Cumulative Size Distribution Research Articles

A Fractal Model of Hydraulic Conductivity for Saturated Frozen Soil

In cold regions, hydraulic conductivity is a critical parameter for determining the water flow in frozen soil. Previous studies have shown that hydraulic conductivity hinges on the pore structure, which is often depicted as the pore size and porosity. However, these two parameters do not sufficiently represent the pore structure. To enhance the characterization ability of the pore structure, this study introduced fractal theory to investigate the influence of pore structure on hydraulic conductivity. In this study, the pores were conceptualized as a bundle of tortuous capillaries with different radii and the cumulative pore size distribution of the capillaries was considered to satisfy the fractal law. Using the Hagen-Poiseuille equation, a fractal capillary bundle model of hydraulic conductivity for saturated frozen soil was developed. The model validity was evaluated using experimental data and by comparison with previous models. The results showed that the model performed well for frozen soil. The model showed that hydraulic conductivity was related to the maximum pore size, pore size dimension, porosity and tortuosity. Of all these parameters, pore size played a key role in affecting hydraulic conductivity. The pore size dimension was found to decrease linearly with temperature, the maximum pore size decreased with temperature and the tortuosity increased with temperature. The model could be used to predict the hydraulic conductivity of frozen soil, revealing the mechanism of change in hydraulic conductivity with temperature. In addition, the pore size distribution was approximately estimated using the soil freezing curve, making this method could be an alternative to the mercury intrusion test, which has difficult maneuverability and high costs. Darcy’s law is valid in saturated frozen silt, clayed silt and clay, but may not be valid in saturated frozen sand and unsaturated frozen soil.

VOLUME BASED CLOSED-CYCLE HARDGROVE GRINDABILITY METHOD

This paper deals with the development of a volume based closed-cycle grindability test method based on the recently introduced Universal Hardgrove mill and procedure. Five model materials with various origin and material characteris- tics (hardness, grindability, heterogeneity) were chosen for the experiments, i.e. limestone, quartz, andesite, basalt and cement clinker. The grindability of the material was characterized simultaneously in four various ways: 1) the standard Hardgrove Grindability test (HGI), 2) Bond work index calculated from HGI, 3) the conventional Bond test and 4) the closed-cycle volume based grindability test in the Universal Hardgrove mill. The grindability coefficient (G), and the cumulative particle size distribution of 80% passing size (x80) of the product of the closed-cycle Hardgrove test were determined. Relative deviation of the above parameters was very good (in most cases lower than 3%) which indicates the new proposed method as a robust procedure for rapid determination of specific grinding energy of closed cycle grinding in ring mills. Therefore, this test is able to ease the optimization of grinding conditions relatively fast and reliably.

Process control and in vitro/in vivo evaluation of aripiprazole sustained-release microcrystals for intramuscular injection

This work describes the preparation of aripiprazole sustained-release microcrystals for intramuscular injection, through recrystallization, drying, wet grinding, and solidification steps, which had a great impact on the product quality. Here, we evaluated the crystal form of the drug in each step by differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD), and fourier transform infrared spectroscopy (FT-IR), demonstrating that there is no change in the crystal form of aripiprazole monohydrate (H1) during grinding and freeze-drying. Microscopy and scanning electron microscopy (SEM) data showed that freeze-drying had no effect on the morphology of milled H1, and thermal gravimetric analysis (TGA) results showed that the freeze-dried formulation had acceptable water content. In particular, in this study, a similarity factor fitting was applied to determine the similarity of the particle size cumulative distribution curve, and the similarity factor value (99.00) showed that there was no change in the particle size distribution before and after freeze-drying. A two-chamber transmembrane method was used to investigate the in vitro release of the aripiprazole sustained-release microcrystal (ALSI) and commercial preparations (Abilify Maintena®). The similarity factor fitting of in vitro release profiles and drug cumulative release curves in vivo yielded similarity factor values of 98.00 and 95.43, respectively, indicating similar in vitro release and in vivo bioavailability of rats between the ALSI and Abilify Maintena®. A single-dose administration could produce long-term effects for a month. For a microcrystalline suspension, in addition to the conventional quality control indicators, the similarity of the cumulative particle size distribution, the in vitro release profile, and the similarity of the drug release percentage in vivo can be used to reflect product quality and process control.

