Theoretical Size Distributions Research Articles

Impact of a polysidpersed fuel distribution on the ignition characteristic

Determining the thermal profile of ignition is important because the desired ignition behavior varies with the objective. For example, extended ignition prolongs the time that the engine runs; however, fast ignition offers a higher power gain. The pollution caused by undesirable chemical reactions, as determined by the ignition profile, is another important aspect. Based on a previously developed method, we examined the impact of different theoretical particle size distributions (PSDs) on the thermal ignition profile. We compared different PSDs of polydispersed fuel spray with normal distributions with various means, each corresponding to the same fuel volume. Our results revealed a significant dependence of thermal ignition on the PSD. Systems that comprised only low-radius droplets did not reach ignition, whereas systems with only high-radius droplets required a long time to establish ignition. Moreover, the change in the mean droplet radius unexpectedly resulted in a double hump in the maximum temperature of the combustion process.

Evaluation and updates to the Leggett model for pharmacokinetic modeling of exposure to lead in the workplace – Part II adjustments to the adult exposure model, confirmation of Leggett+, and modeling of workplace exposure

California’s Office of Environmental Health Hazard Assessment has updated the comprehensive age-specific model of lead metabolism in humans published by Richard W. Leggett in 1993. The updated model, called Leggett+, was introduced in a peer-reviewed report in 2013. The Leggett + model simulates the relationship between blood lead and exposure in the workplace. Leggett + includes a workplace exposure model comprising respiratory tract intake (workplace lead inhaled by a worker) and uptake (lead absorbed into the blood from the respiratory tract plus uptake from ambient air and diet). The latter is calculated as intake times an inhalation transfer coefficient plus background uptake. An adjusted adult systemic model describes the metabolism of the absorbed lead. This paper provides details about the workplace exposure and uptake elements of Leggett+, an updated approach to calibrating an inhalation transfer coefficient, confirmation of the model’s performance in predicting blood lead levels from workplace studies, and predictions of blood lead levels from simulated exposures to workplace airborne lead over a working lifetime. Blood lead relative to airborne lead concentrations in a standard workplace scenario predicted by Leggett + was similar to corresponding relationships from four published workplace studies. Leggett + predictions displayed a good fit to regression equations when other key factors were considered such as pre-employment blood lead and ongoing background intake of lead, workplace air concentration, lead aerosol characteristics, and worker activity levels. The comprehensive Leggett + model can simulate plausible workplace air–blood lead relationships from a broad range of worker exposures. The inhalation transfer coefficient of 0.30, derived from empirical data described in the 2013 report has been reexamined. The original estimate continues to represent a plausible mid-point for a coefficient derived from an expanded range of theoretical particle size distributions deposited in the upper and lower regions of the respiratory tract considering intake during sedentary and outdoor activity breathing scenarios. This coefficient is slightly lower than the value of 0.35 estimated for unknown forms of lead by Leggett in 1993.

Dosage of interlocking paving with ornamental rock waste: An experimental design approach, particle packing and polluting potential

This article proposes a dosing procedure for interlocking concrete pavements that incorporate ornamental rock waste, with a view to meeting mechanical and molding criteria and ensuring the sustainability of the mineral industry, an economically important sector in Brazil despite environmental issues surrounding its waste generation. The procedure involves evaluating the packing density of the sand, coarse aggregate and waste fines via the minimum void ratio. A simplex lattice experimental design and the theoretical particle size distribution (Alfred) model were used, followed by a 22 factorial with a center point to determine the influence of the factors (proportions) and different water-cement (w/c) ratios (levels). The full cubic model obtained a 95.62 % adjustment index for optimal particle size of the aggregates and waste fines, and the lowest MVR (1.961 103kg/m³). This trend was confirmed by the theoretical Alfred model, with a coefficient of 0.29, and the factorial experiment, with an adjustment index of 97.50 %. Dosing indicated an ideal cement content of 20 %, 15.2 % for sand, 44.8 % for the coarse aggregate and waste fine incorporation of 20 % of the total mass (25 % of the aggregate mass), achieving compressive strength of 36.70 MPa for w/c and water/aggregate ratios of 0.5 and 0.123, respectively, and a carboxylate superplasticizer content of 6% of cement consumption, as well as adequate molding and demolding conditions. An ecotoxicological assessment was conducted, which found that waste fine incorporation posed no risk to the environment. Scanning electron microscopy (SEM) demonstrated that this mixture exhibited the best mechanical performance, with adequate aggregate particle size distribution and paste coverage, as well as waste fine stability in the cement matrix.

Cell size distribution of lineage data: Analytic results and parameter inference

SummaryRecent advances in single-cell technologies have enabled time-resolved measurements of the cell size over several cell cycles. These data encode information on how cells correct size aberrations so that they do not grow abnormally large or small. Here, we formulate a piecewise deterministic Markov model describing the evolution of the cell size over many generations, for all three cell size homeostasis strategies (timer, sizer, and adder). The model is solved to obtain an analytical expression for the non-Gaussian cell size distribution in a cell lineage; the theory is used to understand how the shape of the distribution is influenced by the parameters controlling the dynamics of the cell cycle and by the choice of cell tracking protocol. The theoretical cell size distribution is found to provide an excellent match to the experimental cell size distribution of E. coli lineage data collected under various growth conditions.

Evaluation of the textural properties of ultramicroporous carbons using experimental and theoretical methods

Spherical carbon molecular sieves (CMS) have selective adsorptive properties which are suitable for separation and purification of gas mixtures. Precise methods of characterization are needed to understand the performance of CMS in separation processes. To this end, the pore size distribution (PSD) of four carbon molecular sieves were evaluated experimentally using immersion calorimetry and complemented with gas adsorption measurements at cryogenic temperatures for N2, O2 and Ar, and at 273 K for CO2. Theoretical pore size distributions were estimated using two-dimensional non-local Density Functional Theory (2D-NLDFT) models. Calorimetry results showed that B and C samples had a narrow pore size distribution with pores below 0.7 nm. Meanwhile, the pore size distributions calculated from O2 and Ar adsorption isotherms, gave an apex in the 0.5–0.6 nm region for all the carbons together with a growing development of porosity at around 0.8 nm and above for carbons A and D. The agreement observed between experiments and theory confirmed the validity of the theoretical 2D-NLDFT models to anticipate the PSD. Carbon C with pores exclusively below 0.7 nm separated CO2 and CH4 while carbon D with pores in the supermicroporous region separated propane and propylene chromatographically.

Establishment of a Laminated Crushed Products Function and Numerical Analysis

A model of the relative compression ratio for single-particle crushed products, based on the distinct element method (DEM) and numerical analysis, was established to describe precisely the crushed products of granular particles during laminated crushing. The relative compression ratio model was used to describe the functional relationship between the total compression ratio and the single-particle compression ratio, which can be described by lognormal distribution. The single-particle crushed products model was used to describe the functional relationship between the single-particle compression ratio and the distribution of single-particle crushed products. The distribution of single-particle crushed products was described by a three-parameter beta distribution. On the basis of the above model, the function of laminated crushed products of granular particles was established. According to the simulation results of EDEM under confining pressure, a functional relationship between total compression ratio, particle size, and height of the granular particles for laminated crushed products of granular particles was built. It was proved that the function of the theoretical particle size distribution coefficient of laminated crushed products of granular particles was not too different from the actual value determined by simulation. The function is universal and can be used to provide a theoretical basis and a design reference for the design of cone crushers, high-pressure roller mills, and other crushing equipment.

A kilometre-sized Kuiper belt object discovered by stellar occultation using amateur telescopes

Kuiper belt objects (KBOs) are thought to be the remnant of the early solar system, and their size distribution provides an opportunity to explore the formation and evolution of the outer solar system. In particular, the size distribution of kilometre-sized (radius = 1-10 km) KBO represents a signature of initial planetesimal sizes when planets form. These kilometre-sized KBOs are extremely faint, and it is impossible to detect them directly. Instead, monitoring of stellar occultation events is one possible way to discover these small KBOs. Hitherto, however, there has been no observational evidence for the occultation events by KBOs with radii of 1-10 km. Here we report the first detection of a single occultation event candidate by a KBO with a radius of $\sim$1.3 km, which is simultaneously provided by two low-cost small telescopes coupled with commercial CMOS cameras. From this detection, we conclude that a surface number density of KBOs with radii exceeding $\sim 1.2$ km is $\sim 6 \times 10^5 \ {\rm deg^{-2}}$. This surface number density favours a theoretical size distribution model with an excess signature at a radius of 1-2 km. If this is a true detection, this implies that planetesimals before their runaway growth phase grow into kilometre-sized objects in the primordial outer solar system and remain as a major population of the present-day Kuiper belt.

