Inelasticity Of Collisions Research Articles

A numerical tool to calculate ion mobility at arbitrary fields from all-atom models

In an effort to calculate electrical mobilities in the free molecular regime using electrical fields that are non-negligible, an algorithm based on the calculation of collision integrals and the two-temperature theory has been created and tested. The algorithm calculates the mobility based on the effective temperature of the ion using a 4-6-12 potential interaction with or without an ion-quadrupole potential (for the case of nitrogen gas). The ion's energy is also approximated so that a relation between the effective temperature of the ion and the field over concentration may be given. The algorithm is parallelized and tested against experimental results for small ions in light gases successfully. The algorithm has also been tested in nitrogen for mid-sized analytes at room temperature and at 100K despite the fact that the inelasticity of collisions has not yet been considered. At 100K, the reduction of the capture radius with the increase of the electric field is apparent for many of the analytes producing “humps” in the reduced mobility vs. the field over concentration curve. For the smallest ions, two humps are observed. One pertaining to the dispersion forces and a second one due to the ion-induced dipole interaction.

The influence of interparticle cohesion on rebounding slow impacts on rubble pile asteroids

The ballistic sorting effect has been proposed to be a driver behind the observed size sorting on the rubble pile asteroid Itokawa. This effect depends on the inelasticity of slow collisions with granular materials. The inelasticity of a collision with a granular material, in turn, depends on grain size. Here we argue that determining the inelasticity of such collisions in an asteroid-like environment is a nontrivial task. We show non-monotonic dependency of the coefficient of restitution (COR) on target particle size using experiments in microgravity. Employing numerical simulations, we explain these results with the growing influence of adhesion for smaller-sized particles. We conclude that there exists an optimum impactor to target particle size ratio for ballistic sorting.

Detachment of strong shocks in confined granular flows

Granular flows are highly dissipative due to frictional resistance and inelasticity in collisions among grains. They are known to exhibit shock waves at velocities that are easily achieved in industrial and nature-driven flows such as avalanches and landslides. This experimental work investigates the formation of strong shock waves on triangular obstacles placed in a dry rapid granular stream in a confined two-dimensional set-up. Oblique attached shock waves are formed for mild turning angles and higher flow velocities, whereas strong bow shock waves are formed for higher turning angles and slower granular streams. A shadowgraph imaging technique elucidates interesting characteristics of the shock waves, especially in the vicinity of shock detachment. Velocity distributions in the form of scatter plots and probability distribution functions are calculated from the flow field data obtained by particle imaging velocimetry. The flow field around the granular shock wave region represents a bimodal distribution of velocities with two distinct peaks, one representing the supersonic flow within the free stream, and the other corresponding to the subsonic faction downstream of a shock wave. Connecting the two is a population that does not directly belong to either of the modes, constituting the non-equilibrium shock wave region. The effect of grain size and scaling, for fixed free-stream conditions and fixed channel width, on the shock detachment is presented. The mechanisms of the static heap formation and the shock detachment process in a confined environment are discussed.

Twistons in graphene nanoribbons on a substrate

Twisted nanoribbons from two-dimensional materials possess many unusual properties tunable by changing the twist angle, for example, electro- and thermal conductivity, chemical properties, and stability against buckling. New interesting phenomena can be observed when a twisted nanoribbon interacts with a substrate. Here we report the results of a classical molecular dynamics study of a graphene nanoribbon twisted about its long axis and interacting with a graphite substrate. Van der Waals interactions with the substrate lead to localization of twisting and the formation of topological solitons called twistons. The topological charge of a twiston obtained with the twist angle $\ensuremath{\beta}$ multiple of $\ensuremath{\pi}$ can be defined as $q=\ensuremath{\beta}/\ensuremath{\pi}$; it can be positive or negative. Twistons can move along the nanoribbon with very little radiation in the form of small-amplitude phonons. Scenarios of twiston collisions are described depending on their topological charge and on the nanoribbon width. In narrow nanoribbons twistons collide practically elastically, preserving their profiles and speeds after the collision, and inelasticity of collisions increases with increasing nanoribbon width. Our results contribute to an understanding of the behavior of two-dimensional material nanoribbons on a substrate.