“TNOs are Cool”: A survey of the trans-Neptunian region

Context.A group of trans-Neptunian objects (TNOs) are dynamically related to the dwarf planet 136108 Haumea. Ten of them show strong indications of water ice on their surfaces, are assumed to have resulted from a collision, and are accepted as the only known TNO collisional family. Nineteen other dynamically similar objects lack water ice absorptions and are hypothesized to be dynamical interlopers.Aims.We have made observations to determine sizes and geometric albedos of six of the accepted Haumea family members and one dynamical interloper. Ten other dynamical interlopers have been measured by previous works. We compare the individual and statistical properties of the family members and interlopers, examining the size and albedo distributions of both groups. We also examine implications for the total mass of the family and their ejection velocities.Methods.We use far-infrared space-based telescopes to observe the target TNOs near their thermal peak and combine these data with optical magnitudes to derive sizes and albedos using radiometric techniques. Using measured and inferred sizes together with ejection velocities, we determine the power-law slope of ejection velocity as a function of effective diameter.Results.The detected Haumea family members have a diversity of geometric albedos ~0.3–0.8, which are higher than geometric albedos of dynamically similar objects without water ice. The median geometric albedo for accepted family members ispV= 0.48−0.18+0.28, compared to 0.08−0.05+0.07for the dynamical interlopers. In the size rangeD= 175−300 km, the slope of the cumulative size distribution isq= 3.2−0.4+0.7for accepted family members, steeper than theq= 2.0 ± 0.6 slope for the dynamical interlopers withD< 500 km. The total mass of Haumea’s moons and family members is 2.4% of Haumea’s mass. The ejection velocities required to emplace them on their current orbits show a dependence on diameter, with a power-law slope of 0.21–0.50.

An experimental study on microstructure of leachate-polluted stabilized clay

Clay-solidified grouting curtain (CSGC) is a new kind of vertical barrier for remediating unregulated waste disposal sites in China that combines vertical-barrier and cement-based solidification-stabilization treatment techniques. The cement, stabilizing agents and landfill leachate clearly influence penetration. Although CSGC is becoming widely used because it is effective and economical, little is known about how it works. There is no clear consensus on the penetration mechanism, especially under actual continuous leachate percolation. The present work, therefore, studies the microstructure of CSGC under actual continuous leachate percolation. The cement and self-development stabilizing agents (CERSM-B) and their combined effect on the cumulative intrusion and pore size distribution were investigated using mercury intrusion porosimetry and scanning electron microscope images. The experimental results demonstrated that the unhydrated cement particles first create a large pore space. With increasing cement content, cementation products fill the large pores, thus decreasing the total pore volume. Fine-needle hydration ettringite crystal and calcium silicate hydrate gels are found when the cement content is below 15%. Stabilizing agents (CERSM-B) play an important role in the microstructure of CSGC. A close structure of flaky crystals with small, infrequent pores can be observed in samples treated with stabilizing agents (CERSM-B). However, adding too many stabilizing agents (CERSM-B) may increase the continuity of macropores. The peak pore size distribution and corresponding pore size increase with increasing dosage of stabilizing agents (CERSM-B). In engineering applications, the recommended range of cement and stabilizing agents (CERSM-B) is 15–20% percent clay and 7.5–10% cement.

Fractal analysis of low attenuation clusters on computed tomography in chronic obstructive pulmonary disease

