Perimeter Distributions Research Articles

Síndrome do túnel do carpo: estudo comparativo entre a medição ultrassonográfica e cirúrgica do nervo mediano nos casos moderados e severos da doença

OBJETIVO: Comparar os perímetros ultrassonográfico e cirúrgico do nervo mediano, avaliar o diagnóstico da síndrome do túnel do carpo pela área seccional do nervo mediano, verificar associação entre área seccional do nervo mediano e gravidade da síndrome do túnel do carpo. MATERIAIS E MÉTODOS: Estudo de 30 pacientes com síndrome do túnel do carpo. Mediram-se a área seccional e o perímetro ultrassonográfico do nervo mediano. Avaliaram-se correlação clínica-ultrassonográfica e associação com a gravidade da doença. Compararam-se os perímetros ultrassonográfico e cirúrgico. Compararam-se classificação clínica com perímetro cirúrgico, área seccional e perímetro ultrassonográfico. RESULTADOS: Cinco perdas, 25 pacientes estudados; 60% dos pacientes com doença moderada, 60% de casos graves ultrassonográficos (área seccional > 0,15 cm²). Distribuição não normal de perímetro cirúrgico (p = 0,5), distribuição normal de perímetro ultrassonográfico (p = 0). Diferença significativa entre perímetros (teste-t de amostras pareadas; p < 0,0001; intervalo de confiança = 95%). Pearson 0,3913. Pelo diagrama de Bland-Altman, observaram-se maiores perímetros cirúrgicos. Encontrou-se área seccional do nervo mediano > 0,09 cm² em todos os pacientes. CONCLUSÃO: Não houve associação entre perímetro ultrassonográfico e perímetro cirúrgico do nervo mediano. Área seccional do nervo mediano > 0,09 cm² foi válida para o diagnóstico. Não houve associação entre área seccional e gravidade da doença.

Morphological evaluation of the cerebral blood vessels in the late gestation fetal sheep following hypoxia in utero

Hypoxia can significantly contribute to the development of permanent brain injury in the term neonate; however the response of cerebral blood vessels is not well understood. This study aimed to quantitatively measure vascular density and morphology using laminin immunohistochemistry as a marker of blood vessels, and determine the effects of a single, severe bout of hypoxia (umbilical cord occlusion, UCO) late in gestation on the developing cerebrovasculature in fetal sheep. At 124–126days gestation singleton fetal sheep underwent surgery for implantation of catheters and placement of an inflatable cuff around the umbilical cord. A 10min UCO or sham UCO (n=5) occurred at 132days gestation. Fetal brains were collected at 24h (n=5) or 48h (n=4) after UCO for vascular density and morphology analysis of laminin immunohistochemistry. 48h following a single, brief bout of severe hypoxia late in gestation decreased vascular density was seen in the caudate nucleus and no changes in vascular morphology occurred. However closer analysis revealed a significant shift in the frequency of smaller (≤10μm) to larger (≤100μm) perimeter blood vessels in periventricular and subcortical white matter. Close examination of the frequency distribution of vascular perimeter highlights that alterations in vascular morphology persist in the near term fetal brain for up to 48h following a brief (10min) hypoxia in white but not gray matter. These findings suggest that the near term brain may still be vulnerable to white matter injury following in utero hypoxia.

Can the discharge of a hyperconcentrated flow be estimated from paleoflood evidence?

Many flood events involving water and sediments have been characterized using classic hydraulics principles, assuming the existence of critical flow and many other simplifications. In this paper, hyperconcentrated flow discharge was evaluated by using paleoflood reconstructions (based on paleostage indicators [PSI]) combined with a detailed hydraulic analysis of the critical flow assumption. The exact location where this condition occurred was established by iteratively determining the corresponding cross section, so that specific energy is at a minimum. In addition, all of the factors and parameters involved in the process were assessed, especially those related to the momentum equation, existing shear stresses in the wetted perimeter, and nonhydrostatic and hydrostatic pressure distributions. The superelevation of the hyperconcentrated flow, due to the flow elevation curvature, was also estimated and calibrated with the PSI. The estimated peak discharge was established once the iterative process was unable to improve the fit between the simulated depth and the depth observed from the PSI. The methodological approach proposed here can be applied to other higher‐gradient mountainous torrents with a similar geomorphic configuration to the one studied in this paper. Likewise, results have been derived with fewer uncertainties than those obtained from standard hydraulic approaches, whose simplifying assumptions have not been considered.