Methods for Estimating 2D Cloud Size Distributions from 1D Observations

Abstract The two-dimensional (2D) size distribution of clouds in the horizontal plane plays a central role in the calculation of cloud cover, cloud radiative forcing, convective entrainment rates, and the likelihood of precipitation. Here, a simple method is proposed for calculating the area-weighted mean cloud size and for approximating the 2D size distribution from the 1D cloud-chord lengths measured by aircraft and vertically pointing lidar and radar. This simple method (which is exact for square clouds) compares favorably against the inverse Abel transform (which is exact for circular clouds) in the context of theoretical size distributions. Both methods also perform well when used to predict the size distribution of real clouds from a Landsat scene. When applied to a large number of Landsat scenes, the simple method is able to accurately estimate the mean cloud size. As a demonstration, the methods are applied to aircraft measurements of shallow cumuli during the Routine ARM Aerial Facility (AAF) Clouds with Low Optical Water Depths (CLOWD) Optical Radiative Observations (RACORO) campaign, which then allow for an estimate of the true area-weighted mean cloud size.

The Width Distribution of Loops and Strands in the Solar Corona—Are We Hitting Rock Bottom?

Abstract In this study, we analyze Atmospheric Imaging Assembly (AIA) and Hi-C images in order to investigate absolute limits for the finest loop strands. We develop a model of the occurrence–size distribution function of coronal loop widths, characterized by the lower limit of widths w min, the peak (or most frequent) width w p , the peak occurrence number n p , and a power-law slope a. Our data analysis includes automated tracing of curvilinear features with the OCCULT-2 code, automated sampling of the cross-sectional widths of coronal loops, and fitting of the theoretical size distribution to the observed distribution. With Monte Carlo simulations and variable pixel sizes , we derive a first diagnostic criterion to discriminate whether the loop widths are unresolved or fully resolved (if ). For images with resolved loop widths, we can apply a second diagnostic criterion that predicts the lower limit of loop widths as a function of the spatial resolution. We find that the loop widths are marginally resolved in AIA images but are fully resolved in Hi-C images, where our model predicts a most frequent (peak) value at , in agreement with recent results of Brooks et al. This result agrees with the statistics of photospheric granulation sizes and thus supports coronal heating mechanisms operating on the macroscopic scale of photospheric magneto-convection, rather than nanoflare braiding models on unresolved microscopic scales.

Hybrid polymer/MOF membranes for Organic Solvent Nanofiltration (OSN): Chemical modification and the quest for perfection

One of the main challenges in the field of Organic Solvent Nanofiltration (OSN) is to improve the selectivity of membranes, allowing the separation of closely related solutes. This objective might be achieved by constructing membranes with uniform porous structures. Hybrid Polymer/Metal Organic Framework (MOF) membranes were prepared by in-situ growth (ISG) of HKUST-1 within the pores of polyimide membranes. To improve the performances of ISG membranes, chemical modification was performed. Aryl carboxylic acid moieties were introduced to polyimide P84 ultrafiltration membranes allowing coordination of the HKUST-1 directly on to the polymer. Chemically modified ISG membranes outperformed non-modified ISG membranes in both solute retentions and permeance. Retentions of polystyrene solute in acetone were used to calculate theoretical pore size distributions for each of the membranes tested. It was found that the chemically modified ISG membrane had he narrowest calculated pore size distribution.