BackgroundThe fractal dimension characterizing the cumulative size distribution of low attenuation area (LAA) clusters, identified with a fixed threshold such as − 950 Hounsfield Units (HU), on computed tomography (CT) sensitively detects parenchymal destruction in chronic obstructive pulmonary disease (COPD) even when the percent LAA (LAA%), a standard emphysema index, is unchanged. This study examines whether the cumulative size distribution of LAA clusters, defined with thresholds of the 15th, 25th, and 35th percentiles of a CT density histogram instead of the fixed-threshold of − 950 HU, exhibits a fractal property and whether its fractal dimension (D’15, D’25, and D’35, respectively) provides additional structural information in emphysematous lungs that is difficult to detect with the conventional − 950-HU-based fractal dimension (D950).MethodsChest inspiratory CT scans and pulmonary functions were cross-sectionally examined in 170 COPD subjects. A proxy for the inspiration level at CT scan was obtained by dividing CT-measured total lung volume (CT-TLV) by physiologically measured total lung capacity. Moreover, long-term (> 5 years) changes in D950 and the new fractal dimensions were longitudinally evaluated in 17 current and 42 former smokers with COPD.ResultsD950, but not D’15, D’25, or D’35 was weakly correlated with the proxy for the inspiration. D950, D’25, and D’35 but not D’15 correlated with LAA% and diffusion capacity. In the long-term longitudinal study, LAA% was increased and D950 and D’35 were decreased in both current and former smokers, while D’25 was decreased only in current smokers and D’15 was not changed in either group. The longitudinal changes in D’25 but not those in LAA%, D950, D’15, and D’35 were greater in current smokers than in former smokers. This greater change in D’25 in current smokers was confirmed after adjusting the change in CT-TLV and the baseline D’25.ConclusionsD’25 reflects diffusion capacity in emphysematous lungs and is robust against inspiration levels during CT scans. This new fractal dimension might provide additional structural information that is difficult to detect with the conventional D950 and LAA% and allow for more sensitive evaluation of emphysema progression over time.

Implications of the small spin changes measured for large Jupiter-family comet nuclei

Rotational spin-up due to outgassing of comet nuclei has been identified as a possible mechanism for considerable mass-loss and splitting. We report a search for spin changes for three large Jupiter-family comets (JFCs): 14P/Wolf, 143P/Kowal-Mrkos, and 162P/Siding Spring. None of the three comets has detectable period changes, and we set conservative upper limits of 4.2 (14P), 6.6 (143P) and 25 (162P) minutes per orbit. Comparing these results with all eight other JFCs with measured rotational changes, we deduce that none of the observed large JFCs experiences significant spin changes. This suggests that large comet nuclei are less likely to undergo rotationally-driven splitting, and therefore more likely to survive more perihelion passages than smaller nuclei. We find supporting evidence for this hypothesis in the cumulative size distributions of JFCs and dormant comets, as well as in recent numerical studies of cometary orbital dynamics. We added 143P to the sample of 13 other JFCs with known albedos and phase-function slopes. This sample shows a possible correlation of increasing phase-function slopes for larger geometric albedos. Partly based on findings from recent space missions to JFCs, we hypothesise that this correlation corresponds to an evolutionary trend for JFCs. We propose that newly activated JFCs have larger albedos and steeper phase functions, which gradually decrease due to sublimation-driven erosion. If confirmed, this could be used to analyse surface erosion from ground and to distinguish between dormant comets and asteroids.

Dynamic Fragmentation of Jointed Rock Blocks During Rockslide‐Avalanches: Insights From Discrete Element Analyses

AbstractThe dynamic fragmentation of jointed rock blocks during rockslide avalanches has been investigated by discrete element method simulations for a multiple arrangement of a rock block sliding over a simple slope geometry. The rock blocks are released along an inclined sliding plane and subsequently collide onto a flat horizontal plane at a sharp kink point. The contact force chains generated by the impact appear initially at the bottom frontal corner of the rock block and then propagate radially upward to the top rear part of the block. The jointed rock blocks exhibit evident contact force concentration and discontinuity of force wave propagation near the joint, associating with high energy dissipation of granular dynamics. The corresponding force wave propagation velocity can be less than 200 m/s, which is much smaller than that of an intact rock (1,316 m/s). The concentration of contact forces at the bottom leads to high rock fragmentation intensity and momentum boosts, facilitating the spreading of many fine fragments to the distal ends. However, the upper rock block exhibits very low rock fragmentation intensity but high energy dissipation due to intensive friction and damping, resulting in the deposition of large fragments near the slope toe. The size and shape of large fragments are closely related to the orientation and distribution of the block joints. The cumulative fragment size distribution can be well fitted by the Weibull's distribution function, with very gentle and steep curvatures at the fine and coarse size ranges, respectively. The numerical results of fragment size distribution can match well some experimental and field observations.

