Merging Clusters Research Articles

Jet Interaction with Galaxy Cluster Mergers

Active galactic nucleus (AGN) bubbles in cool-core galaxy clusters are believed to facilitate the transport of cosmic-ray electrons (CRe) throughout the cluster. Recent radio observations reveal the complex morphologies of cluster diffuse emission, potentially linked to interactions between AGN bursts and the cluster environment. We perform 3D magnetohydrodynamical simulations of binary cluster mergers and inject a bidirectional jet at the center of the main cluster. Kinetic, thermal, magnetic, and cosmic ray (CR) energy are included in the jet and we use the two-fluid formalism to model the CR component. We explore a wide range of cluster merger and jet parameters. We discuss the formation of various wide-angle-tail and X-shaped sources in the early evolution of the jet and merger. During the last phase of the evolution, we find that the CR material efficiently permeates the central region of the cluster reaching radii of ∼1–2 Mpc within ∼5–6 Gyr, depending on the merger mass ratio. We find that solenoidal turbulence dominates during the binary merger and we explore the possibility for the CR jet material to be reaccelerated by super-Alfvènic turbulence and contribute to cluster scale radio emission. We find high volume fractions, ≳70%, at which the turbulent acceleration time is shorter than the electron cooling time. Finally, we study the merger shock interaction with the CRe material and show that it is unlikely that this material significantly contributes to the radio relic emission associated with the shocks. We suggest that multiple jet outbursts and/or off-center radio galaxies would increase the likelihood of detecting these merger shocks in the radio due to shock reacceleration.

Evolution of strengthening precipitates in Al-4.0Zn-1.8Mg-1.2Cu (at.%) alloy with high Zn/Mg ratio during artificial aging

Evolution of strengthening precipitates, including their types, sizes, volume fraction, and chemical compositions in Al-4.0Zn-1.8Mg-1.2Cu (at.%) alloy during artificial aging, were investigated using anomalous small-angle X-ray scattering (ASAXS), three-dimensional atom probe techniques (APT), high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and density functional theory (DFT) calculation. Upon aging, Cu-containing clusters merge with adjacent clusters to form larger clusters, which then act as nucleation sites for GPη' zones. As aging proceeds, GPη' zones grow up to η'I metastable phase with seven atomic layers on {111}Al planes, and this process is controlled by diffusion of Mg atoms. Cu atoms have a low diffusion rate and do not participate into the growth of precipitates within the first 60mins of aging. As aging time increases, Cu atoms enter the η'I metastable phase, leading to a significant increase in Cu content and (Zn+Cu)/Mg ratio; η'I metastable phase grow, and after exceeding about 7nm, gradually transform into the η'II metastable phase with ten atomic layers by adding three new atomic layers at one side. GPη' zones, η'I metastable phase and η'II metastable phase have symmetric interface structures. The precipitation sequence during aging to peak state can be summarized as: atomic clusters → GPη' zones → η'I metastable phase → η'II metastable phase.

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Are all models wrong? Falsifying binary formation models in gravitational-wave astronomy using exceptional events

Abstract As the catalogue of gravitational-wave transients grows, several entries appear ‘exceptional’ within the population. Tipping the scales with a total mass of ∼150M⊙, GW190521 likely contained black holes in the pair-instability mass gap. The event GW190814, meanwhile, is unusual for its extreme mass ratio and the mass of its secondary component. A growing model-building industry has emerged to provide explanations for such exceptional events, and Bayesian model selection is frequently used to determine the most informative model. However, Bayesian methods can only take us so far. They provide no answer to the question: does our model provide an adequate explanation for exceptional events in the data? If none of the models we are testing provide an adequate explanation, then it is not enough to simply rank our existing models—we need new ones. In this paper, we introduce a method to answer this question with a frequentist p-value. We apply the method to different models that have been suggested to explain the unusually massive event GW190521: hierarchical mergers in active galactic nuclei and globular clusters. We show that some (but not all) of these models provide adequate explanations for exceptionally massive events like GW190521.