Experimental investigation of spray formation as affected by sprinkler geometry

A preliminary study at low water discharge pressures was conducted to investigate the fire sprinkler spray formation as affected by sprinkler geometry using a laser-based shadow imaging system. A sprinkler typically consists of the following components: a deflector with tines and slots, a boss above the deflector and sprinkler frame arms. Prototypes of these components were fabricated to evaluate their effects on the spray formation process. The water sheet thickness formed on non-slotted deflectors, slot spray discharge angle, sheet breakup distance from the deflector perimeter, water flux and drop size distributions were measured. It was found that deflector diameter and boss structure have little impact on drop size and sheet breakup distance. However, wider slots form larger drops. At constant operating pressure, the slot spray discharge angle is insensitive to the slot width, but sensitive to the boss that helps directing the slot spray toward the sprinkler centerline. The frame arm tends to produce a vertical spray sheet downstream of the frame arm, which increases the complexity of overall spray formation. An integral model was developed to calculate the development of water sheet thickness and speed on the deflector for different degrees of viscous effect exerted by the deflector. An empirical correlation was also established to estimate the spray flux fraction discharging from a deflector slot. The above measurements and observations are useful for the development of a spray formation model for fire sprinklers.

A climatologically based long-range fire growth model

A long-range fire growth model was developed to predict the potential size or probable extent of a wildfire if it was allowed to grow unimpeded for the course of the fire season. The model combines the probabilities of fire spread and of survival to produce a probable fire extent map. Probability of spread is determined from exponential distributions of potential rates of spread for various fuel types and eight compass directions, based on 30 years of fire weather data and elliptical fire growth. Probability of survival is determined from the probable evolution of the duff moisture code over the fire season predicted with Markov chains and a duff moisture code of extinction. A comparative study was conducted within Wood Buffalo National Park. The long-term model was compared with a distribution of fire perimeters predicted by repeated simulations using an hourly based, deterministic fire growth model. The study was conducted in stages, starting with a homogeneous fuel type and weather from one station. Later, fuels and weather were introduced to determine their effects on the model. The study showed a close agreement between the long-range model and the deterministic model, supporting the probabilistic approach used by the long-range model.

Groundwater nitrate pollution in Souss-Massa basin (south-west Morocco)

The objective of our study was to determine the current status of alluvial aquifer in the Souss-Massa basin, where the nitrate pollution of groundwater is being increasing along the last decades. A multiapproach methodology using hydrogeology, nitrate concentrations, irrigation type and oxygen-18 and deuterium data, was carried out to identify the sources of this pollution. According to the spatial distribution of nitrate contents, nitrate pollution occurs mainly in Chtouka-Massa plain. More than 36% of the sampled wells exceed the value of 50 mg/L as NO3 -. Groundwater in Souss plain is less polluted comparing it to Chtouka-Massa; only 7% of wells exceed the permitted level. Agricultural practices in the study sites are the main cause of serious nitrate pollution given the uperimposition of high nitrate concentrations with the distribution of irrigated perimeters. High nitrate levels are associated with high
18O values, clearly indicating that significant quantities of evaporated irrigation waters infiltrate along with fertilizer nitrate to groundwater system. Different
18O-NO3 - trends suggest isotopically distinct, non-point source origins which vary spatially and temporally, due to different degrees of evaporation/recharge and amounts of fertilizer applied.

Geometry of phase separation

We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat nonconserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the nonconserved case, it is not in the conserved one. Our results can therefore be considered as a "first-order" approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cutoff. Large structures (areas or perimeters) retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point, respectively. The corresponding distributions are described by a cA-tau tail, where c and tau are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime, the number density of domains with area A scales as A1/2 , as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area A approximately t2/3. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the two-dimensional Ising model.

Modeling and simulation of microstructures using power diagrams: Proof of the concept

Power diagrams are a generalization of Voronoi diagrams for arbitrary dimensions. We present a modeling and optimization scheme for power diagrams in three spacial dimensions based on the statistics of experimental data obtained from cross-sectional images of polycrystalline materials. Our optimization scheme based on the grains’ area and perimeter distributions can be used to obtain realistic three-dimensional polycrystalline structures which can subsequently be used for numerical simulations. As a proof of the concept we apply our scheme to high-performance ceramics and present the results of initial shock-impact simulations of the obtained polycrystalline structures.