Particle size effects on soil reflectance explained by an analytical radiative transfer model

Experimental evidence points to an intimate link between soil reflectance, R, and particle/aggregate diameter, D. Based on this strong correlation, various statistical methods for remote and proximal sensing of soil texture and hydraulic properties have been developed. In this paper, we derive a more fundamental and physically-based analytical radiative transfer model that yields a closed-form functional R(D) relationship for dry soils. Despite several simplifying assumptions, the proposed model shows good agreement with measured spectral reflectance (350–2500 nm) data of six soils covering a broad range of textures, colors, and mineralogies. The proposed S-shaped R(D) function resembles cumulative particle and pore size distributions as well as the soil water characteristic function. These analogies may potentially lead to new avenues for developing novel physical models for extracting important soil properties from remotely sensed reflectance data.

Hypervelocity impact fragmentation of basalt and shale projectiles

Results are presented for the fragmentation of projectiles in laboratory experiments. 1.5 mm cubes and spheres of basalt and shale were impacted onto water at normal incidence and speeds from 0.39 to 6.13 km s−1; corresponding to peak shock pressures 0.7–32 GPa. Projectile fragments were collected and measured (over 100,000 fragments in some impacts, at sizes down to 10 µm). Power laws were fitted to the cumulative fragment size distributions and the evolution of the exponent vs. impact speed and peak shock pressure found. The gradient of each of these power laws increased with increasing impact speed/peak shock pressure. The percentage of the projectiles recovered in the impacts was found and used to estimate projectile remnant survival in different solar system impact scenarios at the mean impact speed appropriate to that scenario. For Pluto, the Moon and in the asteroid belt approximately 55%, 40% and 15%, respectively, of an impactor could survive and be recovered at an impact site. Finally, the catastrophic disruption energy densities of basalt and shale were measured and found to be 24 × 104 J kg−1 and 9 × 104 J kg−1, respectively, a factor of ∼2.5 difference. These corresponded to peak shock pressures of 1 to 1.5 GPa (basalt), and 0.8 GPa (shale). This is for near normal-incidence impacts where tensile strength is dominant. For shallow angle impacts we suggest shear effects dominate, resulting in lower critical energy densities and peak shock pressures. We also determine a method to ascertain information about fragment sizes in solar system impact events using a known size of impactor. The results are used to predict projectile fragments sizes for the Veneneia and Rheasilvia crater forming impacts on Vesta, and similar impacts on Ceres.

Evolution of tar ball aggregates in Caspian Sea: Implications of connectionist tools linked with image analysis

Intensive petroleum activities in the Caspian Sea lead to a considerable oil pollution in the various parts of this region. Tar balls stranded on the south coast of the Caspian Sea evidently cause (and accelerate) this serious environmental threat. In this study, a poloxamine copolymeric surfactant is used to agglomerate tar balls in a system containing the solvent, antisolvent, and Caspian Sea tar balls. This research work is conducted to determine the cumulative size distribution of tar balls in the presence of a poloxamine copolymer. The evolution of tar ball aggregates is experimentally and theoretically investigated and the steady‐state size distribution of the tar balls is estimated by Back Propagation Artificial Neural Network (ANN‐BP) and a new evolutionary algorithm, called Imperialist Competitive Algorithm (ICA). The average size of tar ball aggregates increases with time and reaches a maximum value. It then declines and eventually approaches a steady‐state condition so that an almost constant size for the particles is attained. The statistical analysis shows a good agreement between the predicted values (obtained by the neural network combined with ICA, known as ANN‐ICA) and the real data for the steady‐state size distribution of the aggregates. This research study can considerably help to further understand evolution of tar balls (that hit the beaches) and consequently to find effective and economical ways for tar balls removal from the beaches. © 2018 American Institute of Chemical Engineers Environ Prog, 37: 1901–1907, 2018

On soil textural classifications and soil-texture-based estimations

Abstract. The soil texture representation with the standard textural fraction triplet sand–silt–clay is commonly used to estimate soil properties. The objective of this work was to test the hypothesis that other fraction sizes in the triplets may provide a better representation of soil texture for estimating some soil parameters. We estimated the cumulative particle size distribution and bulk density from an entropy-based representation of the textural triplet with experimental data for 6240 soil samples. The results supported the hypothesis. For example, simulated distributions were not significantly different from the original ones in 25 and 85 % of cases when the sand–silt–clay and very coarse+coarse + medium sand − fine + very fine sand − silt+clay were used, respectively. When the same standard and modified triplets were used to estimate the average bulk density, the coefficients of determination were 0.001 and 0.967, respectively. Overall, the textural triplet selection appears to be application and data specific.

