Collision Radius Research Articles

A Bright First Day for Tidal Disruption Events

Stream–stream collision may be an important prepeak energy dissipation mechanism in tidal disruption events (TDEs). We perform local three-dimensional radiation hydrodynamic simulations in a wedge geometry including the gravity to study stream self-crossing with an emphasis on resolving the collision and following the subsequent outflow. We find that the collision can contribute to prepeak optical emissions by converting ≳5% of the stream kinetic energy to radiation, yielding prompt emission of ∼1042−44 erg s−1. The radiative efficiency is sensitive to stream mass fallback rates and strongly depends on the downstream gas optical depth. Even for a sub-Eddington (10%) mass fallback rate, the strong radiation pressure produced in the collision can form a local super-Eddington region near the collision site, where a fast, aspherical outflow is launched. A higher mass fallback rate usually leads to more optically thick outflow and lower net radiative efficiency. For , the estimated photosphere size of the outflow can expand by 1–2 orders of magnitude, reaching ∼1014 cm. The average gas temperature at this photospheric surface is a few × 104 K, roughly consistent with inferred prepeak photosphere properties for some optical TDEs. We find that the dynamics is sensitive to the collision angle and radius, but the radiative efficiency or outflow properties show more complex dependency than is often assumed in ballistic models.

Coagulation rate coefficients for fractal-like agglomerates in the diffusive and ballistic limits

Predicting agglomeration dynamics in aerosol or colloidal systems requires accurate models for the agglomerate collision rate. In the present work, numerical simulations cover the ballistic and the diffusive collision regimes as limiting cases and are used to derive coagulation rate coefficients for a large number of agglomerate sizes and morphologies. The simulations account for both the translational and rotational motion of agglomerates and allow for the monitoring of individual collision events. The results suggest that the power law suffices to characterize the clusters’ morphologies and that representative collision radii of agglomerates are mainly controlled by two parameters: (i) the radius of gyration, Rg, and (ii) the morphology characterized by the fractal dimension Df. Collision radii for the diffusive regime are up to 10% above the corresponding ballistic results and cluster rotation also increases the effective collision radius. The latter effect can lead to differences of up to 16% in the diffusive regime. In contrast, interpenetration effects, i.e. a small cluster passing through a larger cluster without collision, are less pronounced in the diffusive limit. The results provide strong correlations between collision radii and key parameters for both regimes such that improved analytical expressions for the coagulation rate coefficients can be suggested. Compared to existing models for the ballistic and diffusive regimes, the proposed correlations offer reduced complexity across an extended range of the relevant parameter space.

A mechanism for a “leaky” black hole to catalyze galaxy formation

In the gravitational field of a Schwarzschild-like black hole, particles infalling from rest at infinity, and black hole “wind” particles with relativistic velocity leaking radially out from the nominal horizon both have the same magnitude of velocity at any radius from the hole. Hence when equally massive infalling and wind particles collide at any radius, they yield collision products with zero center of mass radial velocity, which can then nucleate star formation at the collision radius. We suggest that this gives a mechanism by which a central black hole can catalyze galaxy formation. For disk galaxies, this mechanism explains the observed approximately exponential falloff of the surface brightness with radius, and gives an estimate of the associated scale length.

Effect of turbulence dispersion on bubble-particle collision efficiency

In this study, bubble-particle collision efficiency in a single-bubble system (bubble diameter ∼ 1 mm) for different turbulence intensity (Ti ∼ 4% − 20%) and various particle size (diameter ∼ 30 to 100 µm) were theoretically studied by injecting particles on a stationary bubble. A critical distance for particle injection upstream of the bubble was analytically determined ensuring no distortion of the flow streamlines at the particle release location. To quantify the turbulence collision efficiency, an analytical turbulence dispersion (TD) model was proposed. This model was also compared with a 3D computational fluid dynamics (CFD) model incorporating a random walk momentum exchange model. A statistical parameter, 90%-collision radius was introduced to represent effective particle releasing radius, which was shown to increase with the turbulence intensity and particle diameter. A threshold turbulence intensity of 7% was noted below which the analytical model agreed well with the CFD model, however, above this threshold, the analytical model was found to overestimate the collision efficiency and underestimate the 90%-collision radius. The CFD model demonstrated that with increasing turbulence intensity, energy dissipation rate in the system also increased and particles showed more stochastic pattern in their trajectories. A force analysis showed that larger diameter particles approaching the bubble experienced higher horizontal deflections in the higher turbulence intensity cases due to larger inertial forces acting on them, however such effect was not apparent farther downstream of the bubble.

