Initial Impact Parameter Research Articles

On the Origin of the Ancient, Large-scale Cold Front in the Perseus Cluster of Galaxies

The intracluster medium of the Perseus Cluster exhibits spiral-shaped X-ray surface brightness discontinuities known as “cold fronts,” which simulations indicate are caused by the sloshing motion of the gas after the passage of a subcluster. Recent observations of Perseus have shown that these fronts extend to large radii. In this work, we present simulations of the formation of sloshing cold fronts in Perseus using the AREPO magnetohydrodynamics code, to produce a plausible scenario for the formation of the large front at a radius of 700 kpc. Our simulations explore a range of subcluster masses and impact parameters. We find that low-mass subclusters cannot generate a cold front that can propagate to such a large radius, and that small impact parameters create too much turbulence, which leads to the disruption of the cold front before it reaches such a large distance. Subclusters that make only one core passage produce a stable initial front that expands to large radii, but without a second core passage of the subcluster, other fronts are not created at a later time in the core region. We find a small range of simulations with subclusters with mass ratios of R ∼ 1:5 and an initial impact parameter of θ ∼ 20°–25° that not only produce the large cold front but a second set in the core region at later times. These simulations indicate that the “ancient” cold front is ∼6–8.5 Gyr old. For the simulations providing the closest match with observations, the subcluster has completely merged into the main cluster.

Black hole binaries in AGN accretion discs – II. Gas effects on black hole satellite scatterings

ABSTRACT The black hole (BH) binaries in active galactic nuclei (AGN) are expected to form mainly through scattering encounters in the ambient gaseous medium. Recent simulations, including our own, have confirmed this formation pathway is highly efficient. We perform 3D smoothed particle hydrodynamics (SPH) simulations of BH scattering encounters in AGN discs. Using a range of impact parameters, we probe the necessary conditions for binary capture and how different orbital trajectories affect the dissipative effects from the gas. We identify a single range of impact parameters, typically of width ∼0.86−1.59 binary Hill radii depending on AGN disc density, that reliably leads to binary formation. The periapsis of the first encounter is the primary variable that determines the outcome of the initial scattering. We find an associated power law between the energy dissipated and the periapsis depth to be ΔE ∝ r−b with b = 0.42 ± 0.16, where deeper encounters dissipate more energy. Excluding accretion physics does not significantly alter these results. We identify the region of parameter space in initial energy versus impact parameter where a scattering leads to binary formation. Based on our findings, we provide a ready-to-use analytic criterion that utilizes these two pre-encounter parameters to determine the outcome of an encounter, with a reliability rate of >90 per cent. As the criterion is based directly on our simulations, it provides a reliable and highly physically motivated criterion for predicting binary scattering outcomes which can be used in population studies of BH binaries and mergers around AGN.

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature.

We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40m/s, respectively, induced by the long-range van der Waals attraction between the droplets.

Self-force correction to the deflection angle in black-hole scattering: A scalar charge toy model

Using self-force methods, we consider the hyperbolic-type scattering of a pointlike particle carrying a scalar charge $Q$ off a Schwarzschild black hole. For given initial velocity and impact parameter, back-reaction from the scalar field modifies the scattering angle by an amount $\propto\! Q^2$, which we calculate numerically for a large sample of orbits (neglecting the gravitational self-force). Our results probe both strong-field and field-weak scenarios, and in the latter case we find a good agreement with post-Minkowskian expressions. The scalar-field self-force has a component tangent to the four-velocity that exchanges particle's mass with scalar-field energy, and we also compute this mass exchange as a function along the orbit. The expressions we derive for the scattering angle (in terms of certain integrals of the self-force along the orbit) can be used to obtain the gravitational self-force correction to the angle in the physical problem of a binary black hole with a large mass ratio. We discuss the remaining steps necessary to achieve this goal.