Modeling of quantitative relationships between physicochemical properties of active pharmaceutical ingredients and tensile strength of tablets using a boosted tree

Objectives: The aim of this study was to explore the potential of boosted tree (BT) to develop a correlation model between active pharmaceutical ingredient (API) characteristics and a tensile strength (TS) of tablets as critical quality attributes.Methods: First, we evaluated 81 kinds of API characteristics, such as particle size distribution, bulk density, tapped density, Hausner ratio, moisture content, elastic recovery, molecular weight, and partition coefficient. Next, we prepared tablets containing 50% API, 49% microcrystalline cellulose, and 1% magnesium stearate using direct compression at 6, 8, and 10 kN, and measured TS. Then, we applied BT to our dataset to develop a correlation model. Finally, the constructed BT model was validated using k-fold cross-validation.Results: Results showed that the BT model achieved high-performance statistics, whereas multiple regression analysis resulted in poor estimations. Sensitivity analysis of the BT model revealed that diameter of powder particles at the 10th percentile of the cumulative percentage size distribution was the most crucial factor for TS. In addition, the influences of moisture content, partition coefficients, and modal diameter were appreciably meaningful factors.Conclusions: This study demonstrates that BT model could provide comprehensive understanding of the latent structure underlying APIs and TS of tablets.

Mix Design and Flexural Response of Ultra High Performance Fiber Reinforced Concrete (UHPFRC)

The research article addresses on the mix design and investigation of flexural strength development at an increased age of the material is explored through experimental program with addition of hooked end steel fiber, super plasticizer with special densified materials 53 grade cement, micro silica, quartz sand and fine sand. The UHPFRC mix differs from conventional concrete material constitutients by UHPFRC, an Advanced technology Cement based Super plasticized concrete with high workability, improved homogeneity resulting increased compressive strength of the material, the research study is conducted to achieve target flexural strength 25 N/mm2.the material response exhibits improved strain hardening capacity based on the particle packing theory cumulative particle size distribution equations to improve flexural strength cured under elevated temperature accelerates flexural strength yields efficacy of the concrete is highlighted.

A primer on the use of probability generating functions in infectious disease modeling.

We explore the application of probability generating functions (PGFs) to invasive processes, focusing on infectious disease introduced into large populations. Our goal is to acquaint the reader with applications of PGFs, moreso than to derive new results. PGFs help predict a number of properties about early outbreak behavior while the population is still effectively infinite, including the probability of an epidemic, the size distribution after some number of generations, and the cumulative size distribution of non-epidemic outbreaks. We show how PGFs can be used in both discrete-time and continuous-time settings, and discuss how to use these results to infer disease parameters from observed outbreaks. In the large population limit for susceptible-infected-recovered (SIR) epidemics PGFs lead to survival-function based models that are equivalent to the usual mass-action SIR models but with fewer ODEs. We use these to explore properties such as the final size of epidemics or even the dynamics once stochastic effects are negligible. We target this primer at biologists and public health researchers with mathematical modeling experience who want to learn how to apply PGFs to invasive diseases, but it could also be used in an applications-based mathematics course on PGFs. We include many exercises to help demonstrate concepts and to give practice applying the results. We summarize our main results in a few tables. Additionally we provide a small python package which performs many of the relevant calculations.

