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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

The Effect of the Ambient Solar Wind Medium on a CME-driven Shock and the Associated Gradual Solar Energetic Particle Event

We present simulation results of a gradual solar energetic particle (SEP) event detected on 2021 October 9 by multiple spacecraft, including BepiColombo (Bepi) and near-Earth spacecraft such as the Advanced Composition Explorer (ACE). A peculiarity of this event is that the presence of a high-speed stream (HSS) affected the low-energy ion component (≲5 MeV) of the gradual SEP event at both Bepi and ACE, despite the HSS having only a modest solar wind speed increase. Using the EUHFORIA (European Heliospheric FORecasting Information Asset) magnetohydrodynamic model, we replicate the solar wind during the event and the coronal mass ejection (CME) that generated it. We then combine these results with the energetic particle transport model PARADISE (PArticle Radiation Asset Directed at Interplanetary Space Exploration). We find that the structure of the CME-driven shock was affected by the nonuniform solar wind, especially near the HSS, resulting in a shock wave front with strong variations in its properties such as its compression ratio and obliquity. By scaling the emission of energetic particles from the shock to the solar wind compression at the shock, an excellent match between the PARADISE simulation and in situ measurements of ≲5 MeV ions is obtained. Our modeling shows that the intricate intensity variations observed at both ACE and Bepi were influenced by the nonuniform emission of energetic particles from the deformed shock wave and demonstrates the influence of even modest background solar wind structures on the development of SEP events.

Solar energetic particles↗
NASA NTRS2024

Landslide Hazard is Projected to Increase Across High Mountain Asia

High Mountain Asia has long been known as a hotspot for landslide risk, and studies have suggested that landslide hazard is likely to increase in this region over the coming decades. Extreme precipitation may become more frequent, with a nonlinear response relative to increasing global temperatures. However, these changes are geographically varied. This article maps probable changes to landslide hazard, as shown by a landslide hazard indicator (LHI) derived from downscaled precipitation and temperature. In order to capture the nonlinear response of slopes to extreme precipitation, a simple machine-learning model was trained on a database of landslides across High Mountain Asia to develop a regional LHI. This model was applied to statistically downscaled data from the 30 members of the Seamless System for Prediction and Earth System Research large ensembles to produce a range of possible outcomes under the Shared Socioeconomic Pathways 2-4.5 and 5-8.5. The LHI reveals that landslide hazard will increase in most parts of High Mountain Asia. Absolute increases will be highest in already hazardous areas such as the Central Himalaya, but relative change is greatest on the Tibetan Plateau. Even in regions where landslide hazard declines by year 2100, it will increase prior to the mid-century mark. However, the seasonal cycle of landslide occurrence will not change greatly across High Mountain Asia. Although substantial uncertainty remains in these projections, the overall direction of change seems reliable. These findings highlight the importance of continued analysis to inform disaster risk reduction strategies for stakeholders across High Mountain Asia.

Thomas A Stanley↗
DOE OSTI2020

Wabash CarbonSAFE Subtask 4.1 - Application of Policy Frameworks for Improved Carbon Capture and Storage Social Site Characterization & Stakeholder Engagement

Anthropogenic climate change threatens environmental and human health globally. Limiting these threats requires large-scale and innovative greenhouse gas mitigation responses across carbon-intensive energy and industrial sectors. Carbon capture and storage (CCS) technologies present potential opportunities for mitigating climate change while maintaining a diverse energy resource portfolio. Successful development of CCS physical sites requires effective and efficient project management solutions that elicit and incorporate the concerns and perspectives of diverse stakeholders. Due to the urgency of climate change mitigation technology implementation and the costs of CCS development, CCS project developers cannot risk setbacks by poor stakeholder assessment that concern management processes. Thus, this report presents four prominent policy frameworks and associated case studies as opportunities to improve CCS social site characterization and stakeholder engagement. After comparing the relative effectiveness and efficiencies of each framework with regard to CCS, this report concludes that the Advocacy Coalition Framework, Narrative Policy Framework, and Policy Conflict Framework can improve the CCS social site characterization process, while the Collaborative Governance Framework paired with the Q-Methodology provides an ideal framework for direct stakeholder engagement. Overall, this report finds that the Narrative Policy Framework and the Collaborative Governance Framework are most ideally suited for the purposes of CCS social site characterization and stakeholder engagement.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Energy Dependence Analysis of Neutrino-Nucleus Interactions in Scintillator for MINERvA