Cable-path optimization method for industrial robot arms

The production line engineer's task of designing the external path for cables feeding electricity, air, and other resources to robot arms is a labor-intensive one. As the motions of robot arms are complex, the manual task of designing their cable path is a time-consuming and continuous trial-and-error process. Herein, we propose an automatic optimization method for planning the cable paths for industrial robot arms. The proposed method applies current physics simulation techniques for reducing the person–hours involved in cable path design. Our method yields an optimal parameter vector (PV) that specifies the cable length and cable-guide configuration via filtering the candidate PV set through a cable-geometry simulation based on the mass–spring model. The proposed method offers two key features: 1) Increased computational efficiency via an optimization procedure that separates the entire cable into the cable segments. In the proposed method, the entire cable is segmented at the positions of the cable guides into several separate cable segments, and the PVs of the cable segments that satisfy the constraints of collision, stretch, and curvature radius are filtered into the local optimal PV set. The global optimal PV is obtained by finding the combination of the local optimal PVs which have the same guide configuration between the adjacent cable segments and have minimal total length of the adjacent cable segments. 2) Robustness to external disturbances, such as fluctuation in the physical properties of the cables and the accuracy of manually attaching the cables. The PVs of the local optimal PV sets are required to satisfy the above constraints, even if the cable length changes in the predefined range, which ensures the robustness of the obtained cable path. To verify the validity of the proposed method, we obtain the global optimal PVs by applying the method to several pick-and-place motions of a six-axis vertical articulated robot arm in our simulations and implement the cable paths on an actual robot arm based on the obtained PVs. Our results indicate that the proposed method can aid line engineers to efficiently design the cable paths along robot arms.

Hydrodynamic interactions and extreme particle clustering in turbulence

Expanding recent observations by Hammond & Meng (J. Fluid Mech., vol. 921, 2021, A16), we present a range of detailed experimental data of the radial distribution function (r.d.f.) of inertial particles in isotropic turbulence for different Stokes number,$St$, showing that the r.d.f. grows explosively with decreasing separationr, exhibiting$r^{-6}$scaling as the collision radius is approached, regardless of$St$or particle radius$a$. To understand such explosive clustering, we correct a number of errors in the theory by Yavuzet al.(Phys. Rev. Lett., vol. 120, 2018, 244504) based on hydrodynamic interactions between pairs of small, weakly inertial particles. A comparison between the corrected theory and the experiment shows that the theory by Yavuzet al.underpredicts the r.d.f. by orders of magnitude. To explain this discrepancy, we explore several alternative mechanisms for this discrepancy that were not included in the theory and show that none of them are likely the explanation. This suggests new, yet-to-be-identified physical mechanisms are at play, requiring further investigation and new theories.

Giant planet scatterings and collisions: hydrodynamics, merger-ejection branching ratio, and properties of the remnants

ABSTRACT Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers versus ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple ‘sticky-sphere’ prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and N-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with MJ and 2MJ, we find that quick mergers occur when the impact parameter rp (the pericentre separation between the planets) is less than 2RJ, and the merger conserved at least 97 per cent of the initial mass. Strong tidal effects can affect the ‘binary-planet’ orbit when rp is between 2RJ and 4RJ. We quantify these effects using a set of fitting formulae that can be implemented in N-body codes. We run a suite of N-body simulations with and without the formulae for systems of two giant planets initially in unstable, nearly circular and coplanar orbits. The fluid (tidal) effects significantly increase the branching ratio of planetary mergers relative to ejections by doubling the effective collision radius. While the fluid effects do not change the distributions of semimajor axis and eccentricity of each type of remnant planets (mergers versus surviving planets in ejections), the overall orbital properties of planet scattering remnants are strongly affected due to the branching ratio change. We also find that the merger products have broad distributions of spin magnitudes and obliquities.

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particle-particle collisions regulate turbophoresis in a critical way, making simulations sensitive to collisional effects. Lagrangian tracking of every particle in the flow can become computationally expensive when the physical number of particles in the system is large. Artificially reducing the number of particles in the simulation can mitigate the computational cost. When particle-particle collisions are an important aspect determining the simulation outcome, as in the case when turbophoresis plays an active role, simply reducing the number of particles in the simulation significantly alters the computed particle statistics. This paper introduces a computational particle treatment for particle-particle collisions which reproduces the results of a full simulation with a reduced number of particles. This is accomplished by artificially enhancing the particle collision radius based on scaling laws for the collision rates. The proposed method retains the use of deterministic collision models and is applicable for both low and high Stokes number regimes.

