Power-law Size Distribution Research Articles

The Sporadic Activity of (6478) Gault: A YORP-driven Event?

On 2019 January 5 a streamer associated with the 4--10 km main-belt asteroid (6478)~Gault was detected by the ATLAS sky survey, a rare discovery of activity around a main-belt asteroid. Archival data from ATLAS and Pan-STARRS1 show the trail in early December 2018, but not between 2010 and January 2018. The feature has significantly changed over one month, perfectly matching predictions of pure dust dynamical evolution and changes in observing geometry for a short release of dust around 2018 October 28. Follow-up observations with HST show a second narrow trail corresponding to a brief release of dust on 2018 December 30. Both releases occurred with negligible velocity. We find the dust grains to be fairly large, with power-law size distributions in the $10^{-5} - 10^{-3}$~m range and power-law indices of $\sim -1.5$. Three runs of ground-based data find a signature of $\sim 2\,\rm h$ rotation, close to the rotational limit, suggesting that the activity is the result of landslides or reconfigurations after YORP spin-up.

Evolution of fragment size distributions from the crushing of granular materials.

We study fragment size distributions after crushing single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single-particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many-grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives information about the origin of the power-law distributions for the granular assembly under uniaxial compression.

Distribution of interevent avalanche times in disordered and frustrated spin systems

Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality, manifest in power-law distributions of avalanche sizes. Considerably less work has been done on the statistics of the times between avalanches. This paper considers this issue, generalizing the work of Nampoothiri et al. [Phys. Rev. E 96, 032107 (2017)] in one space dimension to higher space dimensions. In addition to the interevent statistics of all avalanches, we also consider what happens when events are restricted to those exceeding a certain threshold size. Doing so raises the possibility of altering the definition of time to count the number of small events between the large ones, which provides for an analog to the concept of natural time introduced by the geophysics community with the goal of predicting patterns in seismic events. We analyze the distribution of time and natural time intervals both in the case of models that include only nearest-neighbor interactions, as well as models with (sparse) long-range couplings.

From solar to stellar flare characteristics

Context. The connection between solar energetic proton events and X-ray flares has been the focus of many studies over the past 13 yr. In the course of these investigations several peak size distribution functions based on Geostationary Operational Environmental Satellite (GOES) measurements of both quantities have been developed. In more recent studies one of these functions has been used to estimate the stellar proton fluence around the M-dwarf star AD Leonis. However, a comparison of the existing peak size distribution functions reveals strong discrepancies with respect to each other. Aims. The aim of this paper is to derive a new peak size distribution function that can be utilized to give a more realistic estimate of the stellar proton flux of G-, K-, and M-dwarf stars. Methods. By updating and extending the GOES-based peak size distribution down to B-class X-ray flare intensities with the help of SphinX data from the solar minimum conditions of 2009 and newly derived GOES data between 1975 and 2005, we developed a new power-law peak size distribution function for solar proton fluxes (E > 10 MeV). However, its resulting slope differs from values reported in the literature. Therefore, we also developed a double-power-law peak size distribution function. An extension to much higher X-ray flare intensities (10−1) W m−2 and above, for the first time, results in an approximation of best- and worst-case scenarios of the stellar proton flux around G-, K-, and M-dwarf stars. Results. Investigating the impact of the newly developed peak size distribution function for G-, K-, and M-dwarf star flare intensities we show that in the worst-case scenario previous studies may underestimate the stellar proton flux by roughly one to five orders of magnitude.

The integrated properties of the molecular clouds from the JCMT CO(3–2) High-Resolution Survey

We define the molecular cloud properties of the Milky Way first quadrant using data from the JCMT CO(3-2) High Resolution Survey. We apply the Spectral Clustering for Interstellar Molecular Emission Segmentation (SCIMES) algorithm to extract objects from the full-resolution dataset, creating the first catalog of molecular clouds with a large dynamic range in spatial scale. We identify $>85\,000$ clouds with two clear sub-samples: $\sim35\,500$ well-resolved objects and $\sim540$ clouds with well-defined distance estimations. Only 35% of the cataloged clouds (as well as the total flux encompassed by them) appear enclosed within the Milky Way spiral arms. The scaling relationships between clouds with known distances are comparable to the characteristics of the clouds identified in previous surveys. However, these relations between integrated properties, especially from the full catalog, show a large intrinsic scatter ($\sim0.5$ dex), comparable to other cloud catalogs of the Milky Way and nearby galaxies. The mass distribution of molecular clouds follows a truncated-power law relationship over three orders of magnitude in mass with a form $dN/dM \propto M^{-1.7}$ with a clearly defined truncation at an upper mass of $M_0 \sim 3 \times 10^6~M_\odot$, consistent with theoretical models of cloud formation controlled by stellar feedback and shear. Similarly, the cloud population shows a power-law distribution of size with $dN/dR \propto R^{-2.8}$ with a truncation at $R_0 = 70$ pc.

