Outcome Of Collisions Research Articles

Outcomes of Sub-Neptune Collisions

Observed high multiplicity planetary systems are often tightly packed. Numerical studies indicate that such systems are susceptible to dynamical instabilities. Dynamical instabilities in close-in tightly packed systems, similar to those found in abundance by Kepler, often lead to planet–planet collisions. For sub-Neptunes, the dominant type of observed exoplanets, the planetary mass is concentrated in a rocky core, but the volume is dominated by a low-density gaseous envelope. For these, using the traditional perfect merger assumption (also known as the “sticky-sphere” approximation) to resolve collisions is questionable. Using both N-body integration and smoothed-particle hydrodynamics, we have simulated sub-Neptune collisions for a wide range in realistic kinematic properties such as impact parameters ( b′ ) and impact velocities ( vim ) to study the possible outcomes in detail. We find that the majority of the collisions with kinematic properties similar to what is expected from dynamical instabilities in multiplanet systems may not lead to mergers of sub-Neptunes. Instead, both sub-Neptunes survive the encounter, often with significant atmosphere loss. When mergers do occur, they can involve significant mass loss and can sometimes lead to complete disruption of one or both planets. Sub-Neptunes merge or disrupt if b′<bc′ , a critical value dependent on vim /v esc, where v esc is the escape velocity from the surface of the hypothetical merged planet assuming perfect merger. For vim/vesc≲2.5 , bc′∝(vim/vesc)−2 , and collisions with b′<bc′ typically leads to mergers. On the other hand, for vim/vesc≳2.5 , bc′ ∝ vim /v esc, and the collisions with b′<bc′ can result in complete destruction of one or both sub-Neptunes.

Accelerating Giant-impact Simulations with Machine Learning

Constraining planet-formation models based on the observed exoplanet population requires generating large samples of synthetic planetary systems, which can be computationally prohibitive. A significant bottleneck is simulating the giant-impact phase, during which planetary embryos evolve gravitationally and combine to form planets, which may themselves experience later collisions. To accelerate giant-impact simulations, we present a machine learning (ML) approach to predicting collisional outcomes in multiplanet systems. Trained on more than 500,000 N-body simulations of three-planet systems, we develop an ML model that can accurately predict which two planets will experience a collision, along with the state of the postcollision planets, from a short integration of the system’s initial conditions. Our model greatly improves on non-ML baselines that rely on metrics from dynamics theory, which struggle to accurately predict which pair of planets will experience a collision. By combining with a model for predicting long-term stability, we create an ML-based giant-impact emulator, which can predict the outcomes of giant-impact simulations with reasonable accuracy and a speedup of up to 4 orders of magnitude. We expect our model to enable analyses that would not otherwise be computationally feasible. As such, we release our training code, along with an easy-to-use user interface for our collision-outcome model and giant-impact emulator (https://github.com/dtamayo/spock).

Direct numerical simulation of coalescence and separation of binary droplet collision with lamella stabilization

Binary droplet collision is a fundamental aspect of various natural phenomena and industrial applications. In this work, direct numerical simulation of coalescence and separation of binary droplet collision is performed over a wide range of Weber numbers and impact factors. The incompressible Navier–Stokes equations are solved by the finite volume approach, coupled with the volume of fluid method. To address the inaccurate prediction of thin lamella in simulation, a lamella stabilization method is introduced to resolve the lamella by adjusting the grid resolution. Compared with experimental data, it is validated that the lamella can be accurately and fully captured with this lamella stabilization method. Moreover, the analysis of shape and energy during the collision is conducted, and the variation of lamella is described in detail, particularly the evolution of the thickness of lamella. The results suggest that for obtaining the full variation of lamella, the maximum refinement size of the grid can reach D/4096. It is also found that without lamella stabilization, excessive dissipation can lead to the failure of predicting coalescence and separation, especially for the cases in the transition between coalescence and separation. Furthermore, even if the same collision outcome can be obtained without lamella stabilization, the number and size of droplets have obvious differences.