All‐Optical Transmission Modulation Due to Inelastic Interactions of Ultrashort Pulses in a Disordered Resonant Medium

AbstractRandom resonant media being one of the possible realizations of disordered metamaterials open a room of opportunities for achieving new fundamental effects and designing advanced nanophotonic devices. Strongly nonlinear optical properties of such media attract ever increasing attention nowadays from both theoretical and experimental points of view. Hereinafter, the case of the photonic‐crystal‐like structure with a randomly varying light–matter coupling provided by the random density of quantum particles is considered. Using numerical solution of the Maxwell–Bloch equations, the effects of the pulse collisions in the medium are studied. It is shown that disorder enables the qualitative changes of the system's response for co‐propagating pulses, whereas this is not the case for the counter‐propagating ones. The scheme for an all‐optical transmission modulation due to the disorder‐induced inelasticity of collisions of co‐propagating pulses is proposed. The ability of precise tuning the modulation via the inter‐pulse distance and background refractive index adjustment is revealed. This novel approach for light control can be utilized for some high demand applications, such as modulation and switching of a pulsed radiation.

Dissipated power within a turbulent flow forced homogeneously by magnetic particles

We report measurements of global dissipated power within a turbulent flow homogeneously forced at small scale by a new forcing technique. The forcing is random in both time and space within the fluid by using magnetic particles in an alternating magnetic field. By measuring the growth rate of the fluid temperature, we show how the dissipated power is governed by the external control parameters (magnetic field, and number N of particles). We experimentally found that the mean dissipated power scales linearly with these parameters, as expected from the magnetic injected power scalings. These experimental results are well described by simple scaling arguments showing that the main origins of the energy dissipation are due to viscous turbulent friction of particles within the fluid and to the inelasticity of collisions. Finally, by measuring the particle collision statistics, we also show that the particle velocity is independent of N, and is only fixed by the magnetic "thermostat".

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks.

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction ϕ, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate γ[over ̇]. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (ϕ,Q) plane for small γ[over ̇], we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing γ[over ̇], the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (ϕ,γ[over ̇]) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing γ[over ̇] at fixed ϕ, we find that discontinuous shear thickening can result if γ[over ̇] is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of γ[over ̇].

Hydrodynamics for a model of a confined quasi-two-dimensional granular gas.

The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and it vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

Granular jet impact: probing the ideal fluid description

AbstractWe investigate the impact of a granular jet on a finite target by means of particle simulations. The resulting hydrodynamic fields are compared with theoretical predictions for the corresponding flow of an incompressible and rotation-free fluid. The degree of coincidence between the field obtained from the discrete granular system and the idealized continuous fluid flow depends on the characteristics of the granular system, such as granularity, packing fraction, inelasticity of collisions, friction and target size. In certain limits we observe a granular–continuum transition under which the geometric and dynamic properties of the particle jet and the fluid jet become almost identical.

State-to-State Time-of-Flight Measurements of NO Scattering from Au(111): Direct Observation of Translation-to-Vibration Coupling in Electronically Nonadiabatic Energy Transfer

Translational motion is believed to be a spectator degree of freedom in electronically nonadiabatic vibrational energy transfer between molecules and metal surfaces, but the experimental evidence available to support this view is limited. In this work, we have experimentally determined the translational inelasticity in collisions of NO molecules with a single-crystal Au(111) surface-a system with strong electronic nonadiabaticity. State-to-state molecular beam surface scattering was combined with an IR-UV double resonance scheme to obtain high-resolution time-of-flight data. The measurements include vibrationally elastic collisions (v = 3→3, 2→2) as well as collisions where one or two quanta of molecular vibration are excited (2→3, 2→4) or de-excited (2→1, 3→2, 3→1). In addition, we have carried out comprehensive measurements of the effects of rotational excitation on the translational energy of the scattered molecules. We find that under all conditions of this work, the NO molecules lose a large fraction (∼0.45) of their incidence translational energy to the surface. Those molecules that undergo vibrational excitation (relaxation) during the collision recoil slightly slower (faster) than vibrationally elastically scattered molecules. The amount of translational energy change depends on the surface temperature. The translation-to-rotation coupling, which is well-known for v = 0→0 collisions, is found to be significantly weaker for vibrationally inelastic than elastic channels. Our results clearly show that the spectator view of the translational motion in electronically nonadiabatic vibrational energy transfer between NO and Au(111) is only approximately correct.

