Cumulative Mass Distribution Research Articles

Cold dust clumps in dynamically hot gas

We present clumps of dust emission from Herschel observations of the Large Magellanic Cloud (LMC) and their physical and statistical properties. We catalog cloud features seen in the dust emission from Herschel observations of the LMC, the Magellanic type irregular galaxy closest to the Milky Way, and compare these features with HI catalogs from the ATCA+Parkes HI survey. Using an automated cloud-finding algorithm, we identify clouds and clumps of dust emission and examine the cumulative mass distribution of the detected dust clouds. The mass of cold dust is determined from physical parameters that we derive by performing spectral energy distribution fits to 250, 350, and 500 micronm emission from SPIRE observations using DUSTY and GRASIL radiative transfer calculation with dust grain size distributions for graphite/silicate in low-metallicity extragalactic environments. The dust cloud mass spectrum follows a power law distribution with an exponent of gamma=-1.8 for clumps larger than 400 solar mass and is similar to the HI mass distribution. This is expected from the theory of ISM structure in the vicinity of star formation.

Fragmentation behaviour in particulate materials processing

Fragmentation simulations are created to provide a basis for understanding how certain particle size distributions emerge in particulate materials processing, such as in atomisation, crushing, or milling. These simulations start with a piece of material that is fractured in a random manner. Subsequent events are governed by simple rules, such as only the largest piece is fractured next, or all pieces are fractured at the same rate, or fracture continues until all of the pieces fall through a screen. Each of these simulations is associated with a sequence practiced in powder formation. Size distribution data and size reduction kinetics are extracted from the simulations. The findings show how uniform distributions and lognormal distributions emerge from random fragmentation events. Empirical laws previously encountered in the field, such as the Rosin–Rammler cumulative particle mass distribution and the Charles equation for particle size reduction, are confirmed by the results.

Distribution of Particulate-Bound Metals for Source Area Snow in the Lake Tahoe Watershed

The porous matrix and long residence time of snow in traffic corridors can result in the accretion of particulate matter (PM) and metals. This temporary repository contributes PM-based and dissolved metals to surrounding environs during snowmelt. This study focused on distribution and settling of PM-based metals (Al, As, Cd, Cr, Cu, Fe, Pb, and Zn) in snow. Snow was sampled from six sites during four winter seasons. PM-based metals are examined herein as a function of PM granulometry, specifically particle-size distributions (PSDs) and PM surface area. Cumulative metal mass distributions across each PSD are modeled as gamma functions. Results indicate Al (15 g/kg) and Fe (4.2 g/kg) are the highest PM-based concentrations; Cd (0.18 mg/kg) and As (4.9 mg/kg) are the lowest. The PM size ( d50 m ) associated with the median metal mass ranges from 179 to 542 μm . The constitutive gamma results are integrated with Hazen’s settling algorithm to model PM-bound metal separation for a sedimentation basin at a local...

Blue hook stars in globular clusters

Blue hook (BHk) stars are a rare class of horizontal branch stars that have so far been found in only very few Galactic globular clusters (GCs). The dominant mechanism for producing these objects is currently still unclear. In order to test if the presence of BHk populations in a given GC is linked to specific physical or structural cluster properties, we have constructed a parent sample of GCs for which existing data are sufficient to establish the presence or absence of BHk populations with confidence. We then compare the properties of those clusters in our parent sample that do contain a BHk population to those that do not. We find that there is only one compelling difference between BHk and non-BHk clusters: all known BHk clusters are unusually massive. However, we also find that the BHk clusters are consistent with being uniformly distributed within the cumulative mass distribution of the parent sample. Thus, while it is attractive to suggest that there is a lower mass cut-off for clusters capable of forming BHk stars, the data do not require this. Instead, the apparent preference for massive clusters could still be a purely statistical effect: intrinsically rare objects can only be found by searching a sufficiently large number of stars.

Drop size distribution below different wet-cooling tower fills

Drop size distribution is measured photographically below three different counter-flow wet-cooling tower fills (cross-fluted film, trickle and fibre cement) and a number of splash grid configurations installed below a trickle fill. The air and water flow rates are varied to investigate their influence on drop size. The data for each test case is presented as a cumulative mass distribution curve, Sauter mean diameter, Rosin–Rammler distribution curve and Rosin–Rammler function. The main objectives are to describe the implemented experimental apparatus and measurement techniques and to determine the drop size distribution beneath different fills and ultimately the drop size reduction capability of grids installed below the fill. An important conclusion is that the Rosin–Rammler distribution curve generally does not fit the measured data adequately and thus should be avoided.

