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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

ezAlign

The ezAlign is aimed at clustering coarse grain simulation to find common or uncommon occurrences and convert coarse (CG) grained coordinate and topology files to atomistic formats. We use a PointNet based approach to map individual frames of simulation to points in a latent space. These points are then clustered using a variety of clustering methods. Clusters are analyzed to associate them with states in the simulation. Frames can be chosen from these clusters based on proximity to cluster centers. ezAlign takes CG coordinate and topology files and converts and outputs their corresponding atomistic formats using an alignment and relaxation procedure. ezAlign is designed to convert complex, solvated biological systems including lipid membranes with drug-like molecules using GROMACS. A GROMACS checkpoint (.cpt) file is also outputted to enable continuation simulations that retain the equilibrated atomic velocities. Independent atomistic coordinates and topologies for every molecule must already be included in ezAlign/files. A number of commonly simulated biological molecules are currently provided.

Bennett, WilliamF.↗
DOE OSTI2021

A multi-step nucleation process determines the kinetics of prion-like domain phase separation

Compartmentalization by liquid-liquid phase separation (LLPS) has emerged as a ubiquitous mechanism underlying the organization of biomolecules in space and time. Here, we combine rapid-mixing time-resolved small-angle X-ray scattering (SAXS) approaches to characterize the assembly kinetics of a prototypical prion-like domain with equilibrium techniques that characterize its phase boundaries and the size distribution of clusters prior to phase separation. We find two kinetic regimes on the micro- to millisecond timescale that are distinguished by the size distribution of clusters. At the nanoscale, small complexes are formed with low affinity. After initial unfavorable complex assembly, additional monomers are added with higher affinity. At the mesoscale, assembly resembles classical homogeneous nucleation. Careful multi-pronged characterization is required for the understanding of condensate assembly mechanisms and will promote understanding of how the kinetics of biological phase separation is encoded in biomolecules.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Coupled-cluster theory for strong entanglement in nuclei

Atomic nuclei can exhibit shape coexistence and multireference physics that enters in their ground states, and accurately capturing the ensuing correlations and entanglement is challenging. Here, we address this problem by applying single-reference coupled-cluster theory based on spherical and deformed reference states and the tailored coupled-cluster method. The latter combines configuration interactions to capture static correlations with coupled-cluster theory for dynamic correlations. We compute the atomic nuclei 12 C, 28 Si, and 56 Ni and find that the tailored coupled-cluster method and the single-reference approach based on a deformed Hartree-Fock state yield the most accurate results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Data-Driven Performance Optimization of Gamma Spectrometers With Many Channels

In gamma spectrometers with variable spectroscopic performance across many channels (e.g., many pixels or voxels), a tradeoff exists between including data from successively worse-performing readout channels and increasing efficiency. Brute-force calculation of the optimal set of included channels is exponentially infeasible as the number of channels grows, and approximate methods are required. In this work, we present a data-driven framework for attempting to find near-optimal sets of included detector channels. The framework leverages non-negative matrix factorization (NMF) to learn the behavior of gamma spectra across the detector and clusters similarly-performing detector channels together. Performance comparisons are then made between spectra with channel clusters removed, which is more feasible than brute force. The framework is general and can be applied to arbitrary, user-defined performance metrics depending on the application. We apply this framework to optimizing gamma spectra measured by H3D M400 CdZnTe (CZT) spectrometers, which exhibit variable performance across their crystal volumes. In particular, we show several examples optimizing various performance metrics for uranium and plutonium gamma spectra in non-destructive assay (NDA) for nuclear safeguards, and explore trends in performance versus parameters such as clustering algorithm type. We also compare the NMF + clustering pipeline to several non-machine-learning (ML) algorithms, including several greedy algorithms. Although, we find that the NMF + clustering pipeline tends to find the best-performing set of detector voxels, significantly improving over the unoptimized spectra, but that a greedy accumulation of spectra segmented by detector depth can, in some cases, give similar performance improvements in much less computation time.