A Multifrequency View of the Radio Phoenix in the A85 Cluster

Radio phoenices are complex and filamentary diffuse radio sources found in both merging and relaxed clusters. The formation of these sources has been proposed to be due to adiabatic compression of old active galactic nucleus plasma in shock waves. Most of the previous spectral studies of these sources have been limited to integrated spectral indices, which were found to be very steep and show a curved spectrum. Here, we have performed a multifrequency investigation of the radio phoenix in the A85 cluster. Owing to the sensitive high-resolution observations, we found some of the finer filamentary structures that had been previously undetected. We produced resolved spectral index maps of the radio phoenix between 323, 700, and 1280 MHz. The orientation of the filaments, as well as the gradient across the spectral index maps, suggest the possible direction of the shock motion from northeast to southwest. The integrated spectrum of the radio phoenix was found to be very steep and curved toward high frequencies. Furthermore, the spectral index of the filaments was found to be less steep compared to the nonfilamentary regions, implying greater energy injection in the filaments. The observed features in the radio phoenix in the A85 cluster seem to be in support of an adiabatic shock compression mechanism.

Magnetic fields in the outskirts of PSZ2 G096.88+24.18 from a depolarization analysis of radio relics

Context. Radio relics are diffuse, non-thermal radio sources present in a number of merging galaxy clusters. They are characterized by elongated arc-like shapes and highly polarized emission (up to ∼60%) at gigahertz frequencies, and are expected to trace shock waves in the cluster outskirts induced by galaxy cluster mergers. Their polarized emission can be used to study the magnetic field properties of the host cluster. Aims. In this paper, we investigate the polarization properties of the double radio relics in PSZ2 G096.88+24.18 using the rotation measure (RM) synthesis, and try to constrain the characteristics of the magnetic field that reproduce the observed depolarization as a function of resolution (beam depolarization). Our aim is to understand the nature of the low polarization fraction that characterizes the southern relic with respect to the northern relic. Methods. We present new 1–2 GHz Karl G. Jansky Very Large Array (VLA) observations in multiple configurations. We derived the RM and polarization of the two relics by applying the RM synthesis technique, and thus solved for bandwidth depolarization in the wide observing bandwidth. To study the effect of beam depolarization, we degraded the image resolution and studied the decreasing trend of polarization fraction with increasing beam size. Finally, we performed 3D magnetic field simulations using multiple models for the magnetic field power spectrum over a wide range of scales, in order to constrain the characteristics of the cluster magnetic field that can reproduce the observed beam depolarization trend. Results. Using RM synthesis, we obtained a polarization fraction of (18.6 ± 0.3)% for the northern relic and (14.6 ± 0.1)% for the southern one. Having corrected for bandwidth depolarization, and after noticing the absence of relevant complex Faraday spectrum, we inferred that the nature of the depolarization for the southern relic is external, and possibly related to the turbulent gas distribution within the cluster, or to the complex spatial structure of the relic. The best-fit magnetic field power spectrum, which reproduces the observed depolarization trend for the southern relic, was obtained for a turbulent magnetic field model, described by a power spectrum derived from cosmological simulations, and defined within the scales of Λmin = 35 kpc and Λmax = 400 kpc. This yields an average magnetic field of the cluster within 1 Mpc3 volume of ∼2 μG.

Dexterous Manipulation Based on Object Recognition and Accurate Pose Estimation Using RGB-D Data.

This study presents an integrated system for object recognition, six-degrees-of-freedom pose estimation, and dexterous manipulation using a JACO robotic arm with an Intel RealSense D435 camera. This system is designed to automate the manipulation of industrial valves by capturing point clouds (PCs) from multiple perspectives to improve the accuracy of pose estimation. The object recognition module includes scene segmentation, geometric primitives recognition, model recognition, and a color-based clustering and integration approach enhanced by a dynamic cluster merging algorithm. Pose estimation is achieved using the random sample consensus algorithm, which predicts position and orientation. The system was tested within a 60° field of view, which extended in all directions in front of the object. The experimental results show that the system performs reliably within acceptable error thresholds for both position and orientation when the objects are within a ±15° range of the camera's direct view. However, errors increased with more extreme object orientations and distances, particularly when estimating the orientation of ball valves. A zone-based dexterous manipulation strategy was developed to overcome these challenges, where the system adjusts the camera position for optimal conditions. This approach mitigates larger errors in difficult scenarios, enhancing overall system reliability. The key contributions of this research include a novel method for improving object recognition and pose estimation, a technique for increasing the accuracy of pose estimation, and the development of a robot motion model for dexterous manipulation in industrial settings.