Radiologic and Functional Analysis of Compensatory Lung Growth After Living-Donor Lobectomy

Whether compensatory lung growth occurs in adult humans is controversial. The aim of this study was to confirm compensatory lung growth by analyzing ipsilateral residual lung after lower lobectomy in living lung transplant donors with quantitative and qualitative computed tomography assessments. Chest computed tomography and pulmonary function tests were performed in 31 eligible donors before and 1 year after donor lobectomy. Ipsilateral residual lung volume was measured with three-dimensional computed tomography volumetry. The computed tomography-estimated volumes of low, middle, and high attenuations in the lung were calculated. Assessment of the D value, a coefficient of the cumulative size distribution of low-density area clusters, was performed to evaluate the structural quality of the residual lung. Postoperative pulmonary function test values were significantly larger than preoperative estimated values. Although postoperative total volume, low attenuation volume, middle attenuation volume, and high attenuation volume of the ipsilateral residual lung were significantly larger than the preoperative volumes, with 50.2%, 50.0%, 41.5%, and 43.1% increase in the median values, respectively (all p < 0.0001), the differences in D values before and after donor lobectomy were not significant (p= 0.848). The total volume of ipsilateral residual lung was increased by more than 600 mL (50%). The volume of ipsilateral residual lung increased, but its structural quality did not change before and after donor lobectomy. The existence of compensatory lung growth in adult humans was suggested by quantitative and qualitative computed tomography assessments.

Difference of the progression of pulmonary cysts assessed by computed tomography among COPD, lymphangioleiomyomatosis, and Birt-Hogg-Dubé syndrome.

Many groups developed the methods to quantitatively analyze low attenuation area (LAA) on chest CT in patients with cystic lung diseases. Especially in COPD, it was reported that the cumulative size distribution of LAA clusters follows a power law characterized by the exponent D, which reflect the fractal dimension of terminal airspace geometry. We hypoyhesized that the quantitative charateristics of LAA clusters including fractal property might indicate the different features of the progression of cysts in cystic lung diseases. The aim of this study was to apply the CT image-based method of characterizing the size distribution of LAA clusters for lymphangioleiomyomatosis (LAM) and Birt-Hogg-Dubé syndrome (BHDS) to disclose their features of the progression of pulmonary cysts. 40 patients with COPD, 52 patients with LAM, and 18 patients with BHDS who had undergone CT scans at our institute between January 2002 and August 2009 were included. Differences among these diseases in the quantitative characteristics of LAA clusters {i.e., extent, number, size, fractal property, and the relationship between these quantitatives} were assessed. The Chi-sqsuare test, unpaired t-test, and one-way analyses of variance with Tukey post-hoc tests were used to compare groups, spline model with an interaction terms were used to assess the relationship between extent and number, and exponential regression model was used to assess the relationship between extent and size. Statistically significant differences separated the three diseases in extent and number (P < 0.001). Number was significantly correlated with extent in COPD (P < 0.001), but was not so in LAM and BHDS when extent exceeded 11.5% and 20.8%, respectively. Size was significantly correlated with extent in COPD and LAM (P < 0.001), but was not so in BHDS. The percentage of CT images with fractal property was higher in COPD than that in LAM and BHDS (95.8%, 92.9% and 63.0%, respectively). In conclusion, our study has demonstrated for the first time the different characteristics of the size distribution of LAA clusters among COPD, LAM and BHDS, and indicated that this method is useful for exploration of the pathophysiology in cystic lung diseases.

Cratering efficiency on coarse-grain targets: Implications for the dynamical evolution of asteroid 25143 Itokawa

