic models of the spacecraftmanipulator system before capture and spacecraft-manipulator-payload system after capture are obtained using the Lagrangian formulation. An impact model is developed to calculate the changes in the generalized velocities caused by the impact. These are then used as initial conditions for simulation of the postimpact dynamics of the combinedspacecraft-manipulator-payloadsystem.Bothrigidande exiblepayloadsareconsidered.Thesimulations show that the dynamics response can besignie cantly differentdepending on whether the capture issmooth or with an impact and whether the payload is e exible or rigid. If the dynamics are uncontrolled, the response can be undesirably large; a control scheme based on feedback linearization is proposed to avoid this.

Vortex velocity pair correlations

The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a nonconserved order parameter is considered. The description includes the effects of other vortices and order parameter fluctuations. At short distances the most probable configuration is that a vortex-antivortex pair have only a nonzero relative velocity which is inversely proportional to the distance between them. The coefficient of proportionality is determined explicitly.

Upper and lower bounds of droplet evaporation in two-phase jets

Abstract This paper examines the limits of evaporation of pure component droplets in two-phase jets emerging from the release of superheated liquids. Two models were developed based on mass, momentum, and energy balances. The first model is used for the calculation of the upper evaporation limit. This model assumes that the liquid droplets travel through stagnant atmospheric air with no back-pressure and with non-zero relative velocity. The second model is used for the calculation of the lower evaporation limit, assuming that the liquid droplets of the released material are carried along with the vapour phase and that there is no relative motion (zero relative velocity) between the phases. Uniform drop size and top-hat profiles (concentration, velocity, and temperature) are assumed. The effects of various parameters (i.e. droplet diameter, released material, superheat, etc.) on the evaporation bounds are revealed through parametric studies. The models' results are also compared with experimental data. Finally, recommendations for future work are given.

Effect of the relative velocity on the collision dipole in a pair of atoms

It is shown that the dispersive collision induced dipole in a pair of atoms is dependent on the relative velocity of the partners. Two formulations taking into account this effect are successively presented. In the first one, the origin of the induced dipole lies in the energy coupling between the fluctuating instantaneous dipole of an atom and the reaction field due to the presence of the neighbor; the effect of the relative velocity is introduced through a Fourier expansion of the time dependent internuclear distance. The second method is based on the consideration of the secular equation for approximate instantaneous normal modes of the whole system. In the two cases, the vanishing velocity limit allows to find again a known result. For a nonzero relative velocity, a limited expansion is obtained and the two lowest order terms are given. Order of magnitude of the effects are estimated in a model of harmonic oscillators.

Energy dissipation in sliding

It is expected that the dissipation of energy in bodies which are sliding will alter their properties and hence affect their behavior in further sliding-in application. A description of the energy dissipation distribution in the sliding of one body over another is attempted. It is first demonstrated that the existence of a non-zero relative velocity between the sliding bodies indicates that sliding is a non-equilibrium process. A near-equilibrium analysis of the process using entropy production is then used to show that in sliding energy is dissipated. Limitations inherent in the near-equilibrium analysis make it necessary to study the far-from-equilibrium sliding process by use of energy conservation concepts. A model of the energy dissipation process in sliding as two coupled non-linear equations is developed. The non-linearity of the model makes many kinds of solution behavior possible. Of special interest is the possibility of cyclic energy dissipation behavior in the sliding bodies.

The Calculation of Aircraft Collision Probabilities

The basic limitation on air traffic compression, from the safety point of view, is the increased risk of collision due to reduced separations. In order to evolve new procedures, and eventually a fully automatic system, it is desirable to have a means of calculating the collision probability for any prescribed flight paths. This paper extends the statistical-probabilistic method of collision probability calculation, which has been limited to parallel, straight line flight paths, to arbitrary flight paths and vehicle shapes. The general formula is specialized to the cases of large relative velocity, nonzero relative velocity, zero relative velocity, and spherical collision surface. The formulas are applied to independent curved landing approaches to parallel runways.