Energy resolution↗
DOE OSTI2022

The DESI N -body simulation project – I. Testing the robustness of simulations for the DESI dark time survey

ABSTRACT Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N-body simulation codes, abacus, gadget-2, and swift, to investigate the regimes in which their results agree. We run N-body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109 h−1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for $s\ \gt\ 20\ h^{-1}$ Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109 h−1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20\ h^{-1}$ Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10 h Mpc−1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-N-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy–halo relation will be presented in a follow-up study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Shocks in the stacked Sunyaev-Zel’dovich profiles of clusters II: Measurements from SPT-SZ + Planck Compton- y map

ABSTRACT We search for the signature of cosmological shocks in stacked gas pressure profiles of galaxy clusters using data from the South Pole Telescope (SPT). Specifically, we stack the latest Compton-y maps from the 2500 deg2 SPT-SZ survey on the locations of clusters identified in that same data set. The sample contains 516 clusters with mean mass $\langle M_{\rm 200m}\rangle = 10^{14.9} \, {\rm M}_\odot$ and redshift 〈z〉 = 0.55. We analyse in parallel a set of zoom-in hydrodynamical simulations from the three hundred project. The SPT-SZ data show two features: (i) a pressure deficit at R/R200m = 1.08 ± 0.09, measured at 3.1σ significance and not observed in the simulations, and; (ii) a sharp decrease in pressure at R/R200m = 4.58 ± 1.24 at 2.0σ significance. The pressure deficit is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions, and the second feature is consistent with accretion shocks seen in previous studies. We split the cluster sample by redshift and mass, and find both features exist in all cases. There are also no significant differences in features along and across the cluster major axis, whose orientation roughly points towards filamentary structure. As a consistency test, we also analyse clusters from the Planck and Atacama Cosmology Telescope Polarimeter surveys and find quantitatively similar features in the pressure profiles. Finally, we compare the accretion shock radius ($R_{\rm sh,\, acc}$) with existing measurements of the splashback radius (Rsp) for SPT-SZ and constrain the lower limit of the ratio, $R_{\rm sh,\, acc}/R_{\rm sp}\gt 2.16 \pm 0.59$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Improving gas adsorption modeling for MOFs by local calibration of Hubbard U parameters

While computational screening with density functional theory (DFT) is frequently employed for the screening of metal–organic frameworks (MOFs) for gas separation and storage, commonly applied generalized gradient approximations (GGAs) exhibit self-interaction errors, which hinder the predictions of adsorption energies. We investigate the Hubbard U parameter to augment DFT calculations for full periodic MOFs, targeting a more precise modeling of gas molecule–MOF interactions, specifically for N2, CO2, and O2. We introduce a calibration scheme for the U parameter, which is tailored for each MOF, by leveraging higher-level calculations on the secondary building unit (SBU) of the MOF. When applied to the full periodic MOF, the U parameter calibrated against hybrid HSE06 calculations of SBUs successfully reproduces hybrid-quality calculations of the adsorption energy of the periodic MOF. The mean absolute deviation of adsorption energies reduces from 0.13 eV for a standard GGA treatment to 0.06 eV with the calibrated U, demonstrating the utility of the calibration procedure when applied to the full MOF structure. Furthermore, attempting to use coupled cluster singles and doubles with perturbative triples calculations of isolated SBUs for this calibration procedure shows varying degrees of success in predicting the experimental heat of adsorption. It improves accuracy for N2 adsorption for cases of overbinding, whereas its impact on CO2 is minimal, and ambiguities in spin state assignment hinder consistent improvements of O2 adsorption. Our findings emphasize the limitations of cluster models and advocate the use of full periodic MOF systems with a calibrated U parameter, providing a more comprehensive understanding of gas adsorption in MOFs.

Chemistry↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration

This work, together with its companion paper, Secco, Samuroff et al., presents the Dark Energy Survey Year 3 cosmic shear measurements and cosmological constraints based on an analysis of over 100 million source galaxies. With the data spanning 4143 deg 2 on the sky, divided into four redshift bins, we produce the highest significance measurement of cosmic shear to date, with a signal-to-noise of 40. We conduct a blind analysis in the context of the ΛCDM model and find a 3% constraint of the clustering amplitude, S 8 ≡ σ 8 (Ω m /0.3) 0.5 = 0.759$^{+0.025}_{-0.023}$. A ΛCDM-Optimized analysis, which safely includes smaller scale information, yields a 2% precision measurement of S 8 = 0.772$^{+0.018}_{-0.017}$ that is consistent with the fiducial case. The two low-redshift measurements are statistically consistent with the Planck Cosmic Microwave Background result, however, both recovered S 8 values are lower than the high-redshift prediction by 2.3σ and 2.1σ (ρ-values of 0.02 and 0.05), respectively. The measurements are shown to be internally consistent across redshift bins, angular scales and correlation functions. The analysis is demonstrated to be robust to calibration systematics, with the S 8 posterior consistent when varying the choice of redshift calibration sample, the modeling of redshift uncertainty and methodology. Similarly, we find that the corrections included to account for the blending of galaxies shifts our best-fit S 8 by 0.5σ without incurring a substantial increase in uncertainty. We examine the limiting factors for the precision of the cosmological constraints and find observational systematics to be subdominant to the modeling of astrophysics. Specifically, we identify the uncertainties in modeling baryonic effects and intrinsic alignments as the limiting systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Connecting galaxy evolution in clusters with their radial profiles and phase space distribution: results from the IllustrisTNG hydrodynamical simulations