The outcome of collisions between gaseous clumps formed by disk instability

The disk instability model is a promising pathway for giant planet formation in various conditions. At the moment, population synthesis models are used to investigate the outcomes of this theory, where a key ingredient of the disk population evolution are collisions of self-gravitating clumps formed by the disk instabilities. In this study, we explored the wide range of dynamics between the colliding clumps by performing state-of-the-art smoothed particle hydrodynamics simulations with a hydrogen-helium mixture equation of state and investigated the parameter space of collisions between clumps of different ages, masses (1--10 Jupiter mass), various impact conditions (head-on to oblique collisions) and a range of relative velocities. We find that the perfect merger assumption used in population synthesis models is rarely satisfied and that the outcomes of most of the collisions lead to erosion, disruption or a hit-and-run. We also show that in some cases collisions can initiate the dynamical collapse of the clump. We conclude that population synthesis models should abandon the simplifying assumption of perfect merging. Relaxing this assumption will significantly affect the inferred population of planets resulting from the disk instability model.

Numerical study of two equal-sized miscible drops undergoing head-on collision

The numerical analysis focuses on investigating head-on collisions between two miscible drops composed of distinct fluids, specifically ethanol and water. The simulations are performed using a coupled level set and volume of fluid approach with different Weber numbers to study the effect of drop inertia. The code is validated against experimental and numerical results from earlier investigations. Additionally, a comparative study involving both water drops and ethanol–water drops is conducted to explore the impact of varying surface tension ratios on collision outcomes. Results show that when miscible drops collide, the merged liquid drop exhibits asymmetric behavior, such as an asymmetric combined drop shape in cases of permanent coalescence or an asymmetric end droplet breakup in cases of reflexive separation. The collision outcome undergoes significant variation as the Weber number changes. At lower Weber numbers, permanent coalescence is observed, while at medium Weber numbers, reflexive separation occurs without the formation of a secondary drop. For medium to large Weber numbers, reflexive separation with the generation of one secondary drop becomes prominent, and in the case of very large Weber numbers, multiple satellite drops form. The maximum vertical elongation of the merged drop and corresponding surface energy increase as the surface tension ratio rises, irrespective of the Weber number. However, for a fixed surface tension ratio, the maximum vertical elongation and associated surface energy vary with an increase in the Weber number. The findings also shed light on the enhanced internal mixing arising from the mismatched surface tension of the colliding drops as the Weber number increases. Furthermore, the study explores the effect of drop inertia on various aspects, including asymmetric collision behavior, energy budget, and mixing index.

Dust evolution during a protostellar collapse: Influence on the coupling between the neutral gas and magnetic field

Context. The extent of the coupling between the magnetic field and the gas during the collapsing phase of star-forming cores is strongly affected by the dust size distribution, which is expected to evolve by means of coagulation, fragmentation, and other collision outcomes. Aims. We aim to investigate the influence of key parameters on the evolution of the dust distribution, as well as on the magnetic resistivities during protostellar collapse. Methods. We performed a set of collapsing single-zone simulations with shark. The code computes the evolution of the dust distribution, accounting for different grain growth and destruction processes, with the grain collisions being driven by brownian motion, turbulence, and ambipolar drift. It also computes the charges carried by each grain species and the ion and electron densities, as well as the magnetic resistivities. Results. We find that the dust distribution significantly evolves during the protostellar collapse, shaping the magnetic resistivities. The peak size of the distribution, population of small grains, and, consequently, the magnetic resistivities are controlled by both coagulation and fragmentation rates. Under standard assumptions, the small grains coagulate very early as they collide by ambipolar drift, yielding magnetic resistivities that are many orders of magnitude apart from the non-evolving dust case. In particular, the ambipolar resistivity, ηAD, is very high prior to nH = 1010 cm−3. As a consequence, magnetic braking is expected to be ineffective. In this case, large size protoplanetary discs should result, which is inconsistent with recent observations. To alleviate this tension, we identified mechanisms that are capable of reducing the ambipolar resistivity during the ensuing protostellar collapse. Among them, electrostatic repulsion and grain-grain erosion feature as the most promising approaches. Conclusions. The evolution of the magnetic resistivities during the protostellar collapse and consequently the shape of the magnetic field in the early life of the protoplanetary disc strongly depends on the possibility to repopulate the small grains or to prevent their early coagulation. Therefore, it is crucial to better constrain the collision outcomes and the dust grain’s elastic properties, especially the grain’s surface energy based on both theoretical and experimental approaches.