Batch effects correction in scRNA-seq based on biological-noise decoupling autoencoder and central-cross loss

Technical or biologically irrelevant differences caused by different experiments, times, or sequencing platforms can generate batch effects that mask the true biological information. Therefore, batch effects are typically removed when analyzing single-cell RNA sequencing (scRNA-seq) datasets for downstream tasks. Existing batch correction methods usually mitigate batch effects by reducing the data from different batches to a lower dimensional space before clustering, potentially leading to the loss of rare cell types. To address this problem, we introduce a novel single-cell data batch effect correction model using Biological-noise Decoupling Autoencoder (BDA) and Central-cross Loss termed BDACL. The model initially reconstructs raw data using an auto-encoder and conducts preliminary clustering. We then construct a similarity matrix and a hierarchical clustering tree to delineate relationships within and between different batches. Finally, we introduce a Central-cross Loss (CL). This loss leverages cross-entropy loss to prompt the model to better distinguish between different cluster labels. Additionally, it employs the Central Loss to encourage samples to form more compact clusters in the embedding space, thereby enhancing the consistency and interpretability of clustering results to mitigate differences between different batches. The primary innovation of this model lies in reconstructing data with an auto-encoder and gradually merging smaller clusters into larger ones using a hierarchical clustering tree. By using reallocated cluster labels as training labels and employing the Central-cross Loss, the model effectively eliminates batch effects in an unsupervised manner. Compared to current methods, BDACL can mitigate batch effects without losing rare cell types.

Decoding the Early Universe: Exploring a Merger Scenario for the High-Redshift Cluster JKCS041 using Numerical Models

Abstract JKCS041 (z = 1.8) is one of the most distant galaxy cluster systems known, seen when the Universe was less than 4 billion years old. Recent Sunyaev-Zeldovich (SZ) observations show a temperature decrement that is less than expected based on mass estimates of the system from X-ray, weak gravitational lensing and galaxy richness measurements. In this paper we seek to explain the observables - in particular the low SZ decrement and single SZ peak, the projected offset between the X-ray and SZ peaks of ≈220 kpc, the gas mass measurements and the lensing mass estimate. We use the GAMER-2 hydrodynamic code to carry out idealized numerical simulations of cluster mergers and compare resulting synthetic maps with the observational data. Generically a merger process is necessary to reproduce the observed offset between the SZ and X-ray peaks. From our exploration of parameter space, seen a few tenths of a Gyr after first core passage, two components with total mass of ≈2 × 1014M⊙, mass ratio of ≈2:3, gas fraction of 0.05 − 0.1 and Navarro, Frenk and White (NFW) mass density profile concentrations c≈5 are scenarios that are consistent with the observational data. For consistency with the SZ and X-ray measurements, our simulations exclude total mass in excess of ≈3 × 1014M⊙, primarily based on the SZ signal. The mass ratio is constrained by the SZ-X-ray offset and magnitude of the SZ signal, ruling out systems with equal and vastly different masses.