ABSTRACT We study the population of galaxies around galaxy clusters in the hydrodynamic simulation suite IllustrisTNG 300-1 to study the signatures of their evolutionary history on observable properties. We measure the radial number density profile, phase space distribution, and splashback radius for galaxies of different masses and colours over the redshift range z = 0−1. The three primary physical effects which shape the galaxy distribution within clusters are the galaxy quenching, angular momentum distribution, and dynamical friction. We find three distinct populations of galaxies by applying a Gaussian mixture model to their distribution in colour and mass. They have distinct evolutionary histories and leave distinct signatures on their distribution around cluster haloes. We find that low-mass red galaxies show the most concentrated distribution in clusters and the largest splashback radius, while high-mass red galaxies show a less concentrated distribution and a smaller splashback radius. Blue galaxies, which mostly quench into the low-mass red population, have the shallowest distribution within the clusters, with those on radial orbits quenched rapidly before reaching pericentre. Comparison with the distribution of galaxies from the Dark Energy Survey survey around Sunyaev–Zeldovich clusters from the Atacama Cosmology Telescope and South Pole Telescope surveys shows evidence for differences in galaxy evolution between simulations and data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A joint SZ–X-ray–optical analysis of the dynamical state of 288 massive galaxy clusters

In this work, we use imaging from the first three years of the Dark Energy Survey to characterize the dynamical state of 288 galaxy clusters at 0.1 ≲ z ≲ 0.9 detected in the South Pole Telescope (SPT) Sunyaev–Zeldovich (SZ) effect survey (SPT-SZ). We examine spatial offsets between the position of the brightest cluster galaxy (BCG) and the centre of the gas distribution as traced by the SPT-SZ centroid and by the X-ray centroid/peak position from Chandra and XMM data. We show that the radial distribution of offsets provides no evidence that SPT SZ-selected cluster samples include a higher fraction of mergers than X-ray-selected cluster samples. We use the offsets to classify the dynamical state of the clusters, selecting the 43 most disturbed clusters, with half of those at z ≳ 0.5, a region seldom explored previously. We find that Schechter function fits to the galaxy population in disturbed clusters and relaxed clusters differ at z > 0.55 but not at lower redshifts. Disturbed clusters at z > 0.55 have steeper faint-end slopes and brighter characteristic magnitudes. Within the same redshift range, we find that the BCGs in relaxed clusters tend to be brighter than the BCGs in disturbed samples, while in agreement in the lower redshift bin. Possible explanations includes a higher merger rate, and a more efficient dynamical friction at high redshift. The red-sequence population is less affected by the cluster dynamical state than the general galaxy population.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

WIYN Open Cluster Study. LXXXII. Radial-velocity Measurements and Spectroscopic Binary Orbits in the Open Cluster NGC 7789

We present an extensive time-series radial-velocity (RV) survey of stars in the rich open cluster NGC 7789 (1.6 Gyr, [Fe/H] = +0.02). The stellar sample lies within an 18′ circular radius from the cluster center (10 pc in projection, or about 2 core radii), and includes giants, red clump stars, blue stragglers, red stragglers, sub-subgiants, and main-sequence stars down to 1 mag below the turnoff. Our survey began in 2005 and comprises more than 9000 RV measurements from the Hydra Multi-Object Spectrograph on the WIYN 3.5 m telescope. We identify 624 likely cluster members and present the orbital solutions for 81 cluster binary stars with periods between 1.45 and 4200 days. From the main-sequence binary solutions we fit a circularization period of 7.2{sub −1.1}{sup +0.6} days. We calculate an incompleteness-corrected main-sequence binary frequency of 31% ± 4% for binaries with periods less than 10{sup 4} days, similar to other WIYN Open Cluster Survey (WOCS) open clusters of all ages. We detect a blue straggler binary frequency of 33% ± 17%, consistent with the similarly aged open cluster NGC 6819. We also find one secure, rapidly rotating sub-subgiant and one red straggler candidate in our sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Selecting samples of galaxies with fewer Fingers-of-God