Scattering of kinks in scalar-field models with higher-order self-interactions

Higher-order scalar field models in two dimensions, including the ϕ8 model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found. However, in physical applications, it is very important to know all the explicit solutions of a model for any minima position. In the present study, with the help of some deformation functions, we have shown that higher-order scalar field theories can be obtained with explicit kinks. In particular, we introduced two deformation functions that, when applied to the well known ϕ4 and ϕ6 models, produce modified ϕ8 and ϕ10 models, respectively, with all their explicit kink-like solutions which depend on a single parameter. Since this parameter controls the position of the minima of the potential, we have found interesting new solutions in many distinct cases. We have also studied the kink mass, the behavior of the excitation spectra and several kink-antikink collisions for these two new modified models. The collision outcome is determined by the initial configuration, specifically the sequence in which the kink-antikink and antikink-kink pairings emerge. Another interesting finding is the suppression of resonance windows, which may be explained by the presence of a set of internal modes in the model.

Experimental study of the collision behavior between moving and sessile droplets on curved surfaces

In this study, we used pure water droplets to investigate the collision interactions of two droplets on curved surfaces. We captured the collision dynamics at different droplet impact velocities with the use of a high-speed camera. We observed three main modes during droplet collisions: deformation, coalescence, and rebound. We also plotted a collision regime map for different surfaces using the Weber number We and presented the critical We value for coalescence and rebound. With the increases of curvature radius, the critical We variates around 6.7 to 12.3 and presenting the tendency of increases first and then decreases. Furthermore, we quantitatively analyzed the transformation laws of droplet rebound height and compression value. Our main findings describe how the surface curvature radius influences droplet interactions, thus affecting the contact time, compression value and droplet deformation factor. The outcomes of droplet collisions on curved surfaces contribute to the development of technologies related to droplet manipulation and their applications in chemical and industrial processes.

Motion dynamics of two-dimensional fundamental and vortex solitons in the fractional medium with the cubic-quintic nonlinearity

Motion dynamics of two-dimensional fundamental and vortex solitons in the fractional medium with the cubic-quintic nonlinearity

Toward Building a Virtual Laboratory to Investigate Rainfall Microphysics at Process Scales

Abstract A 3D numerical model was built to serve as a virtual microphysics laboratory (VML) to investigate rainfall microphysical processes. One key goal for the VML is to elucidate the physical basis of warm precipitation processes toward improving existing parameterizations beyond the constraints of past physical experiments. This manuscript presents results from VML simulations of classical tower experiments of raindrop collisional collection and breakup. The simulations capture large raindrop oscillations in shape and velocity in both horizontal and vertical planes and reveal that drop instability increases with diameter due to the weakening of the surface tension compared with the body force. A detailed evaluation against reference experimental datasets of binary collisions over a wide range of drop sizes shows that the VML reproduces collision outcomes well including coalescence, and disk, sheet, and filament breakups. Furthermore, the VML simulations captured spontaneous breakup, and secondary coalescence and breakup. The breakup type, fragment number, and size distribution are analyzed in the context of collision kinetic energy, diameter ratio, and relative position, with a view to capture the dynamic evolution of the vertical microstructure of rainfall in models and to interpret remote sensing measurements. Significance Statement Presently, uncertainty in precipitation estimation and prediction remains one of the grand challenges in water cycle studies. This work presents a detailed 3D simulator to characterize the evolution of drop size distributions (DSDs), without the space and functional constraints of laboratory experiments. The virtual microphysics laboratory (VML) is applied to replicate classical tower experiments from which parameterizations of precipitation processes used presently in weather and climate models and remote sensing algorithms were derived. The results presented demonstrate that the VML is a robust tool to capture DSD dynamics at the scale of individual raindrops (precipitation microphysics). VML will be used to characterize DSD dynamics across scales for environmental conditions and weather regimes for which no measurements are available.

