Cumulative Number Distribution Research Articles

On the Determination of Stellar Mass and Binary Fraction of Open Clusters within 500 pc from the Sun

We investigated the stellar mass function and the binary fraction of 114 nearby open clusters (OCs) using the high-precision photometric data from Gaia Data Release 3 (Gaia DR3). We estimated the mass of member stars by using a ridge line that is better in line with the observed color–magnitude diagram, thus obtaining more accurate stellar mass and binary mass ratio (q) at the low-mass region. By analyzing the present-day mass function (PDMF) of star clusters, we found that 108 OCs follow a two-stage power-law distribution, whereas six OCs present a single power-law PDMF. Subsequently, we fitted the high(low)-mass index of PDMF ( dN/dm∝m−α ), denoted as α h(α l), and segmentation point m c. For our cluster sample, the median values of α h and α l are 2.65 and 0.95, respectively, which are approximately consistent with the initial mass function results provided by Kroupa. We utilized the cumulative radial number distribution of stars with different masses to quantify the degree of mass segregation. We found a significant positive correlation between the state of dynamical evolution and mass segregation in OCs. We also estimated the fraction of binary stars with q ≥ 0.5, ranging from 6% to 34% with a median of 17%. Finally, we provided a catalog of 114 nearby cluster properties, including the total mass, the binary fraction, the PDMF, and the dynamical state.

Characteristics of ejecta resulting from hypervelocity impact on Al/Mg explosive welding clad materials

In this study, we propose the use of a clad material, created from aluminum alloy A1100P-H24 and magnesium alloy AZ31B-H24 through explosive welding, as a Whipple shield for space applications. Two kinds clad materials with thickness ratios of Mg: Al = 0.5: 0.5 and Mg: Al = 0.7: 0.3 made from explosive welding, are compared to the current standard, the 1 mm thick A6061-T6 Whipple shield utilized in the international space station. By explosive welding low density, high specific strength, and high impact strength magnesium alloy with aluminum alloy, clad materials achieved 16.8% and 23.7% reduction in area density compared to A6061-T6. In the context of space debris mitigation, we performed hypervelocity impact tests on these clad materials. Detailed comparisons were made between the impact characteristics of the explosive welded clad materials and A6061-T6 by examining the perforation hole size and shape, and by collecting and analyzing the ejecta produced during impact. The experimental results revealed that the clad material with the thickness ratio of Mg: Al = 0.7: 0.3 experienced delamination at the material interface due to the penetration of projectile. On the other hand, the Mg: Al = 0.5: 0.5 clad material exhibited a perforation hole pattern comparable to that of monolithic aluminum and magnesium alloy materials. The cumulative number distribution of ejecta indicated that the clad material with a Mg: Al = 0.5: 0.5 ratio could reduce ejecta production. To further evaluate interface delamination, post-impact ultrasonic analyses were performed on the clad materials.

Effects of electron beam irradiation on hypervelocity impact behavior of carbon fiber reinforced plastic plates

The effects of electron beam irradiation were examined on perforation holes and fragments from quasi-isotropic carbon fiber reinforced plastic plates (CFRP plates). CFRP plates with a total dose up to 60 MGy of electron beam irradiation were prepared for hypervelocity impact experiments. The perforation holes of CFRP plates in the hypervelocity impact experiments were decreased with electron beam irradiation when aluminum alloy spherical projectiles (2017-T4) of diameter of 1 mm struck at an impact velocity of 5 km/s. However, a slight reduction in the size of the perforation hole was observed at 2 km/s. Fragments ejected from CFRP plates were examined after collection from the impact side and rear side of the targets. The cumulative number distributions of fragment length and aspect ratio were compared among specimens with different total doses.

