Perimeter Distributions Research Articles

Finding the area and perimeter distributions for flat Poisson processes of a straight line and Voronoi mosaics

Finding the area and perimeter distributions for flat Poisson processes of a straight line and Voronoi mosaics

Finding the Area and Perimeter Distributions for Flat Poisson Processes of a Straight Line and Voronoi Diagrams

Finding the Area and Perimeter Distributions for Flat Poisson Processes of a Straight Line and Voronoi Diagrams

Climatologically invariant scale invariance seen in distributions of cloud horizontal sizes

Abstract. Cloud area distributions are a defining feature of Earth's radiative exchanges with outer space. Cloud perimeter distributions n(p) are also interesting because the shared interface between clouds and clear sky determines exchanges of buoyant energy and air. Here, we test using detailed model output and a wide range of satellite datasets a first-principles prediction that perimeter distributions follow a scale-invariant power law n(p) ∝ p-(1+β), where the exponent β = 1 is evaluated for perimeters within moist isentropic atmospheric layers. In model analyses, the value of β is closely reproduced. In satellite data, β is remarkably robust to latitude, season, and land–ocean contrasts, which suggests that, at least statistically speaking, cloud perimeter distributions are determined more by atmospheric stability than Coriolis forces, surface temperature, or contrasts in aerosol loading between continental and marine environments. However, the satellite-measured value of β is found to be 1.26 ± 0.06 rather than β = 1. The reason for the discrepancy is unclear, but comparison with a model reproduction of the satellite perspective suggests that it may owe to cloud overlap. Satellite observations also show that scale invariance governs cloud areas for a range at least as large as ∼ 3 to ∼ 3 × 105 km2, and notably with a corresponding power law exponent close to unity. Many prior studies observed a much smaller range for power law behavior, and we argue this difference is due to inappropriate treatments of the statistics of clouds that are truncated by the edge of the measurement domain.

Properties of a Random Bipartite Geometric Associator Graph Inspired by Vehicular Networks.

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed.

Geometrical exponents of contour loops on ballistic deposition model with power-law distributed noise

In this paper, we study geometrical properties of contour loops to characterize the morphology of the porous ballistic deposition model with power-law distributed noise. In this model, rod-like particles with variable lengths instead of homogeneous particles are deposited, the length of each rod, l, is determined by a power-law distribution, P(l)∼l−(μ+1), and μ indicates the power-law strength exponent. The accumulation of rods with different lengths leads to a porous structure. The porous structure is converted into contour loops by using the Hoshen–Kopelman algorithm and the complexity and fractal features of the loops are investigated. On the other hand, the distributions of loops indicating the porosity distribution of the growth rough surfaces are investigated. The fractal dimension of the contour set, d, the fractal dimension of each loop, Df, cumulative distributions exponent of areas, ξ, and the perimeter distribution exponent, τ, are calculated for the investigated porous structures. Our results show that enhancement of μ exponent and appearance of the Gaussian ballistic deposition model leads to reduction of structure porosity and enhancement of contour loops area and perimeter. The fractal dimension of the contour set, and the fractal dimension of each loop increases by enhancement of μ exponent. Distributions of loops and geometrical exponents of contour loops in different μ exponent are determined. The results indicate that the hyperscaling relation and Zipf’s law hold for μ≥μc=3 which power-law distributed noise approaches to Gaussian one.

Effect of ultrasonic power on moisture migration and microstructure of contact ultrasound enhanced far-infrared radiation drying on taro slices

To clarify the moisture migration and microstructure of taro in contact ultrasound enhanced far-infrared radiation drying (CUFRD), low-field nuclear magnetic resonance (NMR), scanning electron microscopy (SEM), paraffin sectioning and microscopic observation techniques were applied to explore the changes of the drying curves, water status, microstructure, porosity, microscopic images and distribution curves of cell microstructure parameters of taro under different ultrasound powers of 0, 40, and 80 W. The results showed that applying contact ultrasound (CU) during drying was beneficial to accelerating the dehydration process and improving the porosity of taro slice. With the augment of CU power, the drying times of taro reduced by 16.67% to 25.00%, and the effective water diffusion coefficient was improved by 14.72% to 31.38%. In addition, the application of CU resulted in an increase firstly and then decrease in the cross-sectional area and perimeter distribution curves of taro cells and a widening of the peak shape of the distribution curve of taro cell roundness. In conclusion, CU application could cause faster internal moisture migration, and higher CU power had more obvious effect on microstructure and cell morphological parameters of taro during CUFRD.

Image analysis reveals cellular fragmentation of Spirulina platensis upon treatment with heavy metal ions

Bioremediation is a promising technique that can be used to decrease the environmental discharge of Heavy Metal (HM) such as copper, and zinc. Although studies have addressed the cytotoxic effects of HMs, however, the effect of HMs on the geometry of bacterial species such as Spirulina platensis (S. platensis) remains unknown. Quantitative analysis of parameters such as cell perimeter, cell count, and cell distribution shall greatