Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

Structural characteristics of gels prepared from sonohydrolysis and conventional hydrolysis of TEOS: an emphasis on the mass fractal as determined from the pore size distribution

Silica gels were preparated from fixed proportion mixtures of tetraethoxysilane, water and hydrocloric acid, using either ultrasound stimulation (US) or conventional method (CO) in the hydrolysis step of the process. Wet gets were obtained with the same silica volume concentration and density. According to small-angle X-ray scattering, the structure of the wet gels can be described as mass fractal structures with mass fractal dimension D = 2.20 in a length scale xi = 7.9 nm, in the case of wet gels US, and D = 2.26 in a length scale 6.9 nm, in the case of wet gels CO. The mass fractal characteristics of the wet gels US and CO account for the different structures evolved in the drying of the gels US and CO in the obtaining of xerogels and aerogels. The pore structure of the dried gels was studied by nitrogen adsorption as a function of the temperature. Aerogels (US and CO) present high porosity with pore size distribution (PSD) curves in the mesopore region while xerogels (US and CO) present minor porosity with PSD curves mainly in the micropore region. The dried gels US (aerogels and xerogels) generally present pore volume and specific surface area greater than the dried gels CO. The mass fractal structure of the aerogels has been studied from an approach based on the PSD curves exclusively. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Kinetic Model for Micro Algae Cell Concentration and Size Distribution: Application to Nannochloropsis gaditana

The cell concentration and size distribution of the microalgae Nannochloropsis gaditana were studied over the whole growth process. Various samples were taken during the light and dark periods the algae were exposed to. The distributions obtained exhibited positive skew, and no change in the type of distribution was observed during the growth process. The size distribution shifted to lower diameters in dark periods while in light periods the opposite occurred. The overall trend during the growth process was one where the size distribution shifted to larger cell diameters, with differences between initial and final distributions of individual cycles becoming smaller. A model based on the Logistic model for cell concentration as a function of time in the dark period that also takes into account cell respiration and growth processes during dark and light periods, respectively, was proposed and successfully applied. This model provides a picture that is closer to the real growth and evolution of cultures, and reveals a clear effect of light and dark periods on the different ways in which cell concentration and diameter evolve with time.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Modelling the size distribution of cosmic voids

The Standard Cosmological Model is generally accepted by the scientific community, there are still an amount of unresolved issues. From the observable characteristics of the structures in the Universe,it should be possible to impose constraints on the cosmological parameters. Cosmic Voids (CV) are a major component of the LSS and have been shown to possess great potential for constraining DE and testing theories of gravity. But a gap between CV observations and theory still persists. A theoretical model for void statistical distribution as a function of size exists (SvdW) However, the SvdW model has been unsuccesful in reproducing the results obtained from cosmological simulations. This undermines the possibility of using voids as cosmological probes. The goal of our thesis work is to cover the gap between theoretical predictions and measured distributions of cosmic voids. We develop an algorithm to identify voids in simulations,consistently with theory. We inspecting the possibilities offered by a recently proposed refinement of the SvdW (the Vdn model, Jennings et al., 2013). Comparing void catalogues to theory, we validate the Vdn model, finding that it is reliable over a large range of radii, at all the redshifts considered and for all the cosmological models inspected. We have then searched for a size function model for voids identified in a distribution of biased tracers. We find that, naively applying the same procedure used for the unbiased tracers to a halo mock distribution does not provide success- full results, suggesting that the Vdn model requires to be reconsidered when dealing with biased samples. Thus, we test two alternative exten- sions of the model and find that two scaling relations exist: both the Dark Matter void radii and the underlying Dark Matter density contrast scale with the halo-defined void radii. We use these findings to develop a semi-analytical model which gives promising results.

Uma análise do coeficiente de remoção de poluentes em função do espectro de gotas de chuva em diferentes localidades no Brasil e Alemanha

The pollutant transference among reservoirs atmosphere-hydrosphere, relevant to the atmospheric chemistry, depends upon scavenging coefficient (Λ) calculus, which depends on the raindrop size distribution as well as on the rainfall systems, both different to each locality. In this work, the Λ calculus will be evaluated to gas SO2 and particulate matter fine and coarse among five sites in Germany and two in Brazil. The results show three possible classifications in function of Λ, comparable to literature, however with a greater range due to the differences of rainfall system sites. This preliminary study supports future researches

Robust relations between CCN and the vertical evolution of cloud drop size distribution in deep convective clouds

In-situ measurements in convective clouds (up to the freezing level) over the Amazon basin show that smoke from deforestation fires prevents clouds from precipitating until they acquire a vertical development of at least 4 km, compared to only 1-2 km in clean clouds. The average cloud depth required for the onset of warm rain increased by similar to 350 m for each additional 100 cloud condensation nuclei per cm(3) at a super-saturation of 0.5% (CCN0.5%). In polluted clouds, the diameter of modal liquid water content grows much slower with cloud depth (at least by a factor of similar to 2), due to the large number of droplets that compete for available water and to the suppressed coalescence processes. Contrary to what other studies have suggested, we did not observe this effect to reach saturation at 3000 or more accumulation mode particles per cm(3). The CCN0.5% concentration was found to be a very good predictor for the cloud depth required for the onset of warm precipitation and other microphysical factors, leaving only a secondary role for the updraft velocities in determining the cloud drop size distributions. The effective radius of the cloud droplets (r(e)) was found to be a quite robust parameter for a given environment and cloud depth, showing only a small effect of partial droplet evaporation from the cloud's mixing with its drier environment. This supports one of the basic assumptions of satellite analysis of cloud microphysical processes: the ability to look at different cloud top heights in the same region and regard their r(e) as if they had been measured inside one well developed cloud. The dependence of r(e) on the adiabatic fraction decreased higher in the clouds, especially for cleaner conditions, and disappeared at r(e)>=similar to 10 mu m. We propose that droplet coalescence, which is at its peak when warm rain is formed in the cloud at r(e)=similar to 10 mu m, continues to be significant during the cloud's mixing with the entrained air, cancelling out the decrease in r(e) due to evaporation.