Horizontal branch morphology: A new photometric parametrization

Context. Theory and observations indicate that the distribution of stars along the horizontal branch of Galactic globular clusters mainly depends on the metal content. However, the existence of globular clusters with similar metal content and absolute age but different horizontal branch morphologies, suggests the presence of another parameter affecting the star distribution along the branch. Aims. To investigate the variation of the horizontal branch morphology in Galactic globular clusters, we define a new photometric horizontal branch morphology index, overcoming some of the limitations and degeneracies affecting similar indices available in the literature. Methods. We took advantage of a sample of 64 Galactic globular clusters, with both space-based imaging data (Advanced Camera for Surveys survey of Galactic globular clusters) and homogeneous ground-based photometric catalogues in five different bands (U, B, V, R, I). The new index, τHB, is defined as the ratio between the areas subtended by the cumulative number distribution in magnitude (I) and in colour (V − I) of all stars along the horizontal branch. Results. This new index shows a linear trend over the entire range in metallicity (−2.35 ≤ [Fe/H] ≤ −0.12) covered by our Galactic globular cluster sample. We found a linear relation between τHB and absolute cluster ages. We also found a quadratic anti-correlation with [Fe/H], becoming linear when we eliminate the age effect on τHB values. Moreover, we identified a subsample of eight clusters that are peculiar according to their τHB values. These clusters have bluer horizontal branch morphology when compared to typical ones of similar metallicity. These findings allow us to define them as the ’second parameter’ clusters in the sample. A comparison with synthetic horizontal branch models suggests that they cannot be entirely explained with a spread in helium content.

Estimation of Acid-Hydrolyzed Cellulose Fiber Size Distribution with Exponential and Rosin-Rammler (R-R) Laws

A new method was developed to characterize the cellulose fiber (hardwood dissolving pulp) size distribution after 50 wt% sulfuric acid hydrolysis at different hydrolysis temperatures with exponential and Rosin-Rammler (R-R) laws. The results show that the two above laws can be effective to explain the cellulose hydrolysis process. The exponential and the R-R laws were found to be well fitted to the sulfuric acid hydrolyzed cellulose fiber length distribution. The cumulative number distribution from Fiber Tester was shown to fit the exponential distribution well, while the cumulative mass distribution obtained from the acid hydrolysis was found to be suitable to the R-R law via an approximation process. The results from SEM analyses also supported the above conclusions. This approach can be used to characterize the cellulosic fiber properties before a further process of biorefinery, nanocellulose preparation, or other application of lignocellulosic fibers.

Study of the cumulative number distribution of charged particles produced in He12C interactions at 4.2 A GeV/c

The behavior of the cumulative number distribution along with maximum values of cumulative number of all charged particles (i.e. protons, π±-mesons) produced in He12C-interactions at 4.2 A GeV/c from experimental and simulation data coming from cascade evaporation model has been analyzed in this paper. One could see four different regions in the distributions of cumulative number for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two different regions for negative and positive pions respectively but there is totally absence of the cumulative area for both positive and negative pions. The simulation data obtained from Cascade code could reproduced agreeably the distributions of the cumulative number for protons as well as for maximum values of cumulative number distribution.

Extreme [O iii] Emitters at z ∼ 0.5

Abstract We have found a sample of extreme emission-line galaxies (EELGs) with strong [O iii]λ5007 emission at z ∼ 0.5. Using broadband photometric selection and requiring small uncertainties in photometry, we searched the 14th Data Release of the Sloan Digital Sky Survey (SDSS) and found 2658 candidates with strong i-band excess (i – z ≤ r – i – 0.7). We further obtained 649 SDSS spectra of these objects, and visually identified 22 [O iii] emitters lying at 0.40 < z < 0.63. Having constructed their ultraviolet–infrared spectral energy distributions, we found that they have fairly blue r – W2 and red W1 – W4 colors, indicative of strong, warm dust emission. Their rest-frame [O iii]λ5007 equivalent widths are mostly 200–600 Å, and their high [O iii]λ5007/Hβ ratios put them at the boundary of star-forming galaxies and active galactic nuclei on line ratio classification diagrams. The typical E(B–V) and electron temperature of [O iii] emitters are ∼0.1–0.3 mag and ∼104 K, respectively. The lowest metallicity of our [O iii] emitters with S/N[O iii]λ4363 > 3 is 12 + log(O/H) = , with a median value of . Our [O iii] emitters exhibit remarkably high line luminosity—18/22 have L [O iii]λ5007 > 5 × 1042 erg s−1 and 5/22 have L [O iii]λ5007 > 1043 erg s−1. Their estimated volume number density at z ∼ 0.5 is ∼2 × 10−8 Mpc−3, with L [O iii]λ5007 down to ∼3 × 1042 erg s−1. The cumulative number distribution of EELGs across different redshifts is indicative of a strong redshift evolution at the bright end of the [O iii] luminosity function.