A comprehensive approach for bridge performance evaluation under rockfall impact integrated with geological hazard analysis

Rockfall is one kind of major hazard that seriously threatens the safety of bridge structures passing through mountainous areas. The complexity of geological conditions in mountainous areas makes it difficult to determine the initial impact parameters of falling rock in the bridge performance analysis. At present, the subjective and deterministic methods are adopted to get the initial motion parameters of the falling rock for evaluating the structural responses. In this paper, the probability distributions of falling rocks collision parameters are obtained by the rockfall Monte Carlo simulations. Then the characteristic values from the probability distribution of rock motion parameters are taken as the input parameters in the dynamic simulation of bridge structure. Finally, three-dimensional nonlinear dynamic analysis is employed to evaluate the safety of the bridge structure under rockfall hazards. The residual resistance index (RRI) is presented for quantifying the post-impact performance of bridge pier and girder under rock collision. The structural safety is mainly dominated by the impact mass and translational velocity of the falling rock rather than the rotational velocity and impact angle. The rock shape also has non-negligible influence on the structural dynamic responses and performance, and the cube-like rock induces more severe structural damage than other shapes. According to the RRI and probability distribution of rock mass, the non-exceedance probability of RRI is obtained which can be used for the risk analysis of rockfall impacting on bridges. The proposed comprehensive approach for bridge performance evaluation considers the uncertainty of rockfall characteristics, and it provides more reasonable solution to investigate the impact performance of bridge structure under rockfall disasters.

A study of cool core resiliency and entropy mixing in simulations of galaxy cluster mergers

ABSTRACT We present results from a suite of binary merging cluster simulations. The hydrodynamical cluster simulations are performed employing a smoothed particle hydrodynamics formulation in which gradient errors are strongly reduced by means of an integral approach. We consider adiabatic as well as radiative simulations, in which we include gas cooling, star formation, and energy feedback from supernovae. We explore the effects of merging on the thermodynamic structure of the intracluster gas of the final merger remnant. In particular, we study how core entropy is generated during the merging and the stability properties of the initial cool-core profile against disruption. To this end, we consider a range of initial mass ratio and impact parameters. Final entropy profiles of our adiabatic merging simulations are in good accord with previous findings, with cool-cores being disrupted for all of the initial merging setups. For equal-mass off-axis mergers, we find that a significant contribution to the final primary core entropy is due to hydrodynamic instabilities generated by rotational motions, which are induced by tidal torques during the first pericentre passage. In radiative simulations, cool-cores are more resilient against heating processes; none the less, they are able to maintain their integrity only in the case of off-axis mergers with very unequal masses. We suggest that these results are robust against changes in the gas physical modelling, in particular to the inclusion of AGN thermal feedback. Our findings support the view that the observed core cluster morphology emerges naturally in a merging cluster context, and conclude that the merging angular momentum is a key parameter in shaping the thermodynamical properties of the final merger remnant.

Ion attachment rates and collection forces on dust particles in a plasma sheath with finite ion inertia and mobility.

Ion attachment and ion drag to dust particles near the edge of a nonthermal plasma sheath are of interest to better understand how particles become trapped in such sheath regions. While electron-particle collisions in plasmas and sheaths can often be described by orbital motion limited theory, quantification of ion transport about dust particles in collisional sheath regions requires a distinct modeling approach. In this work, the dimensionless ion attachment coefficients and dimensionless collection forces on negatively charged particles are calculated using ion trajectory models accounting for an external electric field in a collisional sheath, ion inertia, and finite ion mobility. By considering both ion inertia and finite ion mobility, results apply for ion transport from the fully collisional regime into a regime of intermediate collisionality. Ion collection forces are calculated in two related limits; first, the nondissipative limit, wherein the dimensionless collection force function coincides with the dimensionless attachment coefficient (anticipated in the collisionless regime), and second, a dissipative limit, wherein neutral gas collisions dissipate ion momentum, which strongly affects the resulting collection force (anticipated in the fully collisional regime). We show that ion motion about a charged particle can be parametrized by the ion Stokes number, which is the ratio of ion inertia to gas resistance to motion and dimensionless electric field strength (the external field strength normalized by the electric field at the particle surface). At intermediate Stokes numbers (10^{1}-10^{2}), ions adopt trajectories that are extremely sensitive to the initial ion-particle impact parameter. Plots of the resulting collision angle at fixed Stokes number and dimensionless field strength as a function of impact parameter contain multiple discontinuities. Nonetheless, we obtain smooth curves for the ion attachment rates and collection forces in both the nondissipative and fully dissipative limits. Increasing the ion Stokes number is found to significantly decrease the dimensionless ion attachment coefficients and ion collection forces in comparison to coefficients evaluated with expressions derived in the fully collisional limit. In all instances, including the dissipative limit, we find the ion collection force acts in the direction of ion migration. Neural network fits are utilized to parametrize the resulting attachment coefficients and ion collection forces, and we apply these fits to examine the charge levels on 1-μm radius particles in external fields in the 3×10^{2}-3×10^{3}Vm^{-1} range and pressures in the 5×10^{-1}-5×10^{1} Torr (66.7-6667 Pa) range. We find the charge level is strongly sensitive to both field strength and pressure in the plasma sheath, ranging from 6 × 10^{3} to 1.8 × 10^{4} over the conditions examined. Calculations are also used to demonstrate that the ion collection force can be sufficiently strong to trap particles not only close to the bottom electrode of a parallel-plate reactor, but also close to the top electrode, with a critical ion density required for trapping.