An inhomogeneous model for the Galactic halo: a possible explanation for the spread observed ins- andr-process elements

Aims. We propose an explanation for the considerable scatter of the abundances of neutron capture elements observed in lowmetallicity stars in the solar vicinity, compared to the small star-to-star scatter observed for the α-elements. Methods. We have developed a stochastic chemical evolution model in which the main assumption is a random formation of new stars subject to the condition that the cumulative mass distribution follows a given initial mass function. Results. With our model, we are able to reproduce the different spreads of neutron capture elements and α-elements in low-metallicity stars. Conclusions. The reason for different observed spreads in neutron capture elements and α-elements resides in the random birth of stars, coupled with different stellar mass ranges, from which α-elements and neutron capture elements originate. In particular, the site

Massive Clumps in the NGC 6334 Star‐forming Region

We report observations of dust continuum emission at 1.2 mm toward the star forming region NGC 6334 made with the SEST SIMBA bolometer array. The observations cover an area of $\sim 2$ square degrees with approximately uniform noise. We detected 181 clumps spanning almost three orders of magnitude in mass (3\Msun$-6\times10^3$ \Msun) and with sizes in the range 0.1--1.0 pc. We find that the clump mass function $dN/d\log M$ is well fit with a power law of the mass with exponent -0.6 (or equivalently $dN/dM \propto M^{-1.6}$). The derived exponent is similar to those obtained from molecular line emission surveys and is significantly different from that of the stellar initial mass function. We investigated changes in the mass spectrum by changing the assumptions on the temperature distribution of the clumps and on the contribution of free-free emission to the 1.2 mm emission, and found little changes on the exponent. The Cumulative Mass Distribution Function is also analyzed giving consistent results in a mass range excluding the high-mass end where a power-law fit is no longer valid. The masses and sizes of the clumps observed in NGC 6334 indicate that they are not direct progenitors of stars and that the process of fragmentation determines the distribution of masses later on or occurs at smaller spatial scales. The spatial distribution of the clumps in NGC 6334 reveals clustering which is strikingly similar to that exhibited by young stars in other star forming regions. A power law fit to the surface density of companions gives $\Sigma\propto \theta^{-0.62}$.

Three-dimensional cometary dust coma modelling in the collisionless regime: strengths and weaknesses

Inverse coma and tail modelling of comets based on the method developed by Finson & Probstein is commonly used to analyse cometary coma images. Models of this type often contain a large number of assumptions that may not be constrained unless wide temporal or spectral coverage is available and the comets are bright and at relatively small geocentric distance. They are used to predict physical parameters, such as the mass distribution of the dust, but rarely give assessments of the accuracy of the estimate. A three-dimensional cometary dust coma model in the collisionless regime has been developed to allow the effectiveness of such models to constrain dust coma properties to be tested. The model is capable of simulating the coma morphology for the following input parameters: the comet nucleus shape, size, rotation, emission function (including active fraction and jets), grain velocity distribution (and dispersion), size distribution, dust production rate, grain material and light scattering from the cometary dust. Characterization of the model demonstrates that the mass distribution cannot be well constrained as is often assumed; the cumulative mass distribution index α can only be constrained to within ±0.15. The model is highly sensitive to the input grain terminal velocity distribution so model input can be tested with a large degree of confidence. Complex secondary parameters such as jets, rotation and grain composition all have an effect on the structure of the coma in similar ways, so unique solutions for these parameters cannot be derived from a single optical image alone. Multiple images at a variety of geometries close in time can help constrain these effects. The model has been applied to photometric observations of comets 126P/IRAS and 46P/Wirtanen to constrain a number of physical properties including the dust production rate and mass distribution index. The derived dust production rate (Qdust) for 46P/Wirtanen was 3 +7 /−1.5 kg s −1 at a pre-perihelion heliocentric distance of 1.8 au, and for P/IRAS was 50 +100 /−20 kg s −1 at a pre-perihelion heliocentric distance of 1.7 au; both comets exhibited a mass distribution index α = 0.8 ± 0.15.