The distribution of Voronoi cells generated by Southern California earthquake epicenters

AbstractThe cells of Voronoi diagrams generated by epicentral locations of Southern California earthquakes are inspected. The tapered Pareto distribution is shown to fit quite well to the distribution of cell areas and perimeters. This same distribution, which has been used to model the distribution of seismic moments, is also a close approximation to the empirical distributions of times and distances between successive earthquakes for the same catalog of Southern California events. Verification is performed using a variety of different windows and sub‐sampling procedures in order to confirm that the results are not an artifact of the particular parameters of the selected earthquake catalog. Copyright © 2008 John Wiley & Sons, Ltd.

Quantitative evaluation of perimeter of porosity in aluminum alloy die casting

Pore formation in high-pressure die casting is inevitable and pores adversely affect the mechanical properties and pressure tightness. Pores are induced by solidification shrinkage or entrapment of gas. To eliminate pores in die castings in the foundry floor, accurate identification of predominant cause of pores is essential. In this paper, the unbiased quantitative evaluation is proposed so that die casters can take corrective action to reduce pores. We proposed fractal dimension of shape and spatial distribution of porosity perimeter as the quantitative indicator of the identification of pores, namely, shrinkage or gas entrapment. The purpose of the present investigation is to demonstrate the validity of the proposed fractal dimensions by comparing the pores in different regions of die castings, which vary widely in porosity distribution. The proposed fractal dimensions are clearly different from inner region (shrinkage and gas induced pores are mixed) and surface region (only gas induced pores exist) in the die castings.

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.

Morphological changes of the soleus motoneuron pool in chronic midthoracic contused rats

This study investigated the morphological features of the soleus motoneuron pool in rats with chronic (4 months), midthoracic (T 8) contusions of moderate severity. Motoneurons were retrogradely labeled using unconjugated cholera toxin B (CTB) subunit solution injected directly into the soleus muscle of 10 contused and 6 age- and sex-matched, normal controls. Morphometric studies compared somal area, perimeter, diameter, dendritic length, and size distribution of labeled cells in normal and postcontusion animals. In normal animals, motoneurons with a mean of 110.4 ± 5.2 were labeled on the toxin-injected side of the cord (left). By comparison, labeled cells with a mean of 93.0 ± 8.4 (a 16% decrease, P = 0.006) were observed in the chronic spinal-injured animals. A significantly smaller frequency of very small (area, approximately 100 μm 2) and medium (area, 545–914 μm 2) neurons, and a significantly higher frequency of larger (area, >914 μm 2) neurons was observed in the labeled soleus motoneuron pools of injured animals compared with the normal controls. Dendritic bundles in the contused animals were composed of thicker dendrites, were arranged in more closely aggregated bundles, and were organized in a longitudinal axis (rostrocaudal axis). Changes in soleus motoneuron dendritic morphology also included significant decrease of total number of dendrites, increased staining, hypertrophy of primary dendrites, and significant decreased primary, secondary, and tertiary branching. The changes in size distribution and dendritic morphology in the postcontusion animals possibly resulted from cell loss and transformation of medium cells to larger cells and/or injury-associated failure of medium cells to transport the immunolabel.

Physicochemical and structural characterization of a polyionic matrix of interest in biotechnology, in the pharmaceutical and biomedical fields

This paper reports on the swelling degree and the rheological and structural characteristics of a hydrogel composed by chitosan and xanthan. The latter is a polyionic hydrogel obtained by complexation between the both polysaccharides. The swelling degree has been found to be influenced by the time of coacervation, the pH of the solution of chitosan used to form the hydrogel and the pH of the swelling solution. The molecular weight and the degree of acetylation of the chitosan also influence the swelling degree of this matrix. The connectivity between chitosan and xanthan affects the swelling degree of this matrix. A rheological study has been carried out in order to understand the formation of the coacervate and of the subsequent hydrogel. The evolution of the storage modulus with time during the coacervation has allowed to optimize the time of coacervation required for a subsequently hydrogel, with desirable swelling degree. The kinetics has shown that (a) the coacervate is formed in two distinct steps and (b) the storage modulus of the hydrogel reaches a stable plateau. The values of the storage modulus have been correlated with the swelling degree. The microscopic characterization has shown the presence of a porous network with a fibrillar structure. To complete the characterization studies fine powder of this hydrogel has been used to determine the surface, perimeter, Feret diameter and sphericity factor distribution of dry and hydrated (swollen) particles.

Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions.

We show that in the loop-erased random-walk problem, the exponent characterizing the probability distribution of areas of erased loops is superuniversal. In d dimensions, the probability that the erased loop has an area A varies as A(-2) for large A, independent of d, for 2< or =d< or =4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d=2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two dimensions is consistent with the known exact value 5/4. In three dimensions, we get z=1.6183+/-0.0004. The exponent for the distribution of the durations of avalanches in the three-dimensional Abelian sandpile model is determined from this by using scaling relations.

