Collision Sequences Research Articles

An efficient chained-hash-table strategy for collision handling in hard-sphere discrete particle modeling

We develop an efficient algorithm for handling collision events that is suitable for Discrete Particle Modeling (DPM) of dense gas–solid fluidization systems. We improve on previous strategies that are discussed in this paper as a byproduct. The core idea is centered on the use of dynamic crosswise linked data structures. This type of data structures enables an efficient updating and managing of lists of collision events associated with particles. In addition, a chained-hash-table strategy is proposed to efficiently process particle collision sequences. For systems of N p particles, this strategy allows a complexity O(1) time per collision regarding the event list handling operations.

Decimetre dust aggregates in protoplanetary discs

The growth of planetesimals is an essential step in planet formation. Decimetre-size dust agglomerates mark a transition point in this growth process. In laboratory experiments we simulated the formation, evolution, and properties of decimetre-scale dusty bodies in protoplanetary discs. Small sub-mm size dust aggregates consisting of micron-size SiO$_2$ particles randomly interacted with dust targets of varying initial conditions in a continuous sequence of independent collisions. Impact velocities were 7.7 m/s on average and in the range expected for collisions with decimetre bodies in protoplanetary discs. The targets all evolved by forming dust \emph{crusts} with up to several cm thickness and a unique filling factor of 31% $\pm$3%. A part of the projectiles sticks directly. In addition, some projectile fragments slowly return to the target by gravity. All initially porous parts of the surface, i.e. built from the slowly returning fragments, are compacted and firmly attached to the underlying dust layers by the subsequent impacts. Growth is possible at impact angles from 0$^{\circ}$ (central collision) to 70$^{\circ}$. No growth occurs at steeper dust surfaces. We measured the velocity, angle, and size distribution of collision fragments. The average restitution coefficient is 3.8% or 0.29 m/s ejection velocity. Ejecta sizes are comparable to the projectile sizes. The high filling factor is close to the most compact configuration of dust aggregates by local compression ($\sim 33$%). This implies that the history of the surface formation and target growth is completely erased. In view of this, the filling factor of 31% seems to be a universal value in the collision experiments of all self-consistently evolving targets at the given impact velocities. We suggest that decimetre and probably larger bodies can simply be characterised by one single filling factor.

Radiation damage evolution in ceramics

A review is presented of recent results on radiation damage production, defect accumulation and dynamic annealing in a number of ceramics, such as silicon carbide, zircon and zirconia. Under energetic particle irradiation, ceramics can undergo amorphization by the accumulation of point defects and defect clusters (silicon carbide) or direct impact amorphization (zircon). Ceramics that resist radiation-induced amorphization have mechanisms to dissipate the primary knock-on atom energy, such as replacement collision sequences that leave the lattice undisturbed and low-energy cation site exchange. The presence of engineered mobile defects, such as structural vacancies in stabilized zirconia, can dynamically anneal radiation damage. Thus, defect engineering is a promising strategy to design radiation tolerance for applications such as nuclear waste disposal.

How good is damped molecular dynamics as a method to simulate radiation damage in metals?

Classical molecular dynamics (MD) is a frequently used technique in the study of radiation damage cascades because it provides information on very small time and length scales inaccessible to experiment. In a radiation damage process, energy transfer from ions to electrons may be important, yet there is continued uncertainty over how to accurately incorporate such effects in MD. We introduce a new technique based on the quantum mechanical Ehrenfest approximation to evaluate different methods of accounting for electronic losses. Our results suggest that a damping force proportional to velocity is sufficient to model energy transfer from ions to electrons in most low energy cascades. We also find, however, that a larger rate of energy transfer is seen when the ionic kinetic energy is confined to a focused sequence of collisions. A viscous damping coefficient dependent on the local atomic environment is shown to be an excellent model for electronic energy losses in low energy cascades in metals.

Modelling swift heavy ion irradiation in iron

Swift heavy ions moving in metals lose most of their energy to inelastic scattering of electrons. The energy deposited in the electronic system is transferred into the atomic system via electron–ion interactions and can lead to melting and creation of new damage and also annealing of pre-existing atomic defects. Using a combination of molecular dynamics and a consistent treatment of electron energy transfer and transport we have modelled experiments performed in Fe to investigate the annealing effect and damage creation under electronic excitations. We observe both annealing and new damage creation at low and high electronic stopping, respectively. Rapid separation of interstitial atoms and vacant lattice sites is seen due to efficient transport via replacement collision sequences. Our results suggest that the role of electronic excitation can be significant in modeling of the behaviour of metals under swift heavy ion irradiation and attempts to modify metals via ion implantation.