Determination of the properties of ionic vacancy by magnetic field

Ionic vacancy is, being produced as a byproduct in electrode reaction, a polarized free space of the order of 0.1 nm surrounded by oppositely charged ionic cloud. As a perfect gas in electrolyte solution, it does not interplay with other solution particles. On the other hand, magnetic field provides useful means to examine the natures of it. Using a special electrode operated in a magnetic field called cyclotron MHD electrode (CMHDE), we first determined the lifetime of vacancy in copper deposition as 1.2 sec, which is extraordinarily long in comparison with the collision interval of solution particles. Then, using kinetic theory of gas, we measured the collision radius of vacancy gas to be 0.70 nm, which was consistent with theoretical calculation 0.65 nm.

Parameterization of In‐Cloud Aerosol Scavenging Due to Atmospheric Ionization: Part 3. Effects of Varying Droplet Radius

AbstractA new set of simulations of collision rate coefficients for aerosol particles with droplets (in‐cloud scavenging) extends to a droplet radius of 15 μm, with short‐range effects on collisions treated as an increment of droplet effective collision radius (ECR). The simulations are made with our Monte Carlo trajectory model for midtropospheric (~5 km) conditions. The use of ECR allows the results to be expressed as a modified analytic solution (MAS) for the rate coefficients, incorporating both long‐range and short‐range effects. For smaller particles with radius less than 0.2 μm, the increment of ECR is only caused by the particle charge inducing a short‐range image electric force, and results of the MAS match quite well that of our trajectory model. For larger particles, the short‐range effects become complex, including particle size effects (weight, intercept, and flow around the particle), with image forces induced by both droplet and particle charges. An ECR based on these factors gives average errors between the MAS and the trajectory model of less than 10%, with smaller errors for larger droplets. We have now completed the parameterizations of rate coefficients for midtropospheric conditions that can be applied to cloud models. One application would be to test whether electrically induced changes in scavenging rates, which have been proposed to significantly affect cloud processes dependent on condensation nucleus concentration and contact ice nucleation, can explain observed cloud responses to changes in current flow in the global electric circuit.

The influence of molecular structure on collision radius for optical sensing of molecular oxygen based on cyclometalated Ir(iii) complexes.

Three triphenylamine (TPA) substituted cyclometalated Ir(iii) complexes IrA1, IrA2, and IrA3 based on Ir(ppy)3 were synthesized and applied as phosphorescent probes for the monitoring of molecular oxygen. The phosphorescence intensity of all the Ir(iii) complexes in tetrahydrofuran (THF) was gradually quenched with an increase of oxygen concentration. The increase of TPA substituents on the meta-position of 2-phenylpyridine (IrA1-IrA3) gradually improved the oxygen sensitivity of cyclometalated Ir(iii) complexes. IrA3 showed the highest oxygen sensitivity in THF with a KappSV of 204.8 bar−1 and a limit of detection (LOD) of 0.27 mbar. The relationship between molecular structure and the collision radiuses (σ) of all the Ir(iii) complexes has been investigated on the basis of the Demas model and the fundamental expression of luminescence quenching systems by oxygen. The ratio of collision radiuses are σIrA1/σIr(ppy)3 = 1.27 ± 0.05, σIrA2/σIr(ppy)3 = 1.72 ± 0.10, and σIrA3/σIr(ppy)3 = 2.13 ± 0.07, respectively. The introduction and increase of TPA substituents can obviously increase the collision radiuses of cyclometalated Ir(iii) complexes which leading to potential oxygen sensitivity. And the incremental effect of collision radiuses caused by the introduction of TPA substituents resulted in outstanding oxygen sensitivity of IrA3. The results demonstrate for the first time evidence between molecular structure and oxygen sensitivity of the emitters for optical sensing.

Simplified Derivation of the Collision Probability of Two Objects in Independent Keplerian Orbits

Abstract Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Öpik and Wetherill, the collision probability was derived by linearizing the motion near the collision points, and there is now a vast amount of literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Öpik–Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.

Coagulation-agglomeration of fractal-like particles: structure and self-preserving size distribution.