The Large‐ and Small‐Scale Structures of Dust in the Star‐forming Perseus Molecular Cloud

We present an analysis of ~3.5 deg2 of submillimeter continuum and extinction data of the Perseus molecular cloud. We identify 58 clumps in the submillimeter map, and we identify 39 structures ("cores") and 11 associations of structures ("super cores") in the extinction map. The cumulative mass distributions of the submillimeter clumps and extinction cores have steep slopes (α ~ 2 and 1.5-2, respectively), steeper than the Salpeter initial mass function (IMF; α = 1.35), while the distribution of extinction super cores has a shallow slope (α ~ 1). Most of the submillimeter clumps are well fit by stable Bonnor-Ebert spheres with 10 K < T < 19 K and 5.5 <(Pext/k) < 6.0. The clumps are found only in the highest column density regions (AV > 5-7 mag), although Bonnor-Ebert models suggest that we should have been able to detect them at lower column densities if they exist. These observations provide a stronger case for an extinction threshold than that found in analysis of less sensitive observations of the Ophiuchus molecular cloud (Johnstone et al.). The relationship between submillimeter clumps and their parent extinction core has been analyzed. The submillimeter clumps tend to lie offset from the larger extinction peaks, suggesting that the clumps formed via an external triggering event, consistent with previous observations.

The specification of armourstone gradings and EN 13383 (2002)

The grading, whether in terms of mass or size distribution of rock, is critical in the design of hydraulic civil engineering works such as breakwaters, coastal protection revetments, river training works and dam face protection. In the quarry, more effort is needed to control these rock properties than all the others. However, in practice, a poor level of understanding of relatively simple statistical concepts and the recent introduction of an elaborate specification system have contributed to many pitfalls in quality control. The acceptable size and mass ranges for consignments of rock materials are set down in the European standard for armourstone, EN 13383:2002 ( BSI 2002 ). Armourstone pieces are substantially coarser than traditional aggregates and typically include large rock blocks sometimes weighing several tonnes. This standard, in force since 2004, introduced a system of standard gradings and requirements. Although similar to that promoted in CIRIA/CUR (1991) , a detailed explanation is long overdue. In this paper, the Rosin–Rammler equation for cumulative mass and size distributions is adopted. A purchaser or designer can then visualize from a single idealized curve, together with acceptance limits, the most reasonable expectation for a specified grading, rather than work with an envelope of acceptable grading limits. The research also draws upon actual mass distributions measured from projects dating from 1991. These are combined with theoretical data sets. The result is a new expression for what has become a contractually important ratio. The ratio is that between the mean mass as given by bulk weighing and counting, and the median mass used by designers. Non-standard grading specification is also treated, providing further background to recommended best practice as presented in the forthcoming update to the 1991 rock manual.

The Mass Spectra of Giant Molecular Clouds in the Local Group

ABSTRACTWe reanalyze the catalogs of molecular clouds in the Local Group to determine the parameters of their mass distributions in a uniform manner. The analysis uses the error‐in‐variables method of parameter estimation, which accounts not only for the variance of the sample when drawn from a parent distribution, but also for errors in the mass measurements. Testing the method shows that it recovers the underlying properties of cumulative mass distribution without bias while accurately reflecting uncertainties in the parameters. Clouds in the inner disk of the Milky Way follow a truncated power‐law distribution with index γ = -1.5 ± 0.1 and maximum mass of 106.5 M⊙. The distributions of cloud mass for the outer Milky Way and M33 show significantly steeper indices (γOMW = -2.1 ± 0.2 and γM33 = -2.9 ± 0.4, respectively), with no evidence of a cutoff. The mass distribution of clouds in the Large Magellanic Cloud has a marginally steeper distribution than the inner disk of the Milky Way (γ = -1.7 ± 0.2) and also shows evidence of a truncation, with a maximum mass of 106.5 M⊙. The mass distributions of molecular clouds vary dramatically across the Local Group, even after accounting for the systematic errors that arise in comparing heterogeneous data and catalogs. These differences should be accounted for in studies that aim to reproduce the molecular cloud mass distributions, or in studies that use the mass spectrum as a parameter in a model.

Explosive Fragmentation of a Thin Ceramic Tube Using Pulsed Power

This study experimentally examined the explosive fragmentation of thin ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin copper wire, and high voltage was applied to the wire using a pulsed power generator. This melted the wire and the resulting vapor put pressure on the ceramic tube, causing it to fragment. We examined the statistical properties of the fragment mass distribution. The cumulative fragment mass distribution obeyed the double exponential or power law with exponential decay. Both distributions agreed well with the experimental data. Finally, we obtained universal scaling for fragmentation, which is applicable to both impact and explosive fragmentation.