Cumulative damage in strength-dominated collisions of rocky asteroids: Rubble piles and brick piles

Laboratory impact experiments were performed to investigate the conditions that produce large-scale damage in rock targets. Aluminum cylinders (6.3 mm diameter) impacted basalt cylinders (69 mm diameter) at speeds ranging from 0.7 to 2.0 km/s. Diagnostics included measurements of the largest fragment mass, velocities of the largest remnant and large fragments ejected from the periphery of the target, and X-ray computed tomography imaging to inspect some of the impacted targets for internal damage. Significant damage to the target occurred when the kinetic energy per unit target mass exceeded roughly 1 4 of the energy required for catastrophic shattering (where the target is reduced to one-half its original mass). Scaling laws based on a rate-dependent strength were developed that provide a basis for extrapolating the results to larger strength-dominated collisions. The threshold specific energy for widespread damage was found to scale with event size in the same manner as that for catastrophic shattering. Therefore, the factor of four difference between the two thresholds observed in the lab also applies to larger collisions. The scaling laws showed that for a sequence of collisions that are similar in that they produce the same ratio of largest fragment mass to original target mass, the fragment velocities decrease with increasing event size. As a result, rocky asteroids a couple hundred meters in diameter should retain their large ejecta fragments in a jumbled rubble-pile state. For somewhat larger bodies, the ejection velocities are sufficiently low that large fragments are essentially retained in place, possibly forming ordered “brick-pile” structures.

Anomalous behavior of a single particle falling through a funnel

We show several surprising phenomena that occur in an extremely simple system of a single frictionless, inelastic, spherical particle falling under gravity through a symmetric funnel. One might naively expect that particles would fall through funnels with steeper sides more quickly, exert a smaller total impulse on the funnel walls, and lose less energy. However, we show that there are special ranges of angles of the funnel walls for which exactly the opposite occurs. Typically, the particle will experience a sequence of collisions that is highly sensitive to the location at which it enters the funnel and nearby particle trajectories become widely dispersed. However, in the special angular ranges this is not the case and the particle can experience sequences of collisions that have a highly coherent structure. We provide a theoretical analysis that can predict and explain this surprising behavior.

Forensic Engineering Analysis Of Multi-Vehicle Impact Sequence

Forensic Engineers Are Often Called Upon To Reconstruct The Speeds, Severity Levels And Sequence Of Multiple-Vehicle Co-Linear Collisions, Such As Those That Occur In Heavy Traffic Or Resulting From Quick Stops In Response To Traffic Control Devices. Witnesses May Provide Accounts Of The Accident Sequence That Are Incomplete, Inaccurate, Self-Serving Or Simply Events That They Are Not In A Position To See, But May Reconstruct In Their Memories As Occurring, Making The Reliance Upon Witness Or Driver Statements Often Suspect. This Paper Provides A Straight Forward And Proven Methodology Of Determining The Sequence And Speeds Of A Multiple-Vehicle Collision Event Based Upon The Analysis Of Reproducible Collision Data, Scientific Principles And Reliable Analysis Techniques.

Angular distributions of atoms sputtered from NiAl{1 1 0} and Ni{1 0 0}

Using the laser post-ionization surface analysis technique, I have for the first time studied angular distributions of Ni and Al atoms sputtered from NiAl{1 1 0}. Emission angular distributions from Ni{1 0 0} have also been measured. I have observed preferential emissions of Ni and Al atoms along 〈1 1 1〉 and 〈1 0 0〉crystallographic directions for NiAl{1 1 0} and of Ni atoms along 〈1 1 0〉 and 〈1 0 0〉 directions for Ni{1 0 0}. The observed preferential ejections can be explained in terms of the theory of focusing-collision sequences. Because of the difference in surface binding energy between Al and Ni atoms, preferential ejection angles of Ni atoms are slightly different from those of Al atoms along the 〈1 1 1〉 ejections. For NiAl, the 〈1 1 1〉 preferential ejections were less prominent than the 〈1 0 0〉 preferential ejections and this can be related to the low efficiency of momentum transfer in Ni–Al collision sequences along 〈1 1 1〉 lattice directions. The low efficiency of momentum transfer due to the mass mismatch can also be responsible for the experimental observation that the preferential ejections in the alloy were less prominent than those in the Ni metal.