This thesis is on the intrinsic energy dependence in neutrino-nucleus interaction models, especially quasielastic scattering and 2p2h process, and the implications for understanding data from MINERvA, NOvA, and DUNE. Neutrino-nucleus interactions are modeled using fve structure functions, W1, W2, W3, W4 and W5, and each structure function contributes diferently to the energy dependence once it enters the cross-section calculations. The energy independent term in the calculations contains only W2 and the next lower order term (of the order 1/E) contains W3 also. In this thesis, we show that W2 is good enough to describe MINERvA data and energy dependence coming from the cross-section directly is small. However, W3 will be signifcant for lower energy experiments such as NOvA and DUNE (especially at and below the oscillation maximum). We have also developed a method to extract structure functions directly from MINERvA data though we find that systematic uncertainties present in the data are too big to successfully determine 1/E Term. In addition to this, we have applied muon angle cuts on MINERvA data and MC, which have their own energy dependent effects. An apparent energy dependent discrepancy comes from known shortcomings especially in the pion production model. Finally, because the energy dependence analysis has similarities to the low-$\nu$ method, we have evaluated discrepancies between the data and MC in light of diferent fux constraint techniques. The results suggest including MINERvA s low-$\nu$ method constraint is an improvement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The Milky Way’s stellar streams and globular clusters do not align in a Vast Polar Structure

ABSTRACT There is increasing evidence that a substantial fraction of Milky Way satellite galaxies align in a rotationally supported plane of satellites, a rare configuration in cosmological simulations of galaxy formation. It has been suggested that other Milky Way substructures (namely young halo globular clusters and stellar/gaseous streams) similarly tend to align with this plane, accordingly dubbed the Vast Polar Structure (VPOS). Using systemic proper motions inferred from Gaia data, we find that globular cluster orbital poles are not clustered in the VPOS direction, though the population with the highest VPOS membership fraction is the young halo clusters (∼30 per cent). We additionally provide a current census of stellar streams, including new streams discovered using the Dark Energy Survey and Gaia data sets, and find that stellar stream normals are also not clustered in the direction of the VPOS normal. We also find that, based on orbit modelling, there is a likely association between NGC 3201 and the Gjöll stellar stream and that, based on its orbital pole, NGC 4147 is likely not a Sagittarius globular cluster. That the Milky Way’s accreted globular clusters and streams do not align in the same planar configuration as its satellites suggests that the plane of satellites is either a particularly stable orbital configuration or a population of recently accreted satellites. Neither of these explanations is particularly likely in light of other recent studies, leaving the plane of satellites problem as one of the more consequential open problems in galaxy formation and cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Three-dimensional Map of the Heliosphere from IBEX

The Interstellar Boundary Explorer (IBEX) mission has shown that variations in the energetic neutral atom (ENA) flux from the outer heliosphere are associated with the solar cycle and longer-term variations in the solar wind (SW). In particular, there is a good correlation between the dynamic pressure of the outbound SW and variations in the later-observed IBEX ENA flux. The time difference between observations of the outbound SW and the heliospheric ENAs with which they correlate ranges from approximately 2 to 6 yr or more, depending on ENA energy and look direction. This time difference can be used as a means of "sounding" the heliosheath, that is, finding the average distance to the ENA source region in a particular direction. Here, we apply this method to build a 3D map of the heliosphere. We use IBEX ENA data collected over a complete solar cycle, from 2009 through 2019, corrected for survival probability to the inner heliosphere. Here we divide the data into 56 "macropixels" covering the entire sky. As each point in the sky is sampled once every 6 months, this gives us a time series of 22 points macropixel –1 on which to time-correlate. Consistent with prior studies and heliospheric models, we find that the shortest distance to the heliopause, d HP , is slightly south of the nose direction (d HP ~ 110–120 au), with a flaring toward the flanks and poles (d HP ~ 160–180 au). The heliosphere extends at least ~350 au tailward, which is the distance limit of the technique.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Climatic Effects of 1950-2050 Changes in US Anthropogenic Aerosols: Aerosol Trends and Radiative Forcing - Part 1