Interactions between fractional solitons in bimodal fiber cavities

AbstractWe introduce a system of fractional nonlinear Schrödinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber‐laser cavities with the effective fractional group‐velocity dispersion (FGVD), which were recently made available to the experiment. In the FNLSE system, the FGVD terms are represented by the Riesz derivative, with the respective Lévy index (LI). The FNLSEs, which include the self‐phase‐modulation (SPM) nonlinearity, are coupled by the cross‐phase‐modulation (XPM) terms, and separated by a group‐velocity (GV) mismatch (rapidity). By means of systematic simulations, we analyze collisions and bound states of solitons in the XPM‐coupled system, varying the LI and GV mismatch. Outcomes of collisions between the solitons include rebound, conversion of the colliding single‐component solitons into a pair of two‐component ones, merger of the solitons into a breather, their mutual passage leading to excitation of intrinsic vibrations, and the elastic interaction. Families of stable two‐component soliton bound states are constructed too, featuring a rapidity which is intermediate between those of the two components.

Binary collisions of drying maltodextrin droplets and glass beads

Spray drying is often used in combination with agglomeration to produce powders with good functional properties, yet the mechanistic understanding of this agglomeration is limited. This research is a fundamental study into the binary collision dynamics underlying agglomeration, identifying specific collision outcome regimes. A sessile single drying droplet was subjected to collisions with glass beads. For maltodextrins with a dextrose equivalent of 6, 21 and 38, collisions were performed at different time points in the drying process. A shift in the collision outcome was observed during drying. The transition from merging as sole collision outcome to a regime where also sticking and bouncing were observed was linked to the locking point of the drying droplet. The sticking regime was observed from 0.75 to 1.5 tcollision/tlock. This indicates that precise timing of the collisions between drying droplets and dry fines is needed to optimize the agglomeration within a spray dryer.

Dust-dust collisions in cometary comas: applications to comet 67P/Churyumov-Gerasimenko

Abstract Silica has emerged as a crucial component within inner comet comas. This work investigates silica dust aggregates and their interactions within cometary comas. We study the probability that aggregates in the size range 1-100 μm collide with each other in the coma and analyze the outcomes of such collisions by using the “Collision of Porous Aggregates” (CPA) Software, which incorporates mass, size, and porosity evolution of the dust population. Beginning with assumed initial distributions and physical properties for silica aggregates at the comet nucleus, we compute their collisional evolution from when they depart the nucleus until they traverse the coma. Using data of dust particles observed in the coma of comet 67P/Churyumov-Gerasimenko, we demonstrate that dust-dust collisions in cometary comas cannot be neglected. Our analysis yields final distributions in terms of mass, size, and porosity. To validate our findings, we compare them with in-situ measurements of 67P/Churyumov-Gerasimenko collected by the COSIMA (COmetary Secondary Ion Mass Analyser) instrument of the Rosetta mission. Our investigation reveals a notable agreement between our derived size distributions and the data acquired by COSIMA within the same size range. This study may be applied to any comet that presents a similar dust production as it approaches the Sun. The insights of this work may contribute to estimating other dust properties such as strength, absorption, reflectivity, and thermal conductivity and highlight the importance of considering dust-dust collisions when studying cometary comas and their evolution.