Reversible and irreversible dynamics of a qubit interacting with a small environment

We analyze the dynamics of a system qubit interacting by means of a sequence of pairwise collisions with an environment consisting of just two qubits. We show that the density operator of the qubits approaches a common time-averaged equilibrium state, characterized by large fluctuations, only for a random sequence of collisions. For a regular sequence of collisions the qubit states of the system and of the reservoir undergo instantaneous periodic oscillations and do not relax to a common state. Furthermore we show that pure bipartite entanglement is developed only when at least two qubits are initially in the same pure state while otherwise also genuine multipartite entanglement builds up.

Dynamical collision network in granular gases

We address the problem of recollisions in cooling granular gases. To this aim, we dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an event driven simulation of inelastic hard disks from time 0 until time t . The network is decomposed into its k -core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k -shell, and the set of all shells is a complete and nonoverlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e., a t{-2} energy decay, is unstable toward a strongly inhomogeneous phase with clusters and vortices, where energy decays as t{-1} . The clear transition between those two phases appears in the evolution of the k -shells structure in the collision network. In the homogeneous state the k -shell structure evolves as in a growing network with a fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k{max} approximately 0.9(d) with (d) the average number of collisions experienced by a particle. During the final nonhomogeneous state a growing fraction of collisions is concentrated in small, almost closed, communities of particles: k{max} is no more linear in (d) and the distribution of shells becomes extremely large developing a power-law tail approximately k{-3} for high shell indexes. We conclude proposing a simple algorithm to build a correlated random network that reproduces, with few essential ingredients, the whole observed phenomenology, including the t{-1} energy decay. It consists of two kinds of collisions (links): single random collisions with any other particle and long chains of recollisions with only previously encountered particles. The algorithm disregards the exact spatial arrangement of clusters, suggesting that the observed stringlike structures are not essential to determine the statistics of recollisions and the energy decay.

Study of cascades damage in Ni by MD with different interatomic potentials

Molecular dynamics (MD) simulations, performed with embedded atom potentials, are used to understand the formation of defects following displacement cascades in Ni. Different empirical potentials, presenting large differences in stacking fault energy (SFE), are used. Simulations were conducted with primary knock-on (PKA) atom energies of 5–40 keV at a temperature of 10 K. Defects include, depending on the potential, individual point defects (vacancies and interstitials), dislocation loops and stacking fault tetrahedra (SFT). The results are related to TEM observations, and the mismatch between these two pictures is discussed. It appears that in a collision cascade, the formation of an SFT does not depend only on the SFE but also on other parameters such as the mobility of vacancies and self-interstitials, or the presence of replacement collision sequences. Based on these calculations we suggest that the formation of clusters of vacancies is a prerequisite to the formation of SFTs.

Attosecond-time-scale multielectron collisions in the Coulomb four-body problem: Traces in classical probability densities

In the triple ionization of the Li ground state by single photon absorption the three electrons escape to the continuum mainly through two collision sequences with individual collisions separated by time intervals on the attosecond scale. We investigate the traces of these two collision sequences in the classical probability densities. We show that each collision sequence has characteristic phase space properties which distinguish it from the other. Classical probability densities are the closest analog to quantum mechanical densities allowing our results to be directly compared to quantum mechanical results.

Autoresonant homeostat concept for engineering application of nonlinear vibration modes

Analysis of strongly nonlinear (vibro-impact) systems revealed an existence of nonlinear modes of vibration with spatial and temporal concentration of energy. The modes can be realised, for example, through intensification of the vibration process by condensing the vibration into a sequence of collisions for impulsive action of the tools to the media being treated or can be as a result of some discontinuity (slackening of a contact, arrival of crack, etc.) in the structure. The use of the nonlinear modes to develop useful mechanical work leads to necessity of excitation and control of resonance in ill-defined dynamical systems. This is due to the poorly predictable response of the media being treated. Excitation, stabilisation and control of a nonlinear mode at the top intensity in such systems is an engineering challenge and needs a new method of adaptive control for its realisation. Such a control technique was developed with the use of self-exciting mechatronic systems. The excitation of the nonlinear mode in such systems is a result of artificial instability of mechanical system conducted by positive electronic feedback. The instability is controlled by intelligent identification of the mode and active tracing of the optimal relationship between phase shifting and limitation in the feedback circuitry. This method of control is known as autoresonance. Applications of autoresonant control for development of the new machines are described.