We calculate decadal aerosol direct and indirect (warm cloud) radiative forcings from US anthropogenic sources over the 1950-2050 period. Past and future aerosol distributions are constructed using GEOS-Chem and historical emission inventories and future projections from the IPCC A1B scenario. Aerosol simulations are evaluated with observed spatial distributions and 1980-2010 trends of aerosol concentrations and wet deposition in the contiguous US. Direct and indirect radiative forcing is calculated using the GISS general circulation model and monthly mean aerosol distributions from GEOS-Chem. The radiative forcing from US anthropogenic aerosols is strongly localized over the eastern US. We find that its magnitude peaked in 1970-1990, with values over the eastern US (east of 100 deg W) of −2.0Wm(exp−2 for direct forcing including contributions from sulfate (−2.0Wm−2), nitrate (−0.2Wm(exp−2), organic carbon (−0.2Wm(exp−2), and black carbon (+0.4Wm(exp−2). The uncertainties in radiative forcing due to aerosol radiative properties are estimated to be about 50 %. The aerosol indirect effect is estimated to be of comparable magnitude to the direct forcing. We find that the magnitude of the forcing declined sharply from 1990 to 2010 (by 0.8Wm(exp−2) direct and 1.0Wm(exp−2 indirect), mainly reflecting decreases in SO2 emissions, and project that it will continue declining post-2010 but at a much slower rate since US SO2 emissions have already declined by almost 60% from their peak. This suggests that much of the warming effect of reducing US anthropogenic aerosol sources has already been realized. The small positive radiative forcing from US BC emissions (+0.3Wm(exp−2 over the eastern US in 2010; 5% of the global forcing from anthropogenic BC emissions worldwide) suggests that a US emission control strategy focused on BC would have only limited climate benefit.

climate change↗
NASA NTRS2002

Electron Pitch-Angle Distribution in Pressure Balance Structures Measured by Ulysses/SWOOPS

Pressure balance structures (PBSs) are a common feature in the high-latitude solar wind near solar minimum. From previous studies, PBSs are believed to be remnants of coronal plumes. Yamauchi et al [2002] investigated the magnetic structures of the PBSs, applying a minimum variance analysis to Ulysses/Magnetometer data. They found that PBSs contain structures like current sheets or plasmoids, and suggested that PBSs are associated with network activity such as magnetic reconnection in the photosphere at the base of polar plumes. We have investigated energetic electron data from Ulysses/SWOOPS to see whether bi-directional electron flow exists and we have found evidence supporting the earlier conclusions. We find that 45 ot of 53 PBSs show local bi-directional or isotopic electron flux or flux associated with current-sheet structure. Only five events show the pitch-angle distribution expected for Alfvenic fluctuations. We conclude that PBSs do contain magnetic structures such as current sheets or plasmoids that are expected as a result of network activity at the base of polar plumes.

Yamauchi, Yohei↗
DOE OSTI2025

Thermodynamics and collisionality in firehose-susceptible high- β plasmas

We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma β, the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high-β plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time τ exceeds the ion-Larmor frequency by a β-dependent critical parameter, can support linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is ν eff ∼ β/τ, in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.

astrophysical plasmas↗
DOE OSTI2020

Simulations of the Biodegradation of Citrate Based Polymers for Artificial Scaffolds Using Accelerated Reactive Molecular Dynamics

Here, we explore the reactivity and mechanical properties of poly(1,6-hexanediol-co-Citric acid) via ReaxFF molecular dynamics simulations. We implement an accelerated scheme within the ReaxFF framework to study the hydrolysis reaction of the polymer which is provided with sufficient amount of energy known as the restrain energy after a suitable pre-transition state configuration is obtained to overcome the activation energy barrier and the desired product is obtained. The validity of the ReaxFF force field is established by comparing the ReaxFF energy barriers of ester and ether hydrolysis with benchmark DFT values in literature. We perform chemical and mechanical degradation of polymer chain bundles at 300 K. We find that ester hydrolyzes faster than ether due to lower activation energy barrier of the reaction. The selectivity of the bond-boost scheme has been demonstrated by lowering the boost parameters of the accelerated simulation which almost stops the ether hydrolysis. Mechanical degradation of pre-hydrolyzed and intermittent hydrolyzed polymer bundles is performed along the longitudinal direction at two different strain rates. We find that the tensile modulus of the polymers are increases with increase in strain rates which shows that polymers show a strain dependent behavior. The tensile modulus of the Polyester-ether is higher than Polyester yet reaches yield-stress faster than Polyester. This makes Polyester more ductile than Polyester-ether.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Preventing Failures By Dataset Shift Detection in Safety-Critical Graph Applications

Dataset shift refers to the problem where the input data distribution may change over time (e.g., between training and test stages). Since this can be a critical bottleneck in several safety-critical applications such as healthcare, drug-discovery, etc., dataset shift detection has become an important research issue in machine learning. Though several existing efforts have focused on image/video data, applications with graph-structured data have not received sufficient attention. Therefore, in this paper, we investigate the problem of detecting shifts in graph structured data through the lens of statistical hypothesis testing. Specifically, we propose a practical two-sample test based approach for shift detection in large-scale graph structured data. Our approach is very flexible in that it is suitable for both undirected and directed graphs, and eliminates the need for equal sample sizes. Using empirical studies, we demonstrate the effectiveness of the proposed test in detecting dataset shifts. We also corroborate these findings using real-world datasets, characterized by directed graphs and a large number of nodes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Buckling response of laminates with spatially varying fiber orientations