Spin-Orbit Suppression of Cold Inelastic Collisions of Aluminum and Helium

We present a quantitative study of suppression of cold inelastic collisions by the spin-orbit interaction. We prepare cold ensembles of >10(11) Al(2P(1/2)) atoms via cryogenic buffer-gas cooling and use a single-beam optical pumping method to measure their magnetic (m(J)-changing) and fine-structure (J-changing) collisions with 3He atoms at millikelvin temperatures over a range of magnetic fields from 0.5 to 6 T. The experimentally determined rates are in good agreement with the functional form predicted by quantum scattering calculations using ab initio potentials. This comparison provides direct experimental evidence for a proposed model of suppressed inelasticity in collisions of atoms in 2P(1/2) states [T. V. Tscherbul et al., Phys. Rev. A 80, 040701(R) (2009)], which may allow for sympathetic cooling of other 2P(1/2) atoms (e.g., In, Tl and metastable halogens).

Thermal diffusion segregation in granular binary mixtures described by the Enskog equation

The diffusion induced by a thermal gradient in a granular binary mixture is analyzed here in the context of the (inelastic) Enskog equation. Although the Enskog equation neglects velocity correlations among particles that are about to collide, it retains the spatial correlations arising from volume exclusion effects and thus is expected to be applicable for moderate densities. In the steady state with gradients only along a given direction, a segregation criterion is obtained from the thermal diffusion factor Λ by measuring the amount of segregation parallel to the thermal gradient. As expected, the sign of the factor Λ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the mixture (the masses and sizes of particles, concentration, solid volume fraction and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail for several systems, with special emphasis on the significant role played by the inelasticity of collisions. In particular, an effect already found in dilute gases (segregation in a binary mixture of identical masses and sizes but different coefficients of restitution) is extended to dense systems. A comparison with recent computer simulation results reveals good qualitative agreement at the level of the thermal diffusion factor. The present analysis generalizes to arbitrary concentration previous theoretical results derived in the tracer limit case.

The Fourier state of a dilute granular gas described by the inelastic Boltzmannequation

The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastichard spheres or disks is investigated. They are restricted neither to weak dissipation nor tosmall gradients. The one-particle distribution functions are assumed to have a scalingproperty, namely that all the position dependence occurs through the density and thetemperature. At the macroscopic level, the state corresponding to both is characterized byuniform pressure, no mass flow, and a linear temperature profile. Moreover, the stateexhibits two peculiar features. First, there is a relationship between the inelasticity ofcollisions, the pressure, and the temperature gradient. Second, the heat flux can beexpressed as being linear in the temperature gradient, i.e. a Fourier-like law is obeyed.One of the solutions is singular in the elastic limit. The theoretical predictionsfollowing from the other one are compared with molecular dynamics simulationresults and a good agreement is obtained in the parameter region in which theFourier state can be actually observed in the simulations, namely not too stronginelasticity.

Resonant oscillations of a granular cluster

AbstractDriven granular media is a fascinating example of intrinsically non‐equilibrium system. I consider an ensemble of inelastically colliding hard disks in a channel driven by two opposite thermal walls with different temperatures. When the inelasticity of collisions is large enough, a dense cluster, located closer to the colder wall, is formed. The steady state profiles are computed from the equations of granular hydrodynamics, and a good agreement with the results of molecular dynamics simulations is found. When the temperature of one of the thermal walls is varied periodically, a dense cluster develops oscillations. The oscillations amplitude reaches its maximum in a resonance, when the frequency of driving is roughly equal to the hydrodynamic frequency of oscillatory acoustic modes in the system. © 2008 Wiley Periodicals, Inc. Complexity, 2008.