Agglomeration occurs in environmental and industrial processes, especially at low temperatures where particle sintering or coalescence is rather slow. Here, the growth and structure of particles undergoing agglomeration (coagulation in the absence of coalescence, condensation, or surface growth) are investigated from the free molecular to the continuum regime by discrete element modeling (DEM). Particles coagulating in the free molecular regime follow ballistic trajectories described by an event-driven method, whereas in the near-continuum (gas-slip) and continuum regimes, Langevin dynamics describe their diffusive motion. Agglomerates containing about 10-30 primary particles, on the average, attain their asymptotic fractal dimension, D(f), of 1.91 or 1.78 by ballistic or diffusion-limited cluster-cluster agglomeration, corresponding to coagulation in the free molecular or continuum regimes, respectively. A correlation is proposed for the asymptotic evolution of agglomerate D(f) as a function of the average number of constituent primary particles, n̅(p). Agglomerates exhibit considerably broader self-preserving size distribution (SPSD) by coagulation than spherical particles: the number-based geometric standard deviations of the SPSD agglomerate radius of gyration in the free molecular and continuum regimes are 2.27 and 1.95, respectively, compared to ∼1.45 for spheres. In the transition regime, agglomerates exhibit a quasi-SPSD whose geometric standard deviation passes through a minimum at Knudsen number Kn ≈ 0.2. In contrast, the asymptotic D(f) shifts linearly from 1.91 in the free molecular regime to 1.78 in the continuum regime. Population balance models using the radius of gyration as collision radius underestimate (up to about 80%) the small tail of the SPSD and slightly overpredict the overall agglomerate coagulation rate, as they do not account for cluster interpenetration during coagulation. In the continuum regime, when a recently developed agglomeration rate is used in population balance equations, the resulting SPSD is in excellent agreement with that obtained by DEM.

<i>Ab Initio</i> Molecular Dynamics Simulations on High-Temperature Reaction Rates of Reactions KO+CO==K+CO<sub>2</sub>, KO+C=K+CO, and K<sub>2</sub>O+CO<sub>2</sub>==K<sub>2</sub>CO<sub>3</sub>

In this paper, we present a novel approach for calculating chemical reaction rates based on molecular collision theory, in which molecular collision cross sections are calculated by averaging over all reactive trajectories from ab initio molecular dynamics simulations. The molecular collision radius is determined by both reactive and non-reactive trajectories of molecular dynamics under constant temperature. Thus, both steric and temperature effects have been take into account for molecular collision cross sections. We have applied this approach to calculate reaction rates of reactions KO+CO==K+CO2, KO+C==K+CO, and K2O+CO2==K2CO3 under high temperature. It also shows that under higher temperature, the probabilities of a successful reaction resulting from particle collision are low, because the products are not stable.

Classical aspects of the reduced collision cross section for elastic scattering in ion mobility spectrometry

A classical theory for the collision cross section associated with elastic scattering in ion mobility spectrometry is developed. The collision cross section is found to be equal to a hard-sphere collision cross section evaluated at the turning radius plus a potential scattering term inversely proportional to the effective temperature. The results of the theory are compared to current theories by fitting reduced collision cross sections for both small-ion and large-ion mobility data using a molecular modeled hard-sphere collision cross section as reference. The turning point radius is found to be 0.7 of the hard-sphere collision radius and the interaction potential evaluated at the turning point varies inversely as the square of the turning radius. Taken in combination, classical theory provides an incomplete description of the scattering event.

Hydrodynamic interactions of self-propelled swimmers

The hydrodynamic interactions of a suspension of self-propelled particles are studied using a direct numerical simulation method which simultaneously solves for the host fluid and the swimming particles. A modified version of the “Smoothed Profile” (SP) method is developed to simulate microswimmers as squirmers, which are spherical particles with a specified surface-tangential slip velocity between the particles and the fluid. This simplified swimming model allows one to represent different types of propulsion (pullers and pushers) and is thus ideal to study the hydrodynamic interactions among swimmers. We use the SP method to study the diffusive behavior which arises due to the swimming motion of the particles, and show that there are two basic mechanisms responsible for this phenomena: the hydrodynamic interactions caused by the squirming motion of the particles, and the particle–particle collisions. This dual nature gives rise to two distinct time- and length-scales, and thus to two diffusion coefficients, which we obtain by a suitable analysis of the swimming motion. We show that the collisions between swimmers can be interpreted in terms of binary collisions, in which the effective collision radius is reduced due to the collision dynamics of swimming particles in viscous fluids. At short time-scales, the dynamics of the swimmer is analogous to that of an inert tracer particle in a swimming suspension, in which the diffusive motion is caused by fluid-particle collisions. Our results, along with the simulation method we have introduced, will allow us to gain a better understanding of the complex hydrodynamic interactions of self-propelled swimmers.