The buckling response of a symmetrically laminated composite panel with a spatially varying fiber orientation has been analyzed. Variation of the fiber orientation angle as a function of the position in the panel results in a composite laminate with stiffness properties that are functions of the panel coordinates. The laminates are therefore termed variable stiffness panels. The fiber orientation is assumed to vary only in one spatial direction, although the analysis can be extended to fiber orientations that vary in two spatial directions. The Ritz Method has been used to find the buckling loads and buckling modes for the variable stiffness panels for two different cases. In one of the cases the fiber orientation is assumed to change in the direction of the applied load. The other case is the one in which the fiber orientation varies in a direction perpendicular to the loading direction. Improvements in the buckling load of up to 80 percent over straight fiber configurations were found. Results for three different panel aspect ratios are presented.

Olmedo, Reynaldo↗
NASA NTRS2007

The Prelude to and Aftermath of the Giant Flare of 2004 December 27: Persistent and Pulsed X-ray Properties of SGR 1806-20 from 1993 to 2005

We report on the evolution of key spectral and temporal parameters of SGR 1806-20 prior to and following the highly energetic giant flare of 2004 December 27. Using RXTE, we track the pulse frequency of the SGR and find that the spin-down rate varied erratically in the months before and after the flare. Contrary to the giant flare in SGR 1900+14, we find no evidence for a discrete jump in spin frequency at the time of the December 27th flare (Absolute value of (Delta * upsilon/upsilon) < 5 10 (exp -6)). In the months surrounding the flare, we find a strong correlation between pulsed flux and torque consistent with the model for magnetar magnetosphere electrodynamics proposed. As with the flare in SGR 1900+14, the pulse morphology of SGR 1806-20 changes drastically following the flare. Using Chandra and other publicly available imaging X-ray detector observations, we construct a spectral history of SGR 1806-20 from 1993 to 2005. The usual magnetar persistent emission spectral model of a power law plus a blackbody provides an excellent fit to the data. We confirm the earlier finding of increasing spectral hardness of SGR 1806-20 between 1993 and 2004. However, our results indicate significant differences in the temporal evolution of the spectral hardening. Rather than a direct correlation between torque and spectral hardness, we find evidence for a sudden torque change that preceded a gradual hardening of the energy spectrum on a timescale of years. Interestingly, the spectral hardness, spin-down rate, phase-averaged flux, and pulsed flux of SGR 1806-20 all peak months before the flare epoch.

Woods, Peter M.↗
DOE OSTI2022

Fabrication of Arrays of Topological Solitons in Patterned Chiral Liquid Crystals for Real-Time Observation of Morphogenesis

Topological solitons have knotted continuous field configurations embedded in a uniform background, and occur in cosmology, biology, and electromagnetism. However, real-time observation of their morphogenesis and dynamics is still challenging because their size and timescale are enormously large or tiny. Liquid crystal (LC) structures are promising candidates for a model-system to study the morphogenesis of topological solitons, enabling direct visualization due to the proper size and timescale. We report a new way is found to rationalize the real-time observation of the generation and transformation of topological solitons using cholesteric LCs confined in patterned substrates. The experimental demonstration shows the topologically protected structures arise via the transformation of topological defects. Numerical modeling based on minimization of free energy closely reconstructs the experimental findings. The fundamental insights obtained from the direct observations pose new theoretical challenges in understanding the morphogenesis of different types of topological solitons within a broad range of scales.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Spin-orbit enabled quantum transport channels in a two-hole double quantum dot

We analyze experimentally and theoretically the transport spectra of a gated lateral GaAs double quantum dot containing two holes. The strong spin-orbit interaction present in the hole subband lifts the Pauli spin blockade and allows to map out the complete spectra of the two-hole system. By performing measurements in both source-drain voltage directions, at different detunings and magnetic fields, we carry out quantitative fitting to a Hubbard two-site model accounting for the tunnel coupling to the leads and the spin-flip relaxation process. We extract the singlet-triplet gap and the magnetic field corresponding to the singlet-triplet transition in the double-hole ground state. Additionally, at the singlet-triplet transition we find a resonant enhancement (in the blockaded direction) and suppression of current (in the conduction direction). The current enhancement stems from the multiple resonance of two-hole levels, opening several conduction channels at once. The current suppression arises from the quantum interference of spin-conserving and spin-flipping tunneling processes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Understanding Cu incorporation in the Cu 2x Hg 2-x GeTe 4 structure using resonant x-ray diffraction