Numerical study of head-on collisions between two glass microsphere droplets

The collision of molten glass microsphere droplets represents a fundamental phenomenon in spheronization, yet a comprehensive understanding of this process remains elusive. A numerical simulation is conducted to investigate the head-on collision dynamics of two molten glass microsphere droplets at varying Weber numbers, by integrating the level set and volume of fluid methods. Three distinct collision regimes are identified: merging, separation into satellite-free droplets, and separation leading to the formation of satellite droplets. Furthermore, the critical Weber numbers delineating the different regimes are presented. Examination of axial and radial variations in the droplets reveals the existence of five distinct states spanning the three collision regimes. The distribution of external vortices around the droplets directly influences the outcomes of droplet collisions. High-pressure regions and high-pressure liquid bridges within droplets serve as key factors in determining the merging or separation of the droplets. Region of high pressure at the end of the liquid bridge acts as a critical indicator for distinguishing between collision separations with and without satellite droplet generation. Observations of velocity and pressure distributions in separations that produce satellite droplets are consistent with the end pinch-off mechanism. This study holds significant implications for controlling high sphericity during the spheronization of glass microsphere droplets.

Mathematical modeling of droplet collisions in sprays under microgravity conditions

Two-phase flows under microgravity conditions play a crucial role in Space technology and science. Studying the behavior of dispersed droplets suspended in a gas flow and their influence on the characteristics of the carrier flow is the main task of computational modeling of turbulent two-phase flows. To understand the features and predict the behavior of such flows, along with experimental studies, it is necessary to develop mathematical models, which adequately describe all the basic physical and chemical processes in a gas-droplet environment at different scales.In this paper we obtain solutions for the problem of two droplets collision, using solutions for cumulative jets, and propose droplet collision outcome criterion. This research will focus on the process of two interacting droplets coalescence into one and coalescence with subsequent separation into two or more droplets. A semi-analytical method has been developed for application of the solution of the cumulative jet problem to the problem of droplet collision. A differential equation has been obtained that describes the following possible outcomes of droplet collision: coalescence and coalescence with subsequent separation. A criterion for determining the outcome of on-head droplet collision has been obtained. In accordance with the developed criterion, the number and size of formed droplets are obtained. The effect of collision on moving droplet evaporation in a heated atmosphere was regarded.

Formation of super-Mercuries via giant impacts

ABSTRACT During the final stage of planetary formation, different formation pathways of planetary embryos could significantly influence the observed variations in planetary densities. Of the approximately 5000 exoplanets identified to date, a notable subset exhibits core fractions reminiscent of Mercury, potentially a consequence of high-velocity giant impacts. In order to better understand the influence of such collisions on planetary formation and compositional evolution, we conducted an extensive set of smoothed particle hydrodynamics giant impact simulations between two-layered rocky bodies. These simulations spanned a broad range of impact velocities from 1 to 11 times the mutual escape velocity. We derived novel scaling laws that estimate the mass and core mass fraction of the largest post-collision remnants. Our findings indicate that the extent of core vaporization markedly influences mantle stripping efficiency at low impact angles. We delineate the distinct roles played by two mechanisms – kinetic momentum transfer and vaporization-induced ejection – in mantle stripping. Our research suggests that collisional outcomes for multilayered planets are more complex than those for undifferentiated planetesimal impacts. Thus, a single universal law may not encompass all collision processes. We found a significant decrease in the mantle stripping efficiency as the impact angle increases. To form a 5 M⊕ super-Mercury at 45°, an impact velocity over 200 km s−1 is required. This poses a challenge to the formation of super-Mercuries through a single giant impact, implying that their formation would favour either relatively low-angle single impacts or multiple collisions.

Protoplanet collisions: New scaling laws from smooth particle hydrodynamics simulations

One common approach for solving collisions between protoplanets in simulations of planet formation is to employ analytical scaling laws. The most widely used one was developed by Leinhardt2012 from a catalog of sim 180 N-body simulations of rubble--pile collisions. In this work, we use a new catalogue of more than 20,000 SPH simulations to test the validity and the prediction capability of Leinhardt2012 scaling laws. We find that these laws overestimate the fragmentation efficiency in the merging regime and they are not able to properly reproduce the collision outcomes in the super--catastrophic regime. In the merging regime, we also notice a significant dependence between the collision outcome, in terms of the largest remnant mass, and the relative mass of the colliding protoplanets. Here, we present a new set of scaling laws that are able to better predict the collision outcome in all regimes and it is also able to reproduce the observed dependence on the mass ratio. We compare our new scaling laws against a machine learning approach and obtain similar prediction efficiency.