Study of the Cumulative Number Distribution of Charged Particles Produced in d12C-Interactions at 4.2 A GeV/c

In this paper the behaviour of the cumulative number distribution and the maximum values of cumulative number in an event of all charged particles (protons,π±-mesons) produced in p12C-interctions at 4.2 A GeV/c from experimental and simulation data has been analysed. One could see four different regions in the cumulative number distributions for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two and three different regions for negative and positive pions respectively but there is totally absence of the cumulative area for negative pions but there are few positive pions in the cumulative area. The simulation data obtained from Cascade code cannot describe satisfactorily the distributions of the cumulative number for protons and positive and negative pions but in case of particles with maximum values of cumulative number cascade code can describe the behaviour of cumulative number distribution well.

Study of the Cumulative Number Distribution of Charged Particles Produced in p12C-Interactions at 4.2 A GeV/c

In this paper the behaviour of the cumulative number distribution and the maximum values of cumulative number in an event of all charged particles (protons,π±-mesons) produced in p12C-interctions at 4.2 A GeV/c from experimental and simulation data has been analysed. One could see four different regions in the cumulative number distributions for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two and three different regions for negative and positive pions respectively but there is totally absence of the cumulative area for negative pions but there are few positive pions in the cumulative area. The simulation data obtained from Cascade code cannot describe satisfactorily the distributions of the cumulative number for protons and positive and negative pions but in case of particles with maximum values of cumulative number cascade code can describe the behaviour of cumulative number distribution well.

Power Scaling and Seasonal Changes of Floe Areas in the Arctic East Siberian Sea

The cumulative number versus floe area distribution of seasonal sea floes from six satellite images of the Arctic Ocean during the summer breakup and melting is fit by two scale-invariant power law scaling regimes for floe areas ranging from 30 to 28,400,000 m2. Scaling exponents, β, for larger floe areas range from −0.6 to −1.0 with an average of −0.8. Scaling exponents, β, for smaller floe areas range from −0.3 to −0.6 with an average of −0.5. The inflection point between the two scaling regimes ranges from 283 × 102 to 4850 × 102 m2 and generally moves from larger to smaller floe areas through the summer melting season. The stability of the power scaling results is demonstrated for two of the images by dividing each in half and analyzing each half separately, with the result that the scaling exponents and the size of the inflection points are nearly the same for each half as for the whole image. We propose that the two scaling regimes and the inflection between them are established during the initial breakup of sea ice solely by the process of fracture. The distributions of floe size regimes retain their scaling exponents as the floe pack evolves from larger to smaller floe areas from the initial breakup through the summer season, due to grinding, crushing, fracture, and melting. The scaling exponents for floe area distribution are in the same range as those reported in previous studies of Arctic floes and for the single scaling exponents found for crushed and ground geologic materials including streambed gravel, lunar debris, and artificially crushed quartz. The single scaling exponent found for fault gouge falls below the range for floes possibly because the fracturing and grinding process in fault gouge takes place under high confining pressure. A probabilistic model of fragmentation is proposed that generates a single power law scaling distribution of fragment size.