The prototypical major cluster merger Abell 754

Context. Abell 754 is a rich galaxy cluster at z = 0.0543 and is considered the prototype of a major cluster merger. As many dynamically unrelaxed systems, it hosts diffuse radio emission on megaparsec-scales. Extended synchrotron sources in the intra-cluster medium (ICM) are commonly interpreted as evidence that a fraction of the gravitational energy released during cluster mergers is dissipated into nonthermal components. Aims. Here, we aim to use new MeerKAT UHF- and L-band observations to study nonthermal phenomena in Abell 754. These data are complemented with archival XMM-Newton observations to investigate the resolved spectral properties of both the radio and X-ray cluster emission. Methods. For the first time, we employed the pipeline originally developed to calibrate LOFAR data to MeerKAT observations. This allowed us to perform a direction-dependent calibration and obtain highly sensitive radio images in UHF and L bands that capture the extended emission with unprecedented detail. By using a large XMM-Newton mosaic, we produced thermodynamic maps of the ICM. Results. Our analysis reveals that the radio halo in the cluster center is bounded by the well-known shock in the eastern direction. Furthermore, in the southwest periphery, we discover an extended radio source that we classify as a radio relic that is possibly tracing a shock driven by the squeezed gas compressed by the merger, outflowing in perpendicular directions. The low-luminosity of this relic appears compatible with direct acceleration of thermal pool electrons. We interpret the observed radio and X-ray features in the context of a major cluster merger with a nonzero impact parameter. Conclusions. Abell 754 is a remarkable galaxy cluster showcasing exceptional features associated with the ongoing merger event. The high quality of the new MeerKAT data motivates further work on this system.

Supermassive black hole formation via collisions in black hole clusters

More than 300 supermassive black holes have been detected at redshifts larger than six, and they are abundant in the centers of local galaxies. Their formation mechanisms, however, are still rather unconstrained. A possible origin of these supermassive black holes could be mergers in dense black hole clusters, forming as a result of mass segregation within nuclear star clusters at the center of galaxies. In this study, we present the first systematic investigation of the evolution of such black hole clusters in which the effect of an external potential is taken into account. Such a potential could be the result of gas inflows into the central region; for example, as a result of galaxy mergers. We show here that the efficiency of the formation of a massive central object is mostly regulated by the ratio of cluster velocity dispersion divided by the speed of light, potentially reaching efficiencies of 0.05–0.08 in realistic systems. Our results show that this scenario is potentially feasible and may provide black hole seeds of at least 103 M⊙. We conclude that the formation of seed black holes via this channel should be taken into account in statistical assessments of the black hole population.

Constructing a Galaxy Cluster Catalog in IllustrisTNG300 Using the Mulguisin Algorithm

We present a new simulated galaxy cluster catalog based on the IllustrisTNG simulation. We use the Mulguisin (MGS) algorithm to identify galaxy overdensities. Our cluster identification differs from the previous friends-of-friends (FoF) cluster identification in two aspects: (1) we identify cluster halos based on the galaxy subhalos instead of unobservable dark matter particles, and (2) we use the MGS algorithm, which separates galaxy overdensities hosted by massive galaxies. Our approach provides a cluster catalog constructed in a way similar to the construction of observed cluster catalogs using spectroscopic surveys. The MGS cluster catalog lists 303 halos with M 200 > 1014 M ⊙, including ∼10% more than the FoF catalog. The MGS catalog includes more systems because we separate some independent massive MGS cluster halos that are bundled into a single FoF halo. These independent MGS halos are apparently distinguishable in the galaxy spatial distribution and the phase-space diagram. Because we construct a refined cluster catalog that identifies local galaxy overdensities, we evaluate the effect of MGS clusters on the evolution of galaxies better than when using the FoF cluster catalog. The MGS halo identification also enables effective identifications of merging clusters by selecting systems with neighboring galaxy overdensities. We thus highlight the fact that the MGS cluster catalog is a useful tool for studying clusters in cosmological simulations and for comparing with observed cluster samples.

Study on the Driver Visual Workload in High-Density Interchange-Merging Areas Based on a Field Driving Test.

A visual workload model was constructed to determine and evaluate drivers' visual workload characteristics in high-density interchange-merging areas. Five interchanges were selected, and a real-vehicle driving test was conducted with 47 participants. To address the differences in drivers' visual characteristics in the interchange cluster merging areas, the Criteria Importance Through Intercriteria Correlation (CRITIC) objective weighting method was employed. Six visual parameters were selected to establish a comprehensive evaluation model for the visual workload in high-density interchange-merging areas. The results show that the average scanning frequency and average pupil area change rate are most strongly correlated with the visual workload, whereas the average duration of a single gaze has the lowest weight in the visual workload assessment system. Different driver visual workloads were observed depending on the environment of the interchange-merging areas, and based on these, recommendations are proposed to decrease drivers' workload, thereby increasing road safety.