The radial positions of galaxies inferred from their measured redshift appear distorted due to their peculiar velocities. We argue that the contribution from stochastic velocities — which gives rise to `Fingers-of-God' (FoG) anisotropy in the inferred maps — does not lend itself to perturbative modelling already on scales targeted by current experiments. To get around this limitation, we propose to remove FoG using data-driven indicators of their abundance that are local in nature and thus avoid selection biases. In particular, we show that the scale where the measured power spectrum quadrupole changes sign is tightly anti-correlated with both the satellite fraction and the velocity dispersion, and can thus be used to select galaxy samples with fewer FoG. In addition, we show that excluding galaxies in haloes more massive than a given mass threshold can help to discard many of the most problematic galaxies. Such selection could be achieved in practice using maps of the thermal Sunyaev-Zel'dovich distortion of the cosmic microwave background frequency spectrum. These techniques could potentially improve reconstructions of the large-scale velocity and displacement fields from the redshift-space positions of galaxies. They may also extend the reach of perturbative models for galaxy clustering, though in practice we find only marginal gains when fitting one-loop EFTofLSS models to simulations with mitigated FoG due to the relevance of other effects entering at two-loop order.

cosmological parameters from LSS↗
DOE OSTI2023

Ubiquitous spin freezing in the superconducting state of UTe 2

In most superconductors electrons form Cooper pairs in a spin-singlet state mediated by either phonons or by long-range interactions such as spin fluctuations. The superconductor UTe 2 is a rare material wherein electrons are believed to form pairs in a unique spin-triplet state with potential topological properties. While spin-triplet pairing may be mediated by ferromagnetic or antiferromagnetic fluctuations, experimentally, the magnetic properties of UTe 2 are unclear. By way of muon spin rotation/relaxation (μSR) measurements on independently grown UTe 2 single crystals we demonstrate the existence of magnetic clusters that gradually freeze into a disordered spin frozen state at low temperatures. Our findings suggest that inhomogeneous freezing of magnetic clusters is linked to the ubiquitous residual linear term in the temperature dependence of the specific heat (C) and the low-temperature upturn in C/T versus T. The omnipresent magnetic inhomogeneity has potential implications for experiments aimed at establishing the intrinsic low-temperature properties of UTe 2 .

36 MATERIALS SCIENCE↗
DOE OSTI2023

The evolution of the Milky Way’s thin disc radial metallicity gradient with K2 asteroseismic ages

ABSTRACT The radial metallicity distribution of the Milky Way’s disc is an important observational constraint for models of the formation and evolution of our Galaxy. It informs our understanding of the chemical enrichment of the Galactic disc and the dynamical processes therein, particularly radial migration. We investigate how the metallicity changes with guiding radius in the thin disc using a sample of red giant stars with robust astrometric, spectroscopic, and asteroseismic parameters. Our sample contains 668 stars with guiding radii 4 < Rg < 11 kpc and asteroseismic ages covering the whole history of the thin disc with precision ${\approx} 25 {{\, \rm per\ cent}}$. We use MCMC analysis to measure the gradient and its intrinsic spread in bins of age and construct a hierarchical Bayesian model to investigate the evolution of these parameters independently of the bins. We find a smooth evolution of the gradient from ≈−0.07 dex kpc−1 in the youngest stars to ≈−0.04 dex kpc−1 in stars older than 10 Gyr, with no break at intermediate ages. Our results are consistent with those based on asteroseismic ages from CoRoT, with that found in Cepheid variables for stars younger than 1 Gyr, and with open clusters for stars younger than 6 Gyr. For older stars we find a significantly lower metallicity in our sample than in the clusters, suggesting a survival bias favouring more metal-rich clusters. We also find that the chemical evolution model of Chiappini '09 is too metal poor in the early stages of disc formation. Our results provide strong new constraints for the growth and enrichment of the thin disc and radial migration, which will facilitate new tests of model conditions and physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Evolution of size-selected Pt cluster catalysts on prototypical oxide supports