Comet 29P/Schwassmann-Wachmann 1 dust environment from photometric observation at the SOAR Telescope

We report photometric observations of comet 29P/Schwassmann-Wachmann 1 made on August 12, 2016 with the broad-band B, V, R and I filters and the SOAR 4.1-meter telescope (Chile). We find the comet active at that time. Enhanced images obtained in all filters reveal three radial features in the 29P/Schwassmann-Wachmann 1 coma, regardless of the image-processing algorithm. Using a high-resolution spectrum of comet 29P/Schwassmann-Wachmann 1 reported by Ivanova et al. (2018) on the same date, we estimate the relative contribution of the gaseous emission and the continuum to the total response measured with our broadband B and V filters. The gaseous-emission contribution appears to be very small, 2.5%. We compute the dust production Afρ in 29P/Schwassmann-Wachmann 1 for the four filters and find its growth with the wavelength, from 3,393 ± 93 cm in the B filter to 8,561 ± 236 cm in the I filter. We model the color slope of dust in Comet 29P/Schwassmann-Wachmann 1 using agglomerated debris particles. Simultaneous analysis of the color slope in the B–R and R–I pairs suggests a single dominant chemical species of 29P/Schwassmann-Wachmann 1 dust particles consisting of Fe–Mg silicates and obeying a power-law size distribution with index n ≈ 2.55. This conclusion is consistent with the previous thermal-emission study of 29P/Schwassmann-Wachmann 1.

Size Distributions of Solar Proton Events and Their Associated Soft X-Ray Flares: Application of the Maximum Likelihood Estimator

Abstract We use the maximum likelihood estimator to determine the slope (α) of the power-law size distribution of the peak proton fluxes of a subsampled set of 106 ∼ 25 MeV solar energetic proton (SEP) events from 1997 to 2016 associated with western hemisphere soft X-ray (SXR) flares: α = 1.28 ± 0.03. For the peak SXR fluxes of a subsample of 110 SEP-associated flares, we find α = 1.51 ± 0.05. In addition, we obtained a slope of 1.61 ± 0.05 for the peak SXR fluxes of a sample of 128 ≥M1 SXR flares from 1996 to 2005 that were associated with coronal mass ejections (CMEs) with speeds ≥1000 km s−1. The slopes of both of these SXR peak-flux distributions (∼1.5 and ∼1.6) are closer to that for proton events (∼1.3) than to the α value of ∼2.1 (2.09 ± 0.08) determined for a subsample of 177 western hemisphere ≥M1 SXR flares considered from 1996 to 2005. These results are consistent with those of a previous study, based on a less reliable method (for small samples), in which it was argued that the flatter size distribution generally found for SEP events versus those for flare electromagnetic emissions was due to the fact that SEP flares are an energetic subset of all flares, characterized by their ∼100% association with fast/wide CMEs that drive coronal/interplanetary shock waves. Shock formation in the corona requires CMEs with speeds ≳400 km s−1, a threshold effect that further distinguishes SEP flares from the general population of all flares.

Avalanche precursors of failure in hierarchical fuse networks

We study precursors of failure in hierarchical random fuse network models which can be considered as idealizations of hierarchical (bio)materials where fibrous assemblies are held together by multi-level (hierarchical) cross-links. When such structures are loaded towards failure, the patterns of precursory avalanche activity exhibit generic scale invariance: irrespective of load, precursor activity is characterized by power-law avalanche size distributions without apparent cut-off, with power-law exponents that decrease continuously with increasing load. This failure behavior and the ensuing super-rough crack morphology differ significantly from the findings in non-hierarchical structures.