A reproducible method to determine the meteoroid mass index

Context. The determination of meteoroid mass indices is central to flux measurements and evolutionary studies of meteoroid populations. However, different authors use different approaches to fit observed data, making results difficult to reproduce and the resulting uncertainties difficult to justify. The real, physical, uncertainties are usually an order of magnitude higher than the reported values. Aims. We aim to develop a fully automated method that will measure meteoroid mass indices and associated uncertainty. We validate our method on large radar and optical datasets and compare results to obtain a best estimate of the true meteoroid mass index. Methods. Using MultiNest, a Bayesian inference tool that calculates the evidence and explores the parameter space, we search for the best fit of cumulative number vs. mass distributions in a four-dimensional space of variables ($a,b,X_1,X_2$). We explore biases in meteor echo distributions using optical meteor data as a calibration dataset to establish the systematic offset in measured mass index values. Results. Our best estimate for the average de-biased mass index for the sporadic meteoroid complex, as measured by radar appropriate to the mass range $10^{-3} > \mathrm{m} > 10^{-5}$ g, was $s=-2.10 \pm 0.08$. Optical data in the $10^{-1} > \mathrm{m} > 10^{-3}$ g range, with the shower meteors removed, produced $s=-2.08 \pm 0.08$. We find the mass index used by Grun et al. 1985 is substantially larger than we measure in the $10^{-4} < m < 10^{-1}$ g range.

Assessing tephra total grain-size distribution: Insights from field data analysis

Abstract The Total Grain-Size Distribution (TGSD) of tephra deposits is crucial for hazard assessment and provides fundamental insights into eruption dynamics. It controls both the mass distribution within the eruptive plume and the sedimentation processes and can provide essential information on the fragmentation mechanisms. TGSD is typically calculated by integrating deposit grain-size at different locations. The result of such integration is affected not only by the number, but also by the spatial distribution and distance from the vent of the sampling sites. In order to evaluate the reliability of TGSDs, we assessed representative sampling distances for pyroclasts of different sizes through dedicated numerical simulations of tephra dispersal. Results reveal that, depending on wind conditions, a representative grain-size distribution of tephra deposits down to ∼100 μm can be obtained by integrating samples collected at distances from less than one tenth up to a few tens of the column height. The statistical properties of TGSDs representative of a range of eruption styles were calculated by fitting the data with a few general distributions given by the sum of two log-normal distributions (bi-Gaussian in Φ -units), the sum of two Weibull distributions, and a generalized log-logistic distribution for the cumulative number distributions. The main parameters of the bi-lognormal fitting correlate with height of the eruptive columns and magma viscosity, allowing general relationships to be used for estimating TGSD generated in a variety of eruptive styles and for different magma compositions. Fitting results of the cumulative number distribution show two different power law trends for coarse and fine fractions of tephra particles, respectively. Our results shed light on the complex processes that control the size of particles being injected into the atmosphere during volcanic explosive eruptions and represent the first attempt to assess TGSD on the basis of pivotal physical quantities, such as magma viscosity and plume height. Our empirical method can be used to assess the main features of TGSD necessary for numerical simulations aimed to real-time forecasting and long-term hazard assessment when more accurate field-derived TGSDs are not available.

Modeling the seasonal evolution of the Arctic sea ice floe size distribution

Abstract To better simulate the seasonal evolution of sea ice in the Arctic, with particular attention to the marginal ice zone, a sea ice model of the distribution of ice thickness, floe size, and enthalpy was implemented into the Pan-arctic Ice–Ocean Modeling and Assimilation System (PIOMAS). Theories on floe size distribution (FSD) and ice thickness distribution (ITD) were coupled in order to explicitly simulate multicategory FSD and ITD distributions simultaneously. The expanded PIOMAS was then used to estimate the seasonal evolution of the Arctic FSD in 2014 when FSD observations are available for model calibration and validation. Results indicate that the simulated FSD, commonly described equivalently as cumulative floe number distribution (CFND), generally follows a power law across space and time and agrees with the CFND observations derived from TerraSAR-X satellite images. The simulated power-law exponents also correlate with those derived using MODIS images, with a low mean bias of –2%. In the marginal ice zone, the modeled CFND shows a large number of small floes in winter because of stronger winds acting on thin, weak first-year ice in the ice edge region. In mid-spring and summer, the CFND resembles an upper truncated power law, with the largest floes mostly broken into smaller ones; however, the number of small floes is lower than in winter because floes of small sizes or first-year ice are easily melted away. In the ice pack interior there are fewer floes in late fall and winter than in summer because many of the floes are “welded” together into larger floes in freezing conditions, leading to a relatively flat CFND with low power-law exponents. The simulated mean floe size averaged over all ice-covered areas shows a clear annual cycle, large in winter and smaller in summer. However, there is no obvious annual cycle of mean floe size averaged over the marginal ice zone. The incorporation of FSD into PIOMAS results in reduced ice thickness, mainly in the marginal ice zone, which improves the simulation of ice extent and yields an earlier ice retreat.