Effects of initial state fluctuations on the mean transverse momentum

We show that in ideal hydrodynamic simulations of heavy-ion collisions, initial state fluctuations result in an increase of the mean transverse momentum of outgoing hadrons, 〈pt〉. Specifically, 〈pt〉 is larger by a few percent if realistic fluctuations are implemented than with smooth initial conditions, the multiplicity and impact parameter being kept fixed. We show that result can be traced back to the fact that for a given total entropy, the initial energy contained in the fluid is larger if the density profile is bumpy. We discuss the implication of these results for the extraction of the equation of state of QCD from experimental data.

Dynamic behaviors and regime map of a molten blast furnace slag droplet impacting a solid surface

The dynamic morphologies of a molten blast furnace slag droplet impacting a quartz glass surface are studied visually for a wide range of dimensionless initial temperatures (1.604–1.951), Reynolds numbers (17.4–124.4), and Weber numbers (197–1191). Five morphological evolution modes are defined based on the final stage of the slag film as deposition, receding, prompt-splashing, retraction-deposition and retraction-splashing. An impact regime map is established with the Reynolds number and dimensionless initial temperatures as the coordinates and six boundaries dividing the different modes are identified in the regime map. The apparent temperature nephograms of the slag film are extracted by a home-developed optical calibration method. The dynamic spreading processes and temperature distributions of the different regimes are not simply determined by the initial impact parameters, the coupling effect of the flow of the high-viscosity liquid slag and the heat transfer at the interface will obstruct the consecutive morphological evolution. The regulation principle for the centrifugal granulation system is promoted based on the analysis on an energy barrier for the sufficient spreading of the droplet and the impact regime map.

Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 101-102 atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO2 (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.

A Parameter Space Exploration of Galaxy Cluster Mergers. II. Effects of Magnetic Fields

Abstract The hot intracluster plasma in clusters of galaxies is weakly magnetized. Mergers between clusters produce gas compression and motions that can increase the magnetic field strength. In this work, we perform high-resolution nonradiative magnetohydrodynamics simulations of binary galaxy cluster mergers with magnetic fields, to examine the effects of these motions on the magnetic field configuration and strength, as well as the effect of the field on the gas itself. Our simulations sample a parameter space of initial mass ratios and impact parameters. During the first core passage of mergers, the magnetic energy increases via gas compression. After this, shear flows produce temporary, megaparsec-scale, strong-field “filament” structures. Lastly, magnetic fields grow stronger by turbulence. Field amplification is most effective for low-mass ratio mergers, but mergers with a large impact parameter can increase the magnetic energy more via shearing motions. The amplification of the magnetic field is most effective in between the first two core passages of each cluster merger. After the second core passage, the magnetic energy in this region gradually decreases. In general, the transfer of energy from gas motions to the magnetic field is not significant enough to have a substantial effect on gas mixing and the subsequent increase in entropy, which occurs in cluster cores as a result. In the absence of radiative cooling, this results in an overall decrease of the magnetic field strength in cluster cores. In these regions, the final magnetic field is isotropic, while it can be significantly tangential at larger radii.

Free Energy and Dynamics of Water Droplet Coalescence

Droplet coalescence is a critical issue in atmospheric sciences. In this work, the coalescence of water nanodroplets was studied by performing equilibrium and nonequilibrium molecular dynamics simulations. To understand the intrinsic nature of the process, we obtained the free energy change as a function of droplet size and droplet–droplet distance. We decomposed the free energy change ΔF into energetic ΔU and entropic TΔS contributions to understand the molecular details. ΔU was dominated by the change in Coulomb interactions, which strongly correlated with the change in the number of hydrogen bonds. We found a strong positive correlation between the mobility of water molecules and TΔS. To analyze the dynamics, two colliding water droplets of the same size were given different initial speeds, impact parameters, and collision angles. We found when the collision is head-on, the time for thorough mixing between interfacial and bulk molecules decreases when the initial speed increases, whereas when the colli...