A common lack of demographic equilibrium among tree species in Białowieża National Park (NE Poland): evidence from long‐term plots

AbstractQuestionsDoes the size structure characterizing particular tree species in natural forest stands converge towards a steady state? What is the main reason for departures of observed tree size distributions from equilibrium models? What is the consequence of long‐term strict protection for the demography of tree species and the conservation of associated biota?LocationStands of natural forest in Białowieża National Park (NE Poland) that have been under strict protection for about 90 yr.MethodsData on recruitment, growth and mortality of approximately 10 000 trees representing 11 species (aspen, birch, alder, pine, oak, maple, ash, elm, spruce, lime and hornbeam), from seven replicated surveys of five permanent monitoring plots (total size = 15.44 ha), established in 1936, were used to derive theoretical, species‐specific equilibrium distributions as a basis for evaluating the demographic changes of the species involved.ResultsOver a monitoring period of 76 yr, there were strong downward trends in the population densities of several tree species of different successional status and light requirements. A vast majority of the conspecific equilibrium curves, modelled on the basis of growth and mortality data, revealed a ‘rotated sigmoid’ shape when plotted in semi‐log plots. In contrast to these equilibrium curves, the observed tree size distributions of most species were unimodal, at both the beginning and the end of the study period. Departures between theoretical and observed distributions increased over time, particularly for shade‐intolerant and intermediate species.ConclusionsThe populations of several tree species occurring in the Białowieża National Park are demographically unstable – a fact reflected in large and steadily increasing differences between theoretical and actual tree size distributions. The main reason for this are the insufficient recruitment rates typical of most species. Some tree species may very soon disappear almost entirely, and this will certainly lead to far‐reaching changes in the functioning of local forest communities. Among other consequences, the current demographic trends, as observed for Białowieża tree species, are very likely to have a strong effect on the long‐term survival of numerous forest organisms (such as insects, fungi, lichens, etc.), which depend, directly or indirectly, on the presence and balanced demography of particular tree species.

Measurement of sizes of colloid particles using dynamic light scattering

Size distribution functions of colloid particles are obtained with the aid of dynamic light scattering for both polarized and depolarized components. Electron microscopy of the colloid particles is used to construct size distribution histograms. Numerical analysis yields good agreement of the experimental and theoretical size distributions. The size distribution function is derived from the solution to the corresponding integral equations using the Tikhonov regularization procedure.

Computational Modelling of Metastasis Development in Renal Cell Carcinoma.

The biology of the metastatic colonization process remains a poorly understood phenomenon. To improve our knowledge of its dynamics, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model that translates this assumption into equations, we challenged this theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. Critically, when calibrated on the growth of the primary tumour and total metastatic burden, the predicted theoretical size distributions were not in agreement with the MRI observations. Moreover, tumour expansion only based on proliferation was not able to explain the volume increase of the metastatic lesions. These findings strongly suggested rejection of the standard theory, demonstrating that the time development of the size distribution of metastases could not be explained by independent growth of metastatic foci. This led us to investigate the effect of spatial interactions between merging metastatic tumours on the dynamics of the global metastatic burden. We derived a mathematical model of spatial tumour growth, confronted it with experimental data of single metastatic tumour growth, and used it to provide insights on the dynamics of multiple tumours growing in close vicinity. Together, our results have implications for theories of the metastatic process and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.

Study of the structural-functional state of disperse precipitations in ion-irradiated materials

The peculiarities of microparticle formation in ion-irradiated materials are described analytically by taking the size factor in a disperse system into account. For this purpose, a method for revealing the similarity and the difference between the characteristics of experimental histograms and the theoretical size distributions of microparticles is developed. This method makes it possible to establish the correlation relation between the peculiarities of the transformation of the experimental distributions (histograms) and intrasystem processes in a disperse system. Reliable experimental results confirm the conclusions of theoretical analysis.

Monte Carlo simulation of silicon nanocrystal formation in the presence of impurities in a SiNx matrix

In the present work, the formation of silicon nanocrystals in the case of the presence of impurities in a SiNx matrix was simulated by using the Monte Carlo (MC) technique. A new pattern describing the distribution of impurities in the simulation matrix was proposed to study using the MC method the formation of silicon nanocrystals. The MC simulation results indicate that the formed crystallites size decreases as the amount of impurities in the matrix increases. The influences of the process temperature and the crystallographic orientation number on the crystallization kinetics were analyzed. The crystallographic orientation number was found to have no significant influence on the obtained nanostructure, and the increase in the temperature values was found to promote the formation of larger silicon crystallites. A strong relationship between the grain boundary energy constant values and the content of impurities introduced in the simulation matrix was established. The proposed approach was applied to analyze an existing experimental dataset. The results revealed a good statistical agreement between the theoretical and experimental grain size distributions and nanostructures.