Study on heat and mass transfer behavior of coupled electrochemical reaction in porous structure of proton exchange membrane fuel cell

Proton exchange membrane fuel cell (PEMFC) is widely used in transportation, aviation and energy storage due to its unique advantages. Improving the performance of fuel cells depends largely on effective hydrothermal management. In this work, a multi-physical field coupling model based on the lattice Boltzmann method (LBM) is established to analyze the oxygen transport, liquid water transport, heat transfer and electrochemical reaction, mainly considering the difference between the overpotential of the cell and the surface wettability of the structure. The results show that the overpotential is closely related to the reaction process. The rate of water production is significantly accelerated by increasing the overpotential, and the breakage and merging of water clusters are observed. The increase of overpotential will lead to more energy loss in the form of heat, thus increasing the heat production. Enhancing the hydrophobicity of the structure has a positive effect on the performance of the fuel cell, and the possibility of local hot spots in the low-hydrophobic structure is greater. It is feasible to improve water management and fuel cell performance through wettability design.

Effect of grain boundaries on the helium degradation mechanisms of alloy 800H: A molecular dynamics study

Alloy 800H is currently used as structural material in light-water cooled nuclear reactors, and it is also considered as candidate materials for various advanced reactor designs. Under operation, the exposure of alloy 800H to neutron irradiation results in the formation of helium (He), mainly from Ni by the transmutation reaction (n, α). In this work, we present a molecular dynamics (MD) simulation study of the behavior and effects of He on the microstructure and mechanical properties of alloy 800H. Our results show that the population of clusters made of 5 to 9 He atoms is nearly constant throughout the simulation time (10 ns), while the population of larger clusters increases as the simulation time increases. The growth of clusters is controlled by either the dissociation and diffusion of smaller clusters towards nearby larger clusters or the merging of larger clusters initially located nearby to each other. A significant accumulation of He is observed at the grain boundaries (GB), while a depletion zone is found at the neighboring regions. As a result, the density of He cluster is significantly higher at the GBs as compared to the intra-granular regions. The nucleation and growth of He clusters also results in the formation of Frenkel pairs (FP), whose associated self-interstitial atoms (SIA) agglomerate into interstitial clusters in the alloy 800H matrix. As a consequence, dislocation segments, mostly of the Shockley type, are generated in the microstructure, and often located next to He clusters. The combination of the aforementioned defect structures and the high density of He clusters at the GBs results in a substantial degradation of the mechanical properties of alloy 800H single crystal and bicrystals.

Iterative site percolation on triangular lattice

The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation cluster, we obtain coarse-grained configurations by merging adjacent clusters that share the same color. It is shown that the process can be infinitely iterated in the infinite-lattice limit, leading to an iterative site percolation model. We conjecture from the self-matching argument that percolation clusters remain fractal for any finite generation, which can even take any positive real number by a generalized process. Extensive simulations are performed, and, from the generation-dependent fractal dimension, a continuous family of previously unknown universalities is revealed. Published by the American Physical Society 2024

Integrating supervised and unsupervised learning approaches to unveil critical process inputs

This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims to (i) discern critical parameters that influence the output and (ii) generate accurate out-of-sample qualitative and quantitative predictions of production outcomes. Specifically, we address the pivotal question of the significance of each input in shaping the process outcome, using an industrial Chemical Vapor Deposition (CVD) process as an example. The initial objective involves merging subject matter expertise and clustering techniques exclusively on the process output, here, coating thickness measurements at various positions in the reactor. This approach identifies groups of production runs that share similar qualitative characteristics, such as film mean thickness and standard deviation. In particular, the differences of the outcomes represented by the different clusters can be attributed to differences in specific inputs, indicating that these inputs are potentially critical to the production outcome. Shapley value analysis corroborates the formed hypotheses. Leveraging this insight, we subsequently implement supervised classification and regression methods using the identified critical process inputs. The proposed methodology proves to be valuable in scenarios with a multitude of inputs and insufficient data for the direct application of deep learning techniques, providing meaningful insights into the underlying processes.