The ability to control carrier concentration based on the extent of Cu solubility in the Cu 2x Hg 2-x GeTe 4 alloy compound (where 0 ≤ x ≤ 1) makes Cu 2x Hg 2-x GeTe 4 an interesting case study in the field of thermoelectrics. While Cu clearly plays a role in this process, it is unknown exactly how Cu incorporates into the Cu 2x Hg 2-x GeTe 4 crystal structure and how this affects the carrier concentration. In this work, we use a combination of resonant energy x-ray diffraction (REXD) experiments and density functional theory (DFT) calculations to elucidate the nature of Cu incorporation into the Cu 2x Hg 2-x GeTe 4 structure. REXD across the Cu k edge facilitates the characterization of Cu incorporation in the Cu 2x Hg 2-x GeTe 4 alloy and enables direct quantification of antisite defects. Here, we find that Cu substitutes for Hg at a 2:1 ratio, wherein Cu annihilates a vacancy and swaps with a Hg atom. DFT calculations confirm this result and further indicate that the incorporation of Cu occurs preferentially on one of the z = 1/4 or z = 3/4 planes before filling the other plane. Furthermore, the amount of Cu Hg antisite defects quantified by REXD was found to be directly proportional to the experimentally measured hole concentration, indicating that the Cu Hg defects are the driving force for tuning carrier concentration in the Cu 2x Hg 2-x GeTe 4 alloy. The link uncovered here between crystal structure, or more specifically antisite defects, and carrier concentration can be extended to similar cation-disordered material systems and will aid the development of improved thermoelectric and other functional materials through defect engineering.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Refining the two-band model for highly compensated semimetals using thermoelectric coefficients

In studying compensated semimetals, the two-band model has proven extremely useful in capturing electrical conductivity under magnetic field, as a function of density and mobility of electronlike and holelike carriers. However, it rarely offers practical insight into magnetothermoelectric properties. Here, in this work, we report the field dependence of thermoelectric (TE) coefficients in a highly compensated semimetal NbSb 2 , where we find the Seebeck (𝑆 𝑥⁢𝑥 ) and Nernst (𝑆 𝑥⁢𝑦 ) coefficients increase quadratically and linearly with applied magnetic field, respectively. Such field dependence was predicted in previous work that studied a system of two parabolic bands, within semiclassical Boltzmann transport theory when the following two conditions are simultaneously met: 𝜔 𝑐 ⁢𝜏 ≫ 1 and tan ⁡𝜃 𝐻 ≪ 1, where 𝜔 𝑐 and 𝜏 refer to the cyclotron frequency and relaxation time, respectively, and 𝜃 𝐻 is the Hall angle. Under these conditions, we find the field dependence of the TE coefficients directly provides a relation between the electronlike (𝑛 𝑒 ) and holelike (𝑛 ℎ ) carrier densities, which in turn can be used to refine two-band model fitting. With this, we find the compensation factor ($\frac{|Δ⁢𝑛|}{𝑛_{𝑒}}$, where Δ⁢𝑛 = 𝑛 𝑒 −𝑛 ℎ ) of NbSb 2 is two orders of magnitude smaller than what was found in unrestricted fitting, resulting in a larger saturation-field scale for magnetoresistance. Within the same framework of the semiclassical theory, we also deduce that the thermoelectric Hall angle tan⁡ 𝜃 𝛾 = $\frac{𝑆_{𝑥⁢𝑦}}{𝑆_{𝑥⁢𝑥}}$ can be expressed as ($\frac{Δ⁢𝑛}{𝑛_{𝑒}}$ ×𝜔 𝑐 ⁢𝜏) −1 , which serves as a parameter to predict the degree of compensation. Our findings offer crucial insights into identifying empirical conditions for field-induced enhancement of TE performance and into engineering-efficient thermoelectric devices based on semimetallic materials.

electrical conductivity↗
NASA NTRS2020

Streaming Instability with Multiple Dust Species – I. Favourable Conditions for the Linear Growth

A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth time-scale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles tomutually validate and study the unstablemodes of the instability in more detail.We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution [Ts, min, Ts, max] and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary is not appreciably sensitive to q or Ts, min.With a wide range of dust sizes present in the disc (e.g. Ts, min  10−3), the growth rate in the slow-growth regime decreases as more dust species are considered.With a narrow range of dust sizes (e.g. Ts, max/Ts, min = 5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by ε  1 or Ts, max  1, which may represent the favourable conditions for planetesimal formation.

Zhaohuan Zhu↗