The current quest for new pathways into sustainable, efficient and durable energy conversion technologies makes the used for a fundamental understanding of the atomic-scale phenomena underlying catalytic processes ever more pressing. In this context, characterizing catalyst particles in situ provides valuable information about the evolution of their composition, structure, oxidation state and charge state during an ongoing process. To disentangle the influence of individual parameters – temperature, pressure, gas composition, cluster size, as well as support acidity, redox state and defect density – it is crucial to control them precisely and separately in experiments. At the example of size-selected Pt n clusters – i.e. sub-nm particles defined to the exact number of atoms – on flat oxide supports, we follow their rich evolution phenomena via (synchrotron-based) X-ray photoelectron spectroscopy (XPS) and scanning tunnelling microscopy (STM) during temperature ramps and in various gas environments. Here, we present our experience with these highly defined, yet complicated-to-create samples in ultra-high vacuum (UHV) and at mbar pressures. We discuss their stability during transport to synchrotrons and under reaction conditions on three prototypical oxide supports and show the various phenomena that can be disentangled. Ptn clusters on the non-reducible silicon dioxide, SiO 2 , remain size-selected and show remarkable stability. Doping strongly influences the size-dependent binding energy shifts and changes the Pt response to oxidative and reaction conditions, which we attribute to different cluster geometries: p-type doping leads to wetting, enhanced sinter resistance and a diminished response to oxidative environments, compared to clusters on n-type doped samples. We compare the system with our previous findings of a similar change in dimensionality for Pt 20 clusters on the reducible ceria, CeO 2 (111), support, induced by modulation of its O vacancy density. The Pt n /CeO 2 system is particularly interesting for strategies to stabilize and redisperse Pt clusters dynamically. Finally, we study the evolution of Pt n clusters on another reducible oxide support, magnetite, Fe 3 O 4 (001), in 0.1 mbar alternating redox conditions at RT and elevated temperature. In analogy to findings previously reported for Pt/TiO 2 (110), the clusters either become encapsulated by a thin oxide film via strong metal–support interaction (SMSI) or deeply buried in the magnetite. Overall, our approach of following the evolution of size-selected clusters on oxide supports leads to fundamental atomic-scale insights on nano-scale catalyst materials, on our path to sustainable, dynamic and self-repairing catalysts.

Falling, Lorenz J. [Technical Univ. of Munich (Ger↗
DOE OSTI2022

Can Thorne-Zytkow objects source GW190814-type events?

The LIGO-Virgo collaboration reported in their third run the coalescence event GW190814 involving a 2.6 M ⊙ object with a 23 M ⊙ black hole. In this article we study the conditions under which Thorne- Zytkow objects (TZOs) can be connected to that type of event. We evaluate first the rate of appearance of TZOs in the local Universe. Under the assumption that TZOs eventually become low mass gap black holes we evaluate how those black holes end up in binaries with other stellar mass black holes and compare to the reported rate for GW190814-type of events (1–23 Gpc –3 yr –1 ). Here, we find that TZOs in dense stellar clusters can not explain the LIGO-Virgo rate without a TZO population in the field providing a dominant contribution. We also find that TZOs formed within hierarchical triple systems in the field with the third more distant star being the progenitor of a stellar mass black hole may be able to give a rate comparable to that of GW190814-type events. In that case, future observations should discover mergers between stellar mass and low mass gap black holes, with the lower mass spanning the entire low mass gap range.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Discovery of a nearby radio relic in the low-mass, merging cluster Abell 4067

Shock waves generated during cluster mergers offer a powerful probe of how large-scale structure grows and evolves in the Universe. As part of the MeerKAT-South Pole Telescope (SPT) survey, we report the discovery of a single arc-like radio relic in the galaxy cluster Abell 4067 ($z=0.099$), one of the lowest-mass clusters known to host such a structure. MeerKAT UHF-band (0.58–1.09 GHz) observations reveal a relic with a largest linear size of $\sim 1.48\pm 0.02$ Mpc, located at a projected distance of 0.95 Mpc from the cluster centre. XMM–Newton X-ray data show that the relic’s position and orientation relative to the intracluster medium (ICM) elongation are consistent with a merger-driven shock-wave scenario. The relic has an estimated radio power of $3.10\pm 0.03\times 10^{24}$ W Hz$^{-1}$ at 150 MHz. When placed in the $P_{150\, \mathrm{MHz}}$–$M_{500}$ scaling relation, the Abell 4067 relic appears less luminous compared to relics in more massive clusters, suggesting an association with weak merger shocks. This finding supports the idea that relics in low-mass clusters may form through less energetic merger events, leading to weak merger shocks. The latter is supported by the absence of a detectable central radio halo in Abell 4067, which reinforces the idea that luminous radio haloes are not a universal outcome of cluster mergers and highlights the role of cluster mass, merger energetics, and evolutionary stage in shaping diffuse radio emission in the ICM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

From canyons to valleys: Numerically continuing sticky-hard-sphere clusters to the landscapes of smoother potentials

Here, we study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for 6 ≤ $\textit{N}$ ≤ 12 hard spheres that are “sticky,” i.e., they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges, the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events and find that most rearrangements occur when a pair of nonbonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, i.e., those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