η′ production in nucleus-nucleus collisions as a probe of chiral dynamics

We argue that, because of the peculiar properties of the $\eta'$ meson, it is a promising probe of "chiral" dynamics. In particular, we show that a rotating gluon-dominated plasma might lead to an enhanced production of $\eta'$ w.r.t. statistical model expectations. The presence of a strong topological susceptibility might give a similar effect. In both cases, unlike the statistical model,we expect a non-trivial dependence on event geometry, such as initial volume and impact parameter. Hence, an observation of $\eta'/\pi^0$ ratio depending strongly on impact parameter might be a good indication of chiral effects, either from vorticity or topological phases of QCD

Analysis of ionospheric structure influences on residual ionospheric errors in GNSS radio occultation bending angles based on ray tracing simulations

Abstract. The Global Navigation Satellite System (GNSS) radio occultation (RO) technique is widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source to RO at upper stratospheric altitudes, and a linear dual-frequency bending angle correction is commonly used to remove the first-order ionospheric effect. However, the higher-order residual ionospheric error (RIE) can still be significant, so it needs to be further mitigated for high-accuracy applications, especially from 35 km altitude upward, where the RIE is most relevant compared to the decreasing magnitude of the atmospheric bending angle. In a previous study we quantified RIEs using an ensemble of about 700 quasi-realistic end-to-end simulated RO events, finding typical RIEs at the 0.1 to 0.5 µrad noise level, but were left with 26 exceptional events with anomalous RIEs at the 1 to 10 µrad level that remained unexplained. In this study, we focused on investigating the causes of the high RIE of these exceptional events, employing detailed along-ray-path analyses of atmospheric and ionospheric refractivities, impact parameter changes, and bending angles and RIEs under asymmetric and symmetric ionospheric structures. We found that the main causes of the high RIEs are a combination of physics-based effects – where asymmetric ionospheric conditions play the primary role, more than the ionization level driven by solar activity – and technical ray tracer effects due to occasions of imperfect smoothness in ionospheric refractivity model derivatives. We also found that along-ray impact parameter variations of more than 10 to 20 m are possible due to ionospheric asymmetries and, depending on prevailing horizontal refractivity gradients, are positive or negative relative to the initial impact parameter at the GNSS transmitter. Furthermore, mesospheric RIEs are found generally higher than upper-stratospheric ones, likely due to being closer in tangent point heights to the ionospheric E layer peaking near 105 km, which increases RIE vulnerability. In the future we will further improve the along-ray modeling system to fully isolate technical from physics-based effects and to use it beyond this work for additional GNSS RO signal propagation studies.

Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations.

In gas phase synthesis systems, clusters form and grow via condensation, in which a monomer binds to an existing cluster. While a hard-sphere equation is frequently used to predict the condensation rate coefficient, this equation neglects the influences of potential interactions and cluster internal energy on the condensation process. Here, we present a collision rate theory-molecular dynamics simulation approach to calculate condensation probabilities and condensation rate coefficients. We use this approach to examine atomic condensation onto 6-56-atom Au and Mg clusters. The probability of condensation depends upon the initial relative velocity (v) between atom and cluster and the initial impact parameter (b). In all cases, there is a well-defined region of b-v space where condensation is highly probable, and outside of which the condensation probability drops to zero. For Au clusters with more than 10 atoms, we find that at gas temperatures in the 300-1200 K range, the condensation rate coefficient exceeds the hard-sphere rate coefficient by a factor of 1.5-2.0. Conversely, for Au clusters with 10 or fewer atoms and for 14- and 28-atom Mg clusters, as cluster equilibration temperature increases, the condensation rate coefficient drops to values below the hard-sphere rate coefficient. Calculations also yield the self-dissociation rate coefficient, which is found to vary considerably with gas temperature. Finally, calculations results reveal that grazing (high b) atom-cluster collisions at elevated velocity (>1000 m s-1) can result in the colliding atom rebounding (bounce) from the cluster surface or binding while another atom dissociates (replacement). The presented method can be applied in developing rate equations to predict material formation and growth rates in vapor phase systems.