Classical molecular dynamics study of primary damage created by collision cascade in a ZrC matrix

Classical molecular dynamics simulation of a high energy collision cascade initiated at 50 keV is used to study the primary damage state in a stoichiometric mono crystalline ZrC matrix. Analysis of the dynamics and the morphology of the displacement cascade reveals three distinct, well-defined time frames: collision phase, thermal spike and relaxation phase. On average, most of the atoms migrate over short distances, typically less than 11 Å, leading to numerous collision sequences in each sublattice. No amorphisation is observed, only a few point defects are created at the end of the collision cascades. All the Zr interstitials form a dumbbell structure oriented in the 〈1 1 1〉 direction and C interstitials are either isolated or form a 〈1 1 1〉 dumbbell structure. However, unlike metals, few antisites are created. Clusters of two interstitials of different species have a tendency to form small interstitial dislocation loops in the (1 1 1) plane.

Application of the Gillespie algorithm to a granular intruder particle

We show how the Gillespie algorithm, originally developed to describe coupled chemical reactions, can be used to perform numerical simulations of a granular intruder particle colliding with thermalized bath particles. The algorithm generates a sequence of collision ``events'' separated by variable time intervals. As input, it requires the position-dependent flux of bath particles at each point on the surface of the intruder particle. We validate the method by applying it to a one-dimensional system for which the exact solution of the homogeneous Boltzmann equation is known and investigate the case where the bath particle velocity distribution has algebraic tails. We also present an application to a granular needle in bath of point particles where we demonstrate the presence of correlations between the translational and rotational degrees of freedom of the intruder particle. The relationship between the Gillespie algorithm and the commonly used Direct Simulation Monte Carlo (DSMC) method is also discussed.

Numerical modeling of ozone production in direct current corona discharge

Ozone has many industrial uses, including treatment of municipal water, wastewater, cooling towers, industrial process water, effluent water treatment, food processing, through to water fit for consumption and marine life. In this paper, we study the ozone production by negative electric corona discharge, witch involves passing the feed of gas, air rich, through an electrical discharge. This is done by applying a high voltage between two electrodes separated. The electrical charge between two surfaces creates a sequence of dissociation and subsequent collisions of oxygen with electrons creating ozone. So to describe this phenomenon we use (1D) numerical model for the charged particles. The electron number density and electric field are determined from solution of the one-dimensional coupled continuity equations of charge carriers and Poisson’s equation. Simulation result show the variation of the electrical field, charged particles density, and ozone (O 3) particle density.

Light emission from Be and BeO surfaces bombarded by 5 keV Kr+ ions

Light emitted during the bombardment of beryllium and beryllium-oxide surfaces by 5keV Kr+ ions is analyzed over the wavelength range 190–590nm. A much larger photon yield is found when the target is an oxide. First, atomic lines are stronger. The analysis of their Doppler profile reveals the importance of collision sequences (Kr–O)–(O–Be) for the ejection of excited Be atoms. Secondly, a BeO target gives rise to luminescence. This is intense for medium angles of incidence and surprisingly declines steeply between 50° and 60°. Possible origins to luminescence are self-trapped excitons and F-centers. The intense emission from the BeO target contrasts with its absence for pure Be, which excludes radiation from surface plasmons. Bombardment of a BeO target also produces well-structured molecular bands.

Displacement cascade initiated with the realistic energy of the recoil nucleus in UO 2 matrix by molecular dynamics simulation

Classical molecular dynamics simulations have been performed to study the primary damage due to α-decay self-radiation in UO 2 matrix. For the first time a displacement cascade initiated with an energy of 80 keV has been performed. Compared with the cascades initiated with lower energies of the primary knock-on atom (PKA), the morphology of the cascade shows the same features; no amorphisation and creation of point defects are observed. The discrepancy with the linear theory NRT (Norton–Robinson–Torrens) law on the creation of the number of point defects is discussed. However, differences have been found; local and temporary amorphisation appears during the thermal spike over large length scale only in the high energy cascade. Proportionally in the high energy cascade, more linear collision sequences are undergone by the uranium atoms and the oxygen atoms recombine over a larger length scale.

3 keV Ar scattering from unreconstructed Si(1 0 0) at grazing incidence: Molecular dynamics simulation

In this paper, grazing scattering of 3keV Ar along the [100] direction of an ideal (unreconstructed) Si(100) surface is simulated using the molecular dynamics (MD) method. A detailed analysis of the scattering trajectories is performed. The scattering process in many cases involves a sequence of simultaneous collisions between projectile and target atoms. The scattered intensity is presented as a function of the polar scattering angle, the azimuthal scattering angle and the energy loss. Various prominent features of the spectra are assigned to specific scattering trajectories.