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Particle–vapor molecule (condensation) and particle–particle (coagulation) collision kernels are critically important parameters for the description of particle size distribution evolution in aerosols. We use mean first passage time calculations to find a dimensionless form of the collision kernel that applies in the limit where the ratio of the masses of colliding entities (aerosol particles or vapor molecules) to gas molecule mass, Z, approaches infinity, and the colliding entities are dilute in concentration. In these calculations, the motion of colliding entities is monitored with Langevin dynamics, and the collision kernel is inferred from the time required for collision. The presented analysis reveals that the dimensionless collisional kernel (H) is a function solely of the diffusive Knudsen number (KnD , the square root of the product of kT and the reduced mass divided by the product of the reduced friction factor and collision radius), and a number of commonly used expressions for the collision kernel also collapse to the functional form H(KnD ), irrespective of whether they were derived for Z → ∞ or Z → 0 conditions. The examined collision kernel expressions are further found to agree within 10% of our calculations as well as with each other across the entire KnD range. This result suggests that a single collision kernel can be used to describe all transition regime collision rates, i.e., both condensation and coagulation rates, with reasonable accuracy, and establishes that Langevin-equation-based mean first passage time calculations can serve as a simple approach to examine transition regime collision phenomena.

Cluster–cluster aggregation simulation in a concentrated suspension

The collision radius of a floc is an indispensable parameter for the precise description of the rate of aggregation during the development of particle flocs with a wide size distribution. Herein, we report on the characteristics of the collision radius of fractal aggregates formed by off-lattice diffusion-limited cluster–cluster aggregation (DLCCA) simulations, and discuss aggregation kinetics based on the value of the estimated collision radius. The collision radius has a fractal relationship with the number of primary particles that compose the floc. Further, the obtained fractal dimensions of flocs increase from the normally accepted value of 1.6–1.8 to a value of ∼2.5 when the initial volume fraction is above 8%. From an assessment of the partial radial distribution function of the particles, the increase of the fractal dimensions determined by the collision radius can be attributed to a change in the spatial distribution of neighboring particles. The DLCCA simulation also reveals an apparent increase in the rate of aggregation upon an increase in the initial volume fraction. For a relatively low initial volume fraction, the enhancement of the aggregation rate is expressed by a population balance equation taking into account additional factors, i.e., transient collision flux among particles/flocs, excluded volumes, and polydispersed features of flocs. However, for cases with high initial volume fractions, the population balance model that accounts for these three factors overestimates the aggregation rate, which supports the concept of a caging effect.

Footstep navigation for dynamic crowds

AbstractThe majority of steering algorithms output only a force or velocity vector to an animation system, without modeling the constraints and capabilities of human‐like movement. This simplistic approach lacks control over how a character should navigate. This paper proposes a steering method that uses footsteps to navigate characters in dynamic crowds. Instead of an oriented particle with a single collision radius, we model a character's center of mass and footsteps using a 2D approximation of an inverted spherical pendulum model of bipedal locomotion. We use this model to generate a timed sequence of footsteps that existing animation techniques can follow exactly. Our approach not only constrains characters to navigate with realistic steps but also enables characters to intelligently control subtle navigation behaviors that are possible with exact footsteps, such as side‐stepping. Our approach can navigate crowds of hundreds of individual characters with collision‐free, natural steering decisions in real‐time. Copyright © 2011 John Wiley & Sons, Ltd.

Molecular Dynamics Simulation of Self-Assembly of n-Decyltrimethylammonium Bromide Micelles

In this paper, a molecular dynamics simulation of surfactant self-assembly using realistic atomistic models is presented. The simulations are long enough to enable the observation of several processes leading to equilibrium, such as monomer addition and detachment, micelle dissolution, and micelle fusion. The self-assembly of DeTAB surfactants takes place in three stages: fast aggregation of monomers to form small disordered oligomers; ripening process by which larger aggregates grow at the expense of smaller ones; slower stage involving collisions between large micelles. The first two stages were described well by a simple kinetic model with a size-independent rate constant estimated from the self-diffusion coefficient and collision radius of an isolated monomer. The average cluster size, area per headgroup, degree of counterion dissociation, and critical micelle concentration estimated from the simulation are in reasonable agreement with experimental values. An all-atom and united-atom surfactant model were compared, and the results were seen to be almost independent of the choice of model. DeTAB micelles are spheroidal, with a hydrophobic core composed of tail atoms surrounded by a hydrophilic corona of head atoms. A Stern layer composed of bromide counterions was also identified. Water molecules solvate the counterions and the head atoms, penetrating into the micelle up to the location of the atom connecting the head to the aliphatic tail, in agreement with recent experimental observations.