Catching spiral – S0 transition in groups. Insights from SPH simulations with chemo-photometric implementation

We are investigating the co-evolution of galaxies within groups combining multi-wavelength photometric and 2D kinematical observations. Here we focus on S0s showing star formation in ring/arm-like structures. We use smooth particle hydrodynamical simulations (SPH) with chemo-photometric implementation which provide dynamical and morphological information together with the spectral energy distribution (SED) at each evolutionary stage. As test cases, we simulate the evolution of two such S0s: NGC 1533 and NGC 3626.The merging of two halos with mass ratio 2:1, initially just composed of DM and gas, well match their observed SEDs, their surface brightness profiles and their overall kinematics. The residual star formation today “rejuvenating” the ring/arm like structures in these S0s is then a mere consequence of a major merger, i.e. this is a phase during the merger episode. The peculiar kinematical features, e.g. gas-stars counter rotation in NGC 3626, depends on the halos initial impact parameters. Furthermore, our simulations allow to follow, in a fully consistent way, the transition of these S0s through the green valley in the NUV-r vs. Mr colour magnitude diagram, which they cross in about 3–5Gyrs, before reaching their current position in the red sequence. We conclude that a viable mechanism driving the evolution of S0s in groups is of gravitational origin.

Critical phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case

In numerical simulations of black hole binaries, Pretorius and Khurana [Class. Quant. Grav. {\bf 24}, S83 (2007)] have observed critical behaviour at the threshold between scattering and immediate merger. The number of orbits scales as $n\simeq -\gamma\ln|p-p_*|$ along any one-parameter family of initial data such that the threshold is at $p=p_*$. Hence they conjecture that in ultrarelavistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent $\gamma$. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by $n_\infty\simeq 0.41/\eta$, where $\eta$ is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.

Mathematical theory and analytical solutions for the wave catching-up phenomena in a nonlinearly elastic composite bar

Cracking induced by tensile wave at the free surface of an impacted target is an important issue in impact-resistant design. Here, we explore the use of material nonlinearity to undermine the strength of the tensile wave. More specifically, we consider waves in a two-material composite bar subjected to impact loading at one end. Multiple reflections cause a tensile wave being transmitted into the second material. The attention is on analytically and numerically studying the phenomenon that the tensile wave catches the first transmitted compressive wave. It turns out that, depending on the interval of the initial impact, catching-up phenomena can happen in two wave patterns. A general mathematical theory is provided to show the existence of these patterns together with some qualitative information. To gain more insights into such phenomena, asymptotic solutions are also constructed, which provide both qualitative and quantitative results on the requirement of the constitutive relation, the time and place at which the catching takes place, and how the initial impact, material and geometric parameters influence the solutions. Numerical simulations are also performed, confirming the validity of the analytical results. The analysis and results presented here could be useful for designing a composite structure that has a good impact-protection performance.

Sensitivity of Collision Simulation Results to Initial Assumptions

PC-Crash simulations of staged collisions require dozens of parameters describing vehicle and impact parameters. The Collision Optimizer will vary initial speeds and impact parameters to obtain a best fit to a desired end state, but vehicle parameters are left unchanged. The present paper allows these other parameters to vary in thousands of combinations, re-optimizing the solution in each to find the relationships between the previously fixed parameters and the resulting impact speeds. The results show that tire friction and vehicle inertial properties have the most influence on impact speeds. Other parameters have little influence on the results. Language: en

A PARAMETER SPACE EXPLORATION OF GALAXY CLUSTER MERGERS. I. GAS MIXING AND THE GENERATION OF CLUSTER ENTROPY

We present a high-resolution set of adiabatic binary galaxy cluster merger simulations using FLASH. These are the highest-resolution simulations to date of such mergers using an AMR grid-based code with Eulerian hydrodynamics. In this first paper in a series we investigate the effects of merging on the entropy of the hot intracluster gas, specifically with regard to the ability of merging to heat and disrupt cluster "cool-cores." We find, in line with recent works, that the effect of fluid instabilities that are well-resolved in grid-based codes is to significantly mix the gases of the two clusters and to significantly increase the entropy of the gas of the final merger remnant. This result is characteristic of mergers over a range of initial mass ratio and impact parameter. In line with this, we find that the kinetic energy associated with random motions is higher in our merger remnants which have high entropy floors, indicating the motions have efficiently mixed the gas and heated the cluster core with gas of initially high entropy. We examine the implications of this result for the maintenance of high entropy floors in the centers of galaxy clusters and the derivation of the properties of dark matter from the thermal properties of the X-ray emitting gas.