Abundant sub-micron grains revealed in newly discovered extreme debris discs

ABSTRACT Extreme debris discs (EDDs) are bright and warm circumstellar dusty structures around main sequence stars. They may represent the outcome of giant collisions occuring in the terrestrial region between large planetesimals or planetary bodies, and thus provide a rare opportunity to peer into the aftermaths of these events. Here, we report on results of a mini-survey we conducted with the aim to increase the number of known EDDs, investigate the presence of solid-state features around 10 μm in eight EDDs, and classify them into the silica or silicate dominated groups. We identify four new EDDs and derive their fundamental properties. For these, and for four other previously known discs, we study the spectral energy distribution around 10 μm by means of VLT/VISIR photometry in three narrow-band filters and conclude that all eight objects likely exhibit solid-state emission features from sub-micron grains. We find that four discs probably belong to the silicate dominated subgroup. Considering the age distribution of the entire EDD sample, we find that their incidence begins to decrease only after 300 Myr, suggesting that the earlier common picture that these objects are related to the formation of rocky planets may not be exclusive, and that other processes may be involved for older objects (≳100 Myr). Because most of the older EDD systems have wide, eccentric companions, we suggest that binarity may play a role in triggering late giant collisions.

Binary collision dynamics of equal-sized nanodroplets

Binary nanodroplet collisions have received increasing attention, whilst the identification of collision outcomes and the viscous dissipation mechanism have remained poorly understood. Using molecular dynamics simulations, this study investigates binary nanodroplet collisions over wide ranges of Weber number (We), Ohnesorge number (Oh) and off-centre distances. Coalescence, stretching separation and shattering are identified; however, bouncing, reflexive separation and rotational separation reported for millimetre-sized collisions are not observed, which is attributed to the enhanced viscous effect caused by the ‘natural’ high-viscosity characteristics of nanodroplets. Intriguingly, as an intermediate outcome, holes form in retracting films at relatively high We, arising from the vibration and thermal fluctuation of the films. Due to the combined effects of inertial, capillary and viscous forces, binary nanodroplet collisions fall into the cross-over regime, so estimating viscous dissipation becomes extremely important for distinguishing outcome boundaries. Based on the criterion that stretching separation is triggered only when the residual off-centre kinetic energy exceeds the surface energy required for separation, the boundary equation between coalescence and stretching separation is established. Here, viscous dissipation is calculated by the extracted flow feature from simulations, showing that the ratio of viscous dissipation to the initial kinetic energy depends only on Oh, not on We. Because of complex viscous dissipation mechanisms, the same boundary equation in the cross-over regime has also not been satisfactorily revealed for macroscale collisions. Therefore, the proposed equation is tested for wide data sources from both macroscale and nanoscale collisions, and satisfying agreement is achieved, demonstrating the universality of the equation.

Collision of two drops moving in the same direction

The collision dynamics of two drops of the same liquid moving in the same direction has been studied numerically. A wide range of radius ratios of trailing drop and leading drop (Rr) and the velocity ratios (Ur) have been deployed to understand the collision outcomes. A volume of fluid based open-source fluid flow solver, Basilisk, has been used with its adaptive mesh refinement feature to capture the nuances of the interface morphology. The simulations are analyzed for the evolving time instances. Different collision outcomes, such as coalescence and reflexive separation with and without the formation of satellite drops, have been observed for various combinations of Ur and Rr. The study analyzes the evolution of kinetic energy and surface energy before and after the collision for plausible outcomes. The collision outcomes are depicted on a regime map with Ur−Rr space, highlighting distinct regimes formed due to variations in relevant governing parameters.