Crossover of weighted mean fragment mass scaling in two-dimensional brittle fragmentation

We performed vertical and horizontal sandwich two-dimensional brittle fragmentation experiments. The weighted mean fragment mass was scaled using the multiplicity mu. The scaling exponent crossed over at log(10) mu(c) approximately equal to -1.4 . In the small mu (<< mu(c) ) regime, the binomial multiplicative (BM) model was suitable and the fragment mass distribution obeyed log-normal form. However, in the large mu (>> mu(c) ) regime, in which a clear power-law cumulative fragment mass distribution was observed, it was impossible to describe the scaling exponent using the BM model. We also found that the scaling exponent of the cumulative fragment mass distribution depended on the manner of impact (loading conditions): it was 0.5 in the vertical sandwich experiment and approximately 1.0 in the horizontal sandwich experiment.

The dust mass distribution of comet 81P/Wild 2

The Dust Flux Monitor Instrument (DFMI) made direct measurements of the dust environment in the mass range 10−14 &lt; m &lt; 10−5 kg at comet 81P/Wild 2 during the Stardust flyby on 2 January 2004. We describe the techniques for derivation of the particle mass distribution, including updated calibration for the acoustic subsystem. The dust coma is characterized by “swarms” and “bursts” of particles with large variations of flux on small spatial scales, which may be explained by jets and fragmentation. The mass of the dust coma is dominated by larger particles, as was found for comets 1P/Halley and 26P/Grigg‐Skjellerup. However, almost 80% of the particles were detected many minutes after closest approach at a distance of ∼4000 km, where small grains dominated the detected mass flux. The mass distribution varies on small spatial scales with location in the coma, consistent with the jets and fragmentation inferred from the highly heterogeneous dust spatial distribution. The cumulative mass distribution index α (where the number of particles of mass m or larger, N(m) ∝ m−α) in the coma ranges from 0.3 to 1.1. It is possible that jets and fragmentation occur in all comets but have not previously been well observed due to the limitations of detectors and flyby geometry. We estimate that 2800 ± 500 particles of diameter 15 μm or larger impacted the aerogel collectors, the largest being ∼6 × 10−7 kg (diameter ∼1 mm), which dominates the total collected mass. Of these, only 500 ± 200, representing just 3% of the collected mass, originated in the far postencounter region.

Measurement of particle deposition in industrial ducts

A new method was developed to measure particle deposition in industrial ducts. Greased wire grids were used to capture particles in situ by impaction upstream and downstream of a duct bend. Particles were recovered from the grid using a hexane extraction procedure. Cumulative mass distributions of the recovered particles were determined with a sedimentation pipette; these distributions were then used to compute particle deposition by size. As these procedures were compatible with solid particles only, the interior surface of the bend was coated with grease to eliminate solid particle bounce so that results obtained here could be compared to published models for droplet deposition in bends. In a 20.3-cm-diameter, 90° bend at an air velocity of 27.4 m s −1 , deposition increased from approximately 35% at 15 μm to nearly 100% at 100 μm . These data generally agreed with models developed for small sampling tubes.

Scaling of impact fragmentation near the critical point.

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low-impact-energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control-parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power law. The exponent of this power law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher-order moments of the fragment mass distributions, and obtained multiscaling exponents that agreed with those of the simple biased cascade model.

Clusters in the inner spiral arms of M 51: The cluster IMF and the formation history

We present the results of an analysis of the HST–WFPC2 observations of the interacting galaxy M 51. From the observations in 5 broadband filters (UBVRI) and two narrowband filters (Hα and [OIII]) we study the cluster population in a region of 3.2 kpc2 in the inner spiral arms of M 51, at a distance of about 1 to 3 kpc from the nucleus. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by means of a comparison between the observed spectral energy distribution and the predictions from cluster synthesis models for instantaneous star formation and solar metallicity. The lack of [OIII] emission in even the youngest clusters with strong Hα emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 . The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, much more severe than can be expected on the basis of evolutionary fading of the clusters. This indicates that cluster dispersion is occurring on a timescale of 10 Myr or longer. The cluster initial mass function has been derived from clusters younger than 10 Myr by a linear regression fit of the cumulative mass distribution. This results in an exponent in the range of but with an overabundance of clusters with . In the restricted range of we find . This exponent is very similar to the value derived for clusters in the interacting Antennae galaxies, and to the exponent of the mass distribution of the giant molecular clouds in our Galaxy. To study the possible effects of the interaction of M 51 with its companion NGC 5195 about 400 Myr ago, which triggered a huge starburst in the nucleus, we determined the cluster formation rate as a function of time for clusters with an initial mass larger than 104 . There is no evidence for a peak in the cluster formation rate at around 200 to 400 Myr ago within 2 σ accuracy, i.e. within a factor two. The formation rate of the detected clusters decreases strongly with age by about a factor 102 between 10 Myr and 1 Gyr. For clusters older than about 150 Myr this is due to the evolutionary fading of the clusters below the detection limit. For clusters younger than 100 Myr this is due to the dispersion of the clusters, unless one assumes that the cluster formation rate has been steadily increasing with time from 1 Gyr ago to the present time.