In situ diagnostic of the size distribution of nanoparticles generated by ultrashort pulsed laser ablation in vacuum

We aim to characterize the size distribution of nanoparticles located in the ablation plume produced by femtosecond laser interaction. The proposed method relies on the use of white-light extinction spectroscopy setup assisted by ultrafast intensified temporal gating. This method allows measurement of optical absorbance of a nickel nanoparticles cloud. Simulation of the extinction section of nickel nanoparticles size distributions has been developed in order to compare the measured optical absorbance to the optical extinction by theoretical and experimental nanoparticles size distributions (measured by scanning electron microscopy). A good agreement has been found between the in situ measured optical absorbance and the optical extinction cross section calculated from ex situ nanoparticles size distribution measurements.

Identifiable analysis of dispersed precipitates and porosity in ion-irradiated materials

Analytical formulas for the analysis of structural states in ion-irradiated materials, namely dispersed precipitates, gas-filled pores, and island films on a solid substrate are proposed. A method for revealing similarities and differences between the characteristics of the theoretical and experimental size distributions of particles is developed. This method for the identification of distributions allows a correlation to be determined between the features of the transformations of experimental distributions (histograms) and processes in a dispersed system.

Theoretical Size Distribution in Linear Step-Growth Polymerization for a Small Number of Reacting Species

The size distributions for the linear step-growth polymerization containing a relatively small number of molecules (in the range of 20-10000) have been calculated using computer simulations. Contrary to the most probable distribution of Flory, which predicts a continuous linear increase of the polydispersity index (PDI) from the value of 1 to 2, it has been found that the PDI increases up to a certain maximum value followed by a decrease to unity as the extent of conversion (p) approaches unity. The maxima of the PDI versus p curves as well as the sharpness of the decrease of these curves to unity have been found to strongly depend on the number of reacting species. In addition, on the basis of a rigorous statistical treatment, the number and the weight-average size distributions have been derived, which are in perfect agreement with those obtained by computer simulation. Furthermore, the derived distributions can also be applied for the description of reaction products of depolymerization reactions.

Estimation of pore size distribution using concentric double pulsed-field gradient NMR

Estimation of pore size distribution of well calibrated phantoms using NMR is demonstrated here for the first time. Porous materials are a central constituent in fields as diverse as biology, geology, and oil drilling. Noninvasive characterization of monodisperse porous samples using conventional pulsed-field gradient (PFG) NMR is a well-established method. However, estimation of pore size distribution of heterogeneous polydisperse systems, which comprise most of the materials found in nature, remains extremely challenging. Concentric double pulsed-field gradient (CDPFG) is a 2-D technique where both q (the amplitude of the diffusion gradient) and φ (the relative angle between the gradient pairs) are varied. A recent prediction indicates this method should produce a more accurate and robust estimation of pore size distribution than its conventional 1-D versions. Five well defined size distribution phantoms, consisting of 1–5 different pore sizes in the range of 5–25μm were used. The estimated pore size distributions were all in good agreement with the known theoretical size distributions, and were obtained without any a priori assumption on the size distribution model. These findings support that in addition to its theoretical benefits, the CDPFG method is experimentally reliable. Furthermore, by adding the angle parameter, sensitivity to small compartment sizes is increased without the use of strong gradients, thus making CDPFG safe for biological applications.

Procedure of the identifiable analysis of dispersed precipitations in alloys

Formulas and analytical and cumulative probabilistic distributions to perform a system analysis of dispersed precipitations in alloys and other materials are proposed. For this purpose, a method for establishing the similarity and difference (identification) between the characteristics of the experimental histogram and theoretical size distribution of the particles is developed. This method of identifying the distributions makes it possible to determine the correlation between the features of transformation of experimental distributions and intrasystem processes.