Statistical properties of starspots on solar-type stars and their correlation with flare activity

AbstractWe analyzed the statistical properties of starspots on solar-type stars and the correlation between properties of starspots and flare activity using observations from the Kepler mission. We found the size distribution of starspots on solar-type stars shows the power-law distribution and both size distributions of starspots on slowly-rotating solar-type stars and of relatively large sunspots are roughly lie on the same power-law line. We also found that the frequency-energy distributions for superflares and solar flares from spots with different sizes are the same for solar-type stars and the Sun. These results suggest that the magnetic activity on solar-type stars and that on the Sun are caused by the same physical processes

Intermittency between avalanche regimes on grain piles.

We experimentally investigate discrete avalanches of grains, driven by a low inflow rate, on an erodible pile in a channel. We observe intermittency between one regime, in which avalanches are quasiperiodic and system spanning, and another, in which they pass at irregular intervals and have a power-law size distribution. Observations are robust to changes of inflow rate and grain type and require no tuning of external parameters. We demonstrate that the state of the pile's surface determines whether avalanche fronts propagate to the end of the channel or stop partway down, and we introduce a toy model for the latter case that reproduces the observed power-law size distribution. We suggest direct applications to avalanches of pharmaceutical and geophysical grains, and the possibility of reconciling the "self-organized criticality" predicted by several authors with the hysteretic behavior described by others.

Scale-free distribution of firm-size distribution in emerging economies

We test firm-size distributions in 10 emerging economies in Europe, using data on total assets of 1 884 006 firms. On the economy level, power-law firm size distribution is plausible for 8 countries with scaling parameter α≈2. At the industry level, power-law firm size distribution is not rejected for 53% of all cases. However, an alternative log-normal distribution that might follow from Gibrat’s law also appears to be likely as at the economy level it was not ruled out for 9 countries and 74% of industry-level cases.

SCALING PATTERNS OF NATURAL URBAN PLACES AS A RULE FOR ENHANCING THEIR URBAN FUNCTIONALITY USING TRAJECTORY DATA

Abstract. With the availability of massive trajectory data, it is highly valuable to reveal their activity information for many domains such as understanding the functionality of urban regions. This article utilizes the scaling patterns of human activities to enhance functional distribution of natural urban places. Specifically, we proposed a temporal city clustering algorithm to aggregate the stopping locations into natural urban places, which are reported to follow remarkable power law distributions of sizes and obey a universal law of economy of scale on human interactions with urban infrastructure. Besides, we proposed a novel Bayesian inference model with damping factor to estimate the most likely POI type associated with a stopping location. Our results suggest that hot natural urban places could be effectively identified from their scaling patterns and their functionality can be very well enhanced. For instance, natural urban places containing airport or railway station can be highly stressed by accumulating the massive types of human activities.

Numerical modelling of microseismicity associated with longwall coal mining

Microseismicity has long been a precursor for underground mining hazards such as rockbursts and coal and gas outbursts. In this research, a methodology combining deterministic stress and failure analysis and stochastic fracture slip evaluation, based upon the widely accepted fracture slip seismicity-generation mechanism, has been developed to simulate microseismic events induced by longwall mining. Using the built-in DFN facility in FLAC3D, discrete fractures following a power law size distribution are distributed throughout a 3D continuum model in a probabilistic way to account for the stochastic nature of microseismicity. The DFN-based modelling approach developed was adopted to simulate the evolution of microseismicity induced by the progressive face advance in a longwall top coal caving (LTCC) panel at Coal Mine Velenje, Slovenia. At each excavation step, global stress and failure analysis with reference to the strain-softening post-failure behaviour characteristic of coal, and fracture slip evaluation for microseismicity are conducted sequentially. The model findings are compared to the microseismic event data recorded during a long-term field monitoring campaign conducted at the same LTCC panel. It was found that the released energy and frequency-magnitude distribution of microseismicity are associated with the slipped fracture sizes and fracture size distribution. These features for recorded microseismic events were fairly constant until a xylite rich heterogeneous zone ahead of the working face was approached, which indicates that fractures within the extracted coal seam follow the same size distribution. The features obtained from modelled microseismic events were consistent over the production period, and matched well the field observations. Furthermore, the model results indicate that the power law fracture size distribution can be used to model longwall-mining-induced microseismicity. This model provides a unique prospective to understand longwall coal mining-induced microseismicity and lays a foundation to predict microseismicity, or even rockburst potential in specific geological realisations.