Hadron rich and Centauro events

An exploratory statistical analysis of the event C16S086I037 was possible to do using two simulations. A γ and hadron induced showers recognition done on this event through a best fitting procedure shows identification of 25 and 37 for γ and hadron induced showers, respectively. Assuming that the most energetic shower is the surviving particle of an interaction and the tertiary produced particles are from normal multiple pion production, the characteristics of the interaction are: Energy of primary particle E 0 = 1 , 061 TeV , Inelasticity of collision K = 0.81 , Mean inelasticity of γ -ray < k γ > = 0.27 , Hadron induced showers energy/Total energy Q h ′ = 0.90 ≈ Q h , Rapidity density N h / Δ Y = ( 8.56 – 9.89 ) , Mean energy of secondary hadrons < E h > = ( 21.5 ± 4 ) TeV , Mean transverse momentum < P T h > = ( 1.2 ± 0.2 ) GeV/c , Upper bound of partial cross section σ ⩽ ( 15 – 39 ) μ barn and life time τ ⩽ 10 −16 s . Without the surviving particle assumption, the values are: E 0 = 873 TeV , K = 1.0 , < k γ > = 1 / 3 , Q h ′ = 0.90 , N h / Δ Y = ( 8.32 – 9.34 ) , < E h > = ( 21 ± 3.5 ) TeV , < P T h > = ( 1.0 ± 0.16 ) GeV/c . Using another simulation for energy determination with χ 2 > 3.16 for best fitting results 22 and 40 for γ and hadron induced showers, respectively. Under the surviving particle assumption, the figures are: Energy of primary particle E 0 = 1 , 047 TeV , Inelasticity of collision K = 0.80 , Mean inelasticity of γ -ray < k γ > = 0.27 , Hadronic induced showers energy/Total energy Q h ′ = 0.89 ≈ Q h , Rapidity density N h / Δ Y = ( 10.25 − 13.19 ) , Mean energy of secondary hadrons < E h > = ( 19 ± 3 ) TeV , Mean transverse momentum < P T h > = ( 1.0 ± 0.2 ) GeV/c . That is, we get almost similar figures independently of simulation and a mean transverse momentum for this hadron-rich event similar to the Centauro events.

Global Pressure of One-Dimensional Polydisperse Granular GasesDriven by Gaussian White Noise

We study the global pressure of a one-dimensionalpolydisperse granular gases system for the first time, in which the sizedistribution of particles has the fractal characteristic and theinhomogeneity is described by a fractal dimension D. The particles aredriven by Gaussian white noise and subject to inelastic mutual collisions.We define the global pressure P of the system as the impulse transferredacross a surface in a unit of time, which has two contributions, one fromthe translational motion of particles and the other from the collisions.Explicit expression for the global pressure in the steady state is derived.By molecular dynamics simulations, we investigate how the inelasticity ofcollisions and the inhomogeneity of the particles influence the globalpressure. The simulation results indicate that the restitution coefficiente and the fractal dimension D have significant effect on the pressure.

Granular Brownian ratchet model

We show by numerical simulations that a nonrotationally symmetric body, whose orientation is fixed and whose center of mass can slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of particles, displays directed motion. We present a theory which explains how the lack of time reversal induced by the inelasticity of collisions can be exploited to generate a steady average drift. In the limit of a heavy ratchet, we derive an effective Langevin equation whose parameters depend on the microscopic properties of the system and obtain a fairly good quantitative agreement between the theoretical predictions and simulations concerning effective friction, diffusivity, and average velocity.

Non-Gaussian and Clustering Behavior in One-Dimensional PolydisperseGranular Gas System

We present a one-dimensional dynamic model of polydispersegranular mixture with the fractal characteristic of the particle sizedistribution, in which the particles are subject to inelastic mutualcollisions and are driven by Gaussian white noise. The inhomogeneity of theparticle size distribution is described by a fractal dimension D. Thestationary state that the mixture reaches is the result of the balancebetween energy dissipation and energy injection. By molecular dynamicssimulations, we have mainly studied how the inhomogeneity of the particlesize distribution and the inelasticity of collisions influence the velocitydistribution and distribution of interparticle spacing in the steady-state.The simulation results indicate that, in the inelasticity case, the velocitydistribution strongly deviates from the Gaussian one and the system has astrong spatial clustering. Thus the inhomogeneity and the inelasticity havegreat effects on the velocity distribution and distribution of interparticlespacing. The quantitative information of the non-Gaussian velocitydistribution and that of clustering are respectively represented.

Energy and number of collision fluctuations in inelastic gases

The two-dimensional Inelastic Maxwell Model (IMM) is studied by numerical simulations. It is shown how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations. These fluctuations are associated to a shrinking of the available phase space. We find the asymptotic scaling of these energy fluctuations and show how they affect the tail of the velocity distribution during long time intervals. We stress that these fluctuations relax like power laws on much slower time scales than the usual exponential relaxations taking place in kinetic theory.

Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0< e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.