Remote sensing observations made by the spacecraft Hayabusa provided the first direct evidence of a rubble-pile asteroid: 25143 Itokawa. Itokawa was found to have a surface structure very different from other explored asteroids; covered with coarse pebbles and boulders ranging at least from cm to meter size. The cumulative size distribution of small circular depressions on Itokawa, most of which may be of impact origin, has a significantly shallower slope than that on the Moon; small craters are highly depleted on Itokawa compared to the Moon. This deficiency of small circular depressions and other features, such as clustered fragments and pits on boulders, suggest that the boulders on Itokawa might behave like armor, preventing crater formation: the “armoring effect”. This might contribute to the low number density of small crater candidates. In this study, the cratering efficiency reduction due to coarse-grained targets was investigated based on impact experiments at velocities ranging from ∼ 70 m/s to ∼ 6 km/s using two vertical gas gun ranges. We propose a scaling law extended for cratering on coarse-grained targets (i.e., target grain size ≳ projectile size). We have found that the crater efficiency reduction is caused by energy dissipation at the collision site where momentum is transferred from the impactor to the first-contact target grain, and that the armoring effect can be classified into three regimes: (1) gravity scaled regime, (2) reduced size crater regime, or (3) no apparent crater regime, depending on the ratio of the impactor size to the target grain size and the ratio of the impactor kinetic energy to the disruption energy of a target grain. We found that the shallow slope of the circular depressions on Itokawa cannot be accounted for by this new scaling law, suggesting that obliteration processes, such as regolith convection and migration, play a greater role in the depletion of circular depressions on Itokawa. Based on the new extended scaling law, we found that the crater retention age on Itokawa is 3–33 Myr in the main belt, which is in good agreement with the cosmic-ray-exposure ages for returned samples from Itokawa which may reflect the age of material a few meters beneath the surface. These ages strongly suggest that the global resurfacing that reset the 1–10 m deep surface layer may have occurred in the main belt long after the possible catastrophic disruption of a rigid parent body of Itokawa suggested by Ar degassing age ( ∼ 1.3 Gyr).

Small Jupiter Trojans Survey with the Subaru/Hyper Suprime-Cam*

Abstract We observed the L4 Jupiter Trojans (JTs) swarm using the Hyper Suprime-Cam attached to the 8.2 m Subaru Telescope on 2015 March 30 (UT). The survey covered ∼26 deg2 of sky area near the opposition and around the ecliptic plane with a 240 s exposure time in the r-band filter through the entire survey. We detected 631 L4 JTs in the survey field with a detection limit of m r = 24.4 mag. We selected 481 objects with absolute magnitude H r &lt; 17.4 mag and heliocentric distance r &lt; 5.5 au as an unbiased sample and then used them to estimate the size distribution. Assuming a geometric albedo of 0.07, the size range of our unbiased sample is ∼2–20 km in diameter (D). We fit a single-slope power law to the cumulative size distribution and found that the best-fit index (b) is b = 1.84 ± 0.05 in . The slope value (α) of the corresponding absolute magnitude distribution ( ) is 0.37 ± 0.01. This α is consistent with that of the faint-end slope presented by Wong &amp; Brown. The size distribution obtained from this survey is slightly different from the results of previous surveys with a similar size range, which reported broken power-law or double power-law slopes in their cumulative size distribution. Our results insist that the slope of b = 1.84 continues from H = 14.0 to at least H = 17.4. Since this work contains the largest L4 JT samples and is 1 mag deeper than the study by Wong &amp; Brown, we believe that our study has obtained the most robust size distribution of small JTs so far. Combining the cataloged L4 JTs and our survey, we show the entire size distribution of L4 JTs up to H r = 17.4 mag.

Application of Three-Parameter Distribution to Approximate the Particle Size Distribution Function of Comminution Products of Dolomitic Type of Copper Ore

AbstractThe paper presents the results of analyze the particle size distribution function of comminution products of dolomitic type of copper ore. The breakage tests for single irregular particles were performed with using a hydraulic press device. The authors prepared five particle size fractions of each material, within ranges: 16-18 mm, 18-20 mm, 20-25 mm, 25-31,5 mm and 31-45 mm. The particle size distribution function of single-particle breakage test was calculated separately for each size fraction. In addition, the cumulative particle size distribution function for five particle size fractions was presented. In theoretical part the study of applied functions of particle size distribution for comminution a set of particles and models of crushing single particles was performed. In that paper the curves of the particle size distribution were approximated by the three-parameter function, which parameters depend on the particle strength and material type. For conformity assessment the model distribution function to the empirical distribution function a residual deviation and non-linear correlation coefficient were calculated. The three-parameter function approximating agrees well with the particle size distribution obtained from experimental data. The dependence of the parameters of a particle size distribution function on the dolomite particle strength was presented. The results indicate the identity of single particle grinding mechanism by slow compression of irregular particles of dolomitic type of copper ore, regardless of the initial particle size.