Analytical results for random line networks applications to fracture networks and disordered fiber composites

We study the geometrical properties of a continuum model consisting of an ensemble of intersecting lines placed within a finite region in two dimensions. We consider the model in the high-density regime where it emulates fiber composites, filtering elements and fracture networks. We report exact results for the probability distribution of segment lengths produced by line intersections. Segment loop perimeter and area distributions are estimated numerically. For the probability distribution of perimeters, we found the interesting phenomenon of small pore perimeter power law repulsion for pores of four or more sides. Two subsidiary models, with infinite line length, are solved exactly and reveal the salient features of the finite line model. Important applications to fiber filter selectivity and optimal intersection trajectories in fracture networks are discussed.

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

Properties of a two-dimensional Poisson-Voronoi tesselation: A Monte-Carlo study

On the basis of simulation of 2 × 10 6 polygons, the distribution of the topological parameter (number of sides) as well as the distributions of area, perimeter, and edge length of the two-dimensional (2D) Poisson-Voronoi polygons have been accurately determined. A two-parameter gamma distribution has been found to be a good fit to both the topological and the area distributions. For sample sizes less than 5000 polygons, the two-parameter lognormal distribution can also be used to accurately describe these distributions. The area, perimeter, and edge length distributions for polygons having a fixed number of edges have also been obtained. The 2D cross section of a three-dimensional Voronoi tesselation has also been studied. The side and area distributions for these cross sections have been found to be significantly different from those in the case of pure 2D Voronoi tesselation. For the former case, our results for the mean number of sides of the neighboring cells of an n-sided cell are in agreement with Aboav's rule as well as his experimental results for the 2D cross section of magnesium oxide grains.

Surface properties of turbulent premixed propane/air flames at various Lewis numbers

Surface properties of turbulent premixed flames including the wrinkled flame perimeter, fraction of the flame pocket perimeter, flame curvature, and orientation distributions have been measured for propane-air flames at Lewis numbers ranging from 0.98 to 1.86 and u′ S L = 1.42–5.71 . The wrinkled flame perimeter is found to be greater for the thermodiffusively unstable Lewis number (Le < 1) by up to 30% in comparison to the most stable condition (Le = 1.86) tested, while the fraction of the flame pocket perimeter shows a similar tendency to be greater for Le < 1. The flame curvature probability density functions are nearly symmetric with respect to the zero mean at all Lewis numbers throughout the range of u′ S L tested, and show a much stronger dependence on the turbulence condition than on the Lewis number. Similarly, the flame orientation distributions show a trend from anisotropy toward a more uniform distribution with increasing u′ S L at a similar rate for all Lewis numbers. Thus, for turbulent premixed propane/air flames for a practical range of Lewis number from 0.98 to 1.86, the effect of Lewis number is primarily to affect the flame structures and thereby flame surface areas and flame pocket areas, while the flame curvature and orientation statistics are essentially determined by the turbulence properties.

Measurement and Characterization of Macropores by using AUTOCAD and Automatic Image Analysis

AbstractMacropores (with equivalent diameters greater than 1600 µm) were quantified under no‐till and conventional tillage practices by using AUTOCAD and automatic image analysis. To quantify macropores, undisturbed soil blocks (50 by 50 cm) were impregnated with plaster of paris slurry. After the plaster of paris set, soil layers were taken out in 5‐cm increments to a total depth of 60 cm. At each soil plane pictures were taken by a 35‐mm camera and macropores were traced on transparent acetate sheets. The pictures and transparent sheets were analyzed by using an automated image analyzer and AUTOCAD, respectively, for total number, perimeter, area, and size frequency distribution of macropores. The AUTOCAD method proved to be simpler and better than the image analysis technique. Larger and continuous cracks accounted for greater macropore area in conventional tillage sites than in no‐till sites. On the other hand, more worm holes and root holes accounted for a greater number and larger perimeters of macropores in no‐till sites in comparison to conventional tillage sites.

A method for systematic site-to-bond conversion of directed graphs

A graph-theoretic method for the complete derivability of bond graphs from their site counterparts is described. Bond perimeter, valence, and cyclomatic number distributions as well as spatial extent measures can be systematically generated when coupled with a site valence partition in the original graph. Relevant consequences for bond configurations include the facts that (i) percolation perimeter and cyclomatic number distributions are equivalent, (ii) geometrical susceptibilities are not independent, and (iii) a critical site/bond ratio exists.