Dynamic fragmentation of shells: scale effects

The effect of the diameter of the shells of structural steel (0.6% C) on the parameters of the cumulative number distribution of fragments by mass and the cumulative mass distribution on fragment length is studied. We tested geometrically similar closed cylinders of different diameters with different wall thicknesses, but maintaining a constant ratio of wall thickness to diameter of the shells equal to 0.175. Detonation velocity and pressure were 8300 m/s and 27 GPa, respectively.It was found that statistical fragment distributions by mass of the shells of different diameters are well described by the linear exponential relations, and with decreasing shell diameter, indices in these relations equal to reciprocal value of the characteristic mass increases. The diameter of the shell may affect the indices of cumulative mass distributions of fragments along their length described by a power function. With the increase in shell diameter, exponents in these equations are reduced, and the distributions are shifted to a shorter length fragments. These changes in the character and location of distributions are explained by change in the fragmentation mechanism. In the diagram, plotted using of the cumulated mass distributions on the fragment length for shells with different diameters, three parts corresponding to the three regimes of fragmentation is marked out.The initial stage of fragmentation of shells of small diameter (section I of the mass-fragment length distribution) is connected with the formation of small but numerous fragments limited by initial shear cracks on the inner surface of the shell. In the middle section II, which is linear in double logarithmic coordinates, the main spectrum fragments are formed, and this process develops steadily on the section II a, and with acceleration on the section II b, probably due to the transition from the shear to radial rupture fracture, accompanied by an increase in thickness of the fragments. On the last section III, corresponding to the fragment distribution of shell with the largest diameter, the length of the fragments is growing, but the cumulative mass remains almost constant, that is likely due to the formation of a relatively small number of longitudinal fragments of lesser thickness.

Sea ice floe size distribution in the marginal ice zone: Theory and numerical experiments

AbstractTo better describe the state of sea ice in the marginal ice zone (MIZ) with floes of varying thicknesses and sizes, both an ice thickness distribution (ITD) and a floe size distribution (FSD) are needed. In this work, we have developed a FSD theory that is coupled to the ITD theory of Thorndike et al. (1975) in order to explicitly simulate the evolution of FSD and ITD jointly. The FSD theory includes a FSD function and a FSD conservation equation in parallel with the ITD equation. The FSD equation takes into account changes in FSD due to ice advection, thermodynamic growth, and lateral melting. It also includes changes in FSD because of mechanical redistribution of floe size due to ice ridging and, particularly, ice fragmentation induced by stochastic ocean surface waves. The floe size redistribution due to ice fragmentation is based on the assumption that wave‐induced breakup is a random process such that when an ice floe is broken, floes of any smaller sizes have an equal opportunity to form, without being either favored or excluded. To focus only on the properties of mechanical floe size redistribution, the FSD theory is implemented in a simplified ITD and FSD sea ice model for idealized numerical experiments. Model results show that the simulated cumulative floe number distribution (CFND) follows a power law as observed by satellites and airborne surveys. The simulated values of the exponent of the power law, with varying levels of ice breakups, are also in the range of the observations. It is found that floe size redistribution and the resulting FSD and mean floe size do not depend on how floe size categories are partitioned over a given floe size range. The ability to explicitly simulate multicategory FSD and ITD together may help to incorporate additional model physics, such as FSD‐dependent ice mechanics, surface exchange of heat, mass, and momentum, and wave‐ice interactions.