Ejecta cloud from the AIDA space project kinetic impact on the secondary of a binary asteroid: II. Fates and evolutionary dependencies

This paper presents a quantitative study of the evolution of the ejecta cloud released from a hypervelocity impact on a binary asteroid. The Asteroid Impact & Deflection Assessment (AIDA) mission project in collaboration between NASA and ESA aims to perform an asteroid deflection demonstration, using a half-ton projectile that will perform a hypervelocity impact on the surface of the secondary of the binary near-Earth asteroid (65803) Didymos, called hereafter Didymoon. We performed numerical simulations of the post-impact dynamics of the ejecta cloud in the framework of the current mission scenario of AIDA. Our analysis relies on a classification of the orbits as a function of the ejecta fates, e.g., a collision with one of the binary components or the escape from the region of influence of the system. A grid search of launching sites of ejecta was defined over the globe of Didymoon, and considering a wide range of possible ejection speeds, we determined the dependency of ejecta fate on launching sites (projectile impact sites) and speeds. This range enables us to track all the complex cases that include different types of dynamical fates. The results reveal the detailed proportions of the ejecta that are either orbiting, escaping or re-accreting on the primary/secondary at the end of the considered timescale, as a function of the ejection speed, which allows us to explore the global characteristics of the ejecta dynamical fates. Two major mechanisms are found to be working broadly during the post-ejection evolution of the ejecta cloud: 1) ejecta on mean motion resonance orbits with Didymoon produce long-term quasi-periodic showers onto Didymoon over at least a couple of weeks after the projectile impact, 2) ejecta on non-resonant orbits produce a rapid and high re-accretion flux. This rapid and high flux occurs just once because ejecta on such orbits leave the system unless they experience a collision during their first encounter. For both mechanisms, swing-bys of Didymoon are found to occur. These swing-bys are a source of chaotic motion because the outcome of the swing-by is extremely sensitive to the ejecta initial conditions. Moreover, for all ejecta speeds, a zone free of ejecta is noticed to emerge around the mid-latitude zone of the celestial sphere about two months after the projectile impact. Also, the extent of this zone depends on the ejecta speed. For the second part of this study, we performed full-scale simulations of the ejecta cloud released from 6 hypothetical impact sites. To define the initial conditions of the ejecta based on cratering scaling laws, we considered two kinds of material composing Didymoon’s subsurface and then combined a power-law size distribution of the ejecta with an ejection speed distribution. We find that the ejecta cloud evolution can be divided in two periods. It starts with a first violent period (<10 h) with fast re-accretion or ejection of the ejecta from the system. A second period is found to be more sensitive to the launching site than the first one. During this second period, ejecta will either re-accrete or being ejected from the system, depending both on their sizes and on their average survival time in close proximity of the binary components. There is thus a size-sorting effect dictated by the solar radiation pressure, which proves to be efficient to move out of the system the dust-size ejecta (<1 mm) for all considered launching sites and material types. On the other hand, the larger ejecta, being less or not affected by the solar radiation pressure, can survive longer in the system.

Breaking the power law: Multiscale simulations of self-ion irradiated tungsten

The initial stage of radiation defect creation has often been shown to follow a power law distribution at short time scales, recently so with tungsten, following many self-organizing patterns found in nature. The evolution of this damage, however, is dominated by interactions between defect clusters, as the coalescence of smaller defects into clusters depends on the balance between transport, absorption, and emission to/from existing clusters. The long-time evolution of radiation-induced defects in tungsten is studied with cluster dynamics parameterized with lower length scale simulations, and is shown to deviate from a power law size distribution. The effects of parameters such as dose rate and total dose, as parameters affecting the strength of the driving force for defect evolution, are also analyzed. Excellent agreement is achieved with regards to an experimentally measured defect size distribution at 30 K. This study provides another satisfactory explanation for experimental observations in addition to that of primary radiation damage, which should be reconciled with additional validation data.