Characterization of micro-bubble size distribution and flow configuration in DAF contact zone by a non-intrusive image analysis system and tracer tests

This paper aims to investigate the influence of some dissolved air flotation (DAF) process variables (specifically: the hydraulic detention time in the contact zone and the supplied dissolved air concentration) and the pH values, as pretreatment chemical variables, on the micro-bubble size distribution (BSD) in a DAF contact zone. This work was carried out in a pilot plant where bubbles were measured by an appropriate non-intrusive image acquisition system. The results show that the obtained diameter ranges were in agreement with values reported in the literature (10-100mm), quite independently of the investigated conditions. The linear average diameter varied from 20 to 30mm, or equivalently, the Sauter (d(3,2)) diameter varied from 40 to 50mm. In all investigated conditions, D(50) was between 75% and 95%. The BSD might present different profile (with a bimodal curve trend), however, when analyzing the volumetric frequency distribution (in some cases with the appearance of peaks in diameters ranging from 90-100mm). Regarding volumetric frequency analysis, all the investigated parameters can modify the BSD in DAF contact zone after the release point, thus potentially causing changes in DAF kinetics. This finding prompts further research in order to verify the effect of these BSD changes on solid particle removal efficiency by DAF.

Comparative physical-chemical characterization of encapsulated lipid-based isotretinoin products assessed by particle size distribution and thermal behavior analyses

Isotretinoin is the drug of choice for the management of severe recalcitrant nodular acne. Nevertheless, some of its physical-chemical properties are still poorly known. Hence, the aim of our study consisted to comparatively evaluate the particle size distribution (PSD) and characterize the thermal behavior of the three encapsulated isotretinoin products in oil suspension (one reference and two generics) commercialized in Brazil. Here, we show that the PSD, estimated by laser diffraction and by polarized light microscopy, differed between the generics and the reference product. However, the thermal behavior of the three products, determined by thermogravimetry (TGA), differential thermal (DTA) analyses and differential scanning calorimetry (DSC), displayed no significant changes and were more thermostable than the isotretinoin standard used as internal control. Thus, our study suggests that PSD analyses in isotretinoin lipid-based formulations should be routinely performed in order to improve their quality and bioavailability. (C) 2010 Elsevier B.V. All rights reserved.

Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.

Muscle fibre types and size distribution in sub-antarctic notothenioid fishes

The presumptive tonic muscles fibres of Cottoperca gobio, Champsocephalus esox, Harpagifer bispinis, Eleginops maclovinus, Patagonothen tessellata, P. cornucola and Paranotothenia magellanica stained weakly or were unstained for glycogen, lipid, succinic dehydrogenase (SDHase) and myosin ATPase (mATPase) activity. Slow, intermediate and fast twitch muscle fibres, distinguished on the basis of the pH stability of their mATPases, showed intense, moderate and low staining activity for SDHase, respectively. Slow fibres were the major component of the pectoral fin adductor profundis muscle. The proportion of different muscle fibre types varied from the proximal to distal end of the muscle, but showed relatively little variation between species. The myotomes contained a lateral superficial strip of red muscle composed of presumptive tonic, slow twitch and intermediate fibres, thickening to a major wedge at the horizontal septum. All species also had characteristic secondary dorsal and ventral wedges of red muscle. The relative abundance and localization of muscle fibre types in the red muscle varied between species and with body size in the protandric hermaphrodite E. maclovinus. The frequency distribution of diameters for fast twitch muscle fibres, the major component of deep white muscle, was determined in fish of a range of body sizes. The absence of fibres <20 mu m diameter was used as a criterion for the cessation of muscle fibre recruitment. Fibre recruitment had stopped in P, tessellata of 13.8 cm L-T and E, maclovinus of 32.8 cm L-T, equivalent to 49 and 36.5% of their recorded maximum sizes respectively. As a result in 20-cm P. tessellata, the maximum fibre diameter was 300 mu m and 36% of fibres were in excess of 200 mu m The unusually large maximum fibre diameter, the general arrangement of the red muscle layer and the extreme pH lability of the mATPase of fast twitch fibres are all common characters of the sub-Antarctic and Antarctic Notothenioids, including Cottoperca gobio, the suggested sister group to the Notothenidae. (C) 2000 The Fisheries Society of the British Isles.

A technological and organisational explanation for the size distribution of firms

This paper combines insights from the literature on the economics of organisation with traditional models of market structure to construct a theory of equilibrium firm size heterogeneity under the assumption of a homogenous product industry. It is possible that configurations consisting entirely of small firms (run by entrepreneurs with limited attention) and with larger firms (using managerial techniques to substitute away these limits to allow increasing returns technologies to become profitable) can arise in equilibrium. However, there also exist equilibrium configurations with the co-existence of large and small firms. The efficiency properties of these respective equilibria are discussed. Finally, the implications of an expanding market size are considered.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.