Ejecta Size Distribution Resulting from Hypervelocity Impacts between Aluminum Alloys

We investigated the effects of impact velocity on ejecta size when aluminum alloy 2017-T4 spheres with a diameter of 3.2 mm impacted aluminum alloy 6061-T6 targets with a thickness of 30 mm at velocities of 2 to 7 km/s. We used a two-stage light-gas gun at the Institute of Space and Astronautical Science (ISAS)/Japan Aerospace Exploration Agency (JAXA). To examine the scattering angles of the ejecta, the following was placed 50 mm in front of the target: a witness plate (150 mm × 150 mm, 2 mm in thickness) made of copper with a hole of 30 mm. The ejection behaviors of fragments were observed using a high-speed video camera. The size distributions of the ejecta were examined in detail. The cumulative number of ejecta was proportional to the square of the impact velocity; in other words, to the impact energy of the projectiles. An experimental formula was created by curve fitting of the cumulative number distribution of the projected areas to a bilinear exponential distribution model when the aluminum alloy spheres struck the aluminum alloy targets.

Impacts experiments onto heterogeneous targets simulating impact breccia: Implications for impact strength of asteroids and formation of the asteroid families

A series of impact experiments onto solid decimeter-sized cylinders made of porous gypsum admixed with approximately 1cm-sized pebbles have been performed. The target densities and their heterogeneous structures could be representative of those of the asteroids Ida, Eros and many others, because asteroid sub-surface could be the consolidated boulders made by self-compaction and/or by impact compaction. Impact velocities in the experiments ranged from 2.0km/s to 6.7km/s (collision velocity in the asteroid main belt is approximately 5km/s). It was found that the slope of the cumulative number distribution of post-impact fragments strongly depends on the specific energy of the impact. The presence of pebbles strongly influences the impact strength of the target as well as the size distribution of the post-impact fragments. Results of the experiments presented here are aimed at identifying the analogy between the laboratory results and the damage of small asteroids or their catastrophic disruption after impacts.

OS1919 斜め衝突におけるクレータ形状とイジェクタサイズ

The effects of oblique impact angle on ejecta fragment size were investigated by striking aluminum alloy 6061-T6 targets with 3.2-mm-diameter aluminum alloy 2017-T4 spheres at velocities 4 km/s. The two-stage lighet-gas gun at the Institute of Space and Aeronautical Science (ISAS)/ Japan Aerospace Exploration Agency (JAXA), was used for the experiments. The cumulative number of ejecta was proportional to the square of the vertical-direction component of the impact velocity. The experimental formula for the cumulative number distribution of ejecta size was created using bilinear exponential distribution.

Ejecta Size Distribution Resulting from Hypervelocity Impact of Spherical Projectiles on CFRP Laminates

The size distributions of ejecta resulting from projectile perforation of CFRP (carbon fiber reinforced plastic) laminates were examined. The shape of the ejecta cone and the debris cloud was observed using a high-speed video camera. The ejecta fragments were collected from the test chamber after impact experiments. The number of fragments ejected on the front side of the target was altered by the impact velocity. Conversely, regardless of impact velocity, the number of fragments ejected on the rear side of the target was almost the same.The results were also compared with the results of NASA's breakup model. The slope on the cumulative number distribution curve of characteristic length, LC, was almost the same as that of NASA's breakup model. The area-to-mass ratio distribution of ejecta fragments from CFRP laminates ranged within and above the area surrounded by ±3σ of NASA's breakup model.

Two novel NPHS1 mutations in a Chinese family with congenital nephrotic syndrome

Congenital nephrotic syndrome of the Finnish type (CNF) is a lethal, autosomal recessive disorder mainly caused by mutations in the NPHS1 gene; it is found at a relatively high frequency in Finns. We investigated the disease-causing mutations in a Chinese family with CNF and developed a prenatal genetic diagnosis for their latest pregnancy. Mutation analysis was made of all exons and exon/intron boundaries of NPHS1 in the fetus, parents and 50 unrelated controls using PCR and direct sequencing. A heterozygous nonsense mutation within exon 20 (c.2783C>A) and a missense mutation within exon 17 (c.2225T>C) in NPHS1 were detected in the proband's father and mother, respectively, but were not found in the fetus or in 50 unrelated controls. Two novel mutations of c.2783C>A and c.2225T>C in NPHS1 were found to be causative in this Chinese CNF family with no known Finnish ancestry. The most recent sibling did not inherit these two mutations and hence was unaffected with CNF. Determining the cumulative number and ethnic distribution of known mutations can help expedite further study of the pathogenesis of CNF.