Laser diffraction and multifractal analysis for the characterization of dry soil volume-size distributions

Fractal scalings of the type N( x> X)≈ X − D f and M( x< X)≈ X d have been studied in previous works for the cumulative number and mass distributions of soil aggregates and particles of size x greater or less, respectively, than a characteristic size X. The exponents D f (fragmentation fractal dimension) and d represent rough estimates of the scale dependence that takes place in the number or mass accumulated, with respect to length scale. A closer look at the mass of soils (aggregates and primary particles) accumulated across the different regions of the interval of sizes would lead, in general, to detect denser or rarer regions across different length scales. These heterogeneity features are present in most real distributions in nature, displaying a behavior named multifractal. The laser scattering method and the multifractal analysis offer the possibility of studying the volume distribution of soils in scales that are not often explored. The goal of this paper is the application of laser diffraction and multifractal analysis to the characterization of dry volume-size distributions in soils. For each of the 20 soil samples considered for the study, an adequate measure is constructed with data corresponding to laser diffraction analysis of those samples. Multifractal analysis techniques are applied to such measures. Volume-size distribution of soils showed, in general, suitable scaling properties that make multifractal analysis a useful mathematical tool for its characterization by means of the singularity spectrum f( α( q)). Samples showed great variability in their multifractal behavior. An adequate range of the parameter q is selected for the characterization of each sample, in such a way that the R 2 values of the corresponding scaling fits are greater than 0.95. In that range, different features of the singularity spectrum f( α( q)) have been analyzed. The singularity spectrum f( α( q)) reveals to be useful for the characterization of soil volume-size distributions.

A Universal Angular Momentum Profile for Galactic Halos

We study the angular momentum profiles of a statistical sample of halos drawn from a high-resolution N-body simulation of the ΛCDM cosmology. We find that the cumulative mass distribution of specific angular momentum j in a halo of mass Mv is well fitted by a universal function, M(< j) = Mvμj/(j0 + j). This profile is defined by one shape parameter (μ or j0) in addition to the global spin parameter λ. It follows a power law M(< j) ∝ j over most of the mass and flattens at large j, with the flattening more pronounced for small values of μ (or large j0 at a fixed λ). Compared to a uniform sphere in solid-body rotation, most halos have a higher fraction of their mass in the low- and high-j tails of the distribution. High-λ halos tend to have high μ values, corresponding to a narrower, more uniform j distribution. The spatial distribution of angular momentum in halos tends to be cylindrical and is well-aligned within each halo for ~80% of the halos. The more misaligned halos tend to have low μ values. When averaged over spherical shells encompassing mass M, the halo j profiles are fitted by j(M) ∝ Ms with s = 1.3 ± 0.3. We investigate two ideas for the origin of this profile. The first is based on a revised version of linear tidal-torque theory combined with extended Press-Schechter mass accretion, and the second focuses on j transport in minor mergers. Finally, we briefly explore implications of the M(< j) profile on the formation of galactic disks assuming that j is conserved during an adiabatic baryonic infall. The implied gas density profile deviates from an exponential disk, with a higher density at small radii and a tail extending to large radii. The steep central density profiles may imply disk scale lengths that are smaller than observed. This is reminiscent of the "angular momentum problem" seen in hydrodynamic simulations, even though we have assumed perfect j conservation. A possible solution is to associate the central excesses with bulge components and the outer regions with extended gaseous disks.

Energy dependence of impact fragmentation of long glass rods

We have performed an experimental study of impact fragmentation with a focus on the dependence on the energy input. Long glass rods were dropped horizontally onto the ground from seven different heights. We find that the energy dependence is better characterized by studying the differential mass distribution rather than the cumulative mass distribution. For lower dropping heights, the differential mass distribution is well approximated by one power law while for higher heights, it has to be represented by two power laws. Moreover, the power-law exponent for small mass fragments increases and approaches an asymptotic value as the dropping height is increased.