Shear strength of granular materials based on fractal fragmentation of particles

The Mohr-Coulomb criterion has two shear strength parameters commonly known as the cohesion and the friction angle. The peak shear strength of granular materials obtained from direct shear tests has common non-linear strength envelopes due to particle crushing. The effective cohesion continues to increase while the effective friction angle decreases with the increase of effective stress in direct shear tests. Particle crushing of granular materials in direct shear tests leads to a power-law distribution of fragment sizes, and is accurately characterized by the fragmentation fractal dimension drawn from the power exponent. Based on the fractal model for particle fragmentation, a power function is advocated to represent the shear strength criterion of granular materials involving only two constant parameters. The exponent of power-law shear strength criterion is found to express using the fragmentation fractal dimension. The proposed power-law shear strength criterion is validated with experimental data of municipal solid waste incineration (MSWI) bottom ashes from direct shear tests.

A generative model for scientific concept hierarchies.

In many scientific disciplines, each new ‘product’ of research (method, finding, artifact, etc.) is often built upon previous findings–leading to extension and branching of scientific concepts over time. We aim to understand the evolution of scientific concepts by placing them in phylogenetic hierarchies where scientific keyphrases from a large, longitudinal academic corpora are used as a proxy of scientific concepts. These hierarchies exhibit various important properties, including power-law degree distribution, power-law component size distribution, existence of a giant component and less probability of extending an older concept. We present a generative model based on preferential attachment to simulate the graphical and temporal properties of these hierarchies which helps us understand the underlying process behind scientific concept evolution and may be useful in simulating and predicting scientific evolution.

Global patterns of tropical forest fragmentation.

Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments-at maximum by a factor of 33 over 50 years-as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.

Investigations on neutron irradiated 3D carbon fibre reinforced carbon composite material

As against conventional graphite materials carbon-carbon (C/C) composite materials are now being contemplated as the promising candidate materials for the high temperature and fusion reactor owing to their high thermal conductivity and high thermal resistance, better mechanical/thermal properties and irradiation stability. The current need is for focused research on novel carbon materials for future new generation nuclear reactors. The advantage of carbon-carbon composite is that the microstructure and the properties can be tailor made. The present study encompasses the irradiation of 3D carbon composite prepared by reinforcement using PAN carbon fibers for nuclear application.The carbon fiber reinforced composite was subjected to neutron irradiation in the research reactor DHRUVA. The irradiated samples were characterized by Differential Scanning Calorimetry (DSC), small angle neutron scattering (SANS), XRD and Raman spectroscopy. The DSC scans were taken in argon atmosphere under a linear heating program. The scanning was carried out at temperature range from 30 °C to 700 °C at different heating rates in argon atmosphere along with reference as unirradiated carbon composite. The Wigner energy spectrum of irradiated composite showed two peaks corresponding to 200 °C and 600 °C. The stored energy data for the samples were in the range 110–170 J/g for temperature ranging from 30 °C to 700 °C. The Wigner energy spectrum of irradiated carbon composite did not indicate spontaneous temperature rise during thermal annealing. Small angle neutron scattering (SANS) experiments have been carried out to investigate neutron irradiation induced changes in porosity of the composite samples. SANS data were recorded in the scattering wave vector range of 0.17 nm−1 to 3.5 nm−1. Comparison of SANS profiles of irradiated and unirradiated samples indicates significant change in pore morphology. Pore size distributions of the samples follow power law size distribution with different exponent. Narrowing of SANS profile of the irradiated sample indicates creation of significant number of larger pores due to neutron irradiation.

Monte Carlo Simulation of the X-Ray Halos of GX 5−1 and GX 13+1 to Test Models of Insterstellar Dust Grains

Abstract Simulated dust-scattered X-ray halos, generated by a three-dimensional ray-tracing Monte Carlo code, are fitted to the observed halos of GX 5−1 and GX 13+1 by automatic adjustment of parameters that specify the distributions of the dust grains in size and location. Three distributions in size a are tested for the quality of fit they yield: the WD01 distribution, the BARE-GR-B distribution, and power laws of the form . The best fits are obtained with multicloud models of the spatial distributions and power-law size distributions. Correlations between the fitted fractional distances of the dust clouds and the distance estimates of molecular clouds toward GX 5−1 and GX 13+1, derived from the velocity spectra of CO and the galactic rotation curve, favor distance estimates of 4.2 and 5.6 kpc for the two sources, respectively.