Spatial segregation of massive clusters in a simulation of colliding dwarf galaxies

The collective properties of star clusters are investigated using a simulation of the collision between two dwarf galaxies. The characteristic power law of the cluster mass function, N(M), with a logarithmic slope dN/dM ~ -1, is present from cluster birth and remains throughout the simulation. The maximum mass of a young cluster scales with the star formation rate (SFR). The relative average minimum separation, R(M)= N(M)^{1/p}D_min(M)/D(M_low), for average minimum distance D_min(M) between clusters of mass M, and for lowest mass, M_low, measured in projection (p=2) or three dimensions (p=3), has a negative slope, d log R/d log M ~ -0.2, for all masses and ages. This agrees with observations of R(M) in low-mass galaxies studied previously. Like the slope of N(M), R(M) is apparently a property of cluster birth for dwarf galaxies that does not depend on SFR or time. The negative slope for R(M) implies that massive clusters are more concentrated relative to lower mass clusters throughout the entire mass range. Cluster growth through coalescence is also investigated. The ratio of the kinetic to potential energy of all near-neighbor clusters is generally large, but a tail of low values in the distribution of this ratio suggests that a fraction of the clusters merge, ~8% by number throughout the ~300 Myr of the simulation and up to 60% by mass for young clusters in their first 10 Myr, scaling with the SFR above a certain threshold.

Streamlining NMR Chemical Shift Predictions for Intrinsically Disordered Proteins: Design of Ensembles with Dimensionality Reduction and Clustering.

By merging advanced dimensionality reduction (DR) and clustering algorithm (CA) techniques, our study advances the sampling procedure for predicting NMR chemical shifts (CS) in intrinsically disordered proteins (IDPs), making a significant leap forward in the field of protein analysis/modeling. We enhance NMR CS sampling by generating clustered ensembles that accurately reflect the different properties and phenomena encapsulated by the IDP trajectories. This investigation critically assessed different rapid CS predictors, both neural network (e.g., Sparta+ and ShiftX2) and database-driven (ProCS-15), and highlighted the need for more advanced quantum calculations and the subsequent need for more tractable-sized conformational ensembles. Although neural network CS predictors outperformed ProCS-15 for all atoms, all tools showed poor agreement with HN CSs, and the neural network CS predictors were unable to capture the influence of phosphorylated residues, highly relevant for IDPs. This study also addressed the limitations of using direct clustering with collective variables, such as the widespread implementation of the GROMOS algorithm. Clustered ensembles (CEs) produced by this algorithm showed poor performance with chemical shifts compared to sequential ensembles (SEs) of similar size. Instead, we implement a multiscale DR and CA approach and explore the challenges and limitations of applying these algorithms to obtain more robust and tractable CEs. The novel feature of this investigation is the use of solvent-accessible surface area (SASA) as one of the fingerprints for DR alongside previously investigated α carbon distance/angles or ϕ/ψ dihedral angles. The ensembles produced with SASA tSNE DR produced CEs better aligned with the experimental CS of between 0.17 and 0.36 r2 (0.18-0.26 ppm) depending on the system and replicate. Furthermore, this technique produced CEs with better agreement than traditional SEs in 85.7% of all ensemble sizes. This study investigates the quality of ensembles produced based on different input features, comparing latent spaces produced by linear vs nonlinear DR techniques and a novel integrated silhouette score scanning protocol for tSNE DR.

Catalytic coagulation.

We introduce an autocatalytic aggregation model in which the rate at which two clusters merge is controlled by the third "catalytic" cluster, whose mass must equal the mass of one of the reaction partners. The catalyst is unaffected by the joining event and can participate in or catalyze subsequent reactions. This model is meant to mimic the self-replicating reactions that occur in models for the origin of life. We solve the kinetics of catalytic coagulation for the case of mass-independent reaction rates and show that the total cluster density decays as t^{-1/3}, while the density of clusters of fixed mass decays as t^{-2/3}. These behaviors contrast with the corresponding t^{-1} and t^{-2} scalings for classic aggregation. We extend our model to mass-dependent reaction rates, to situations where only "magic" mass clusters can catalyze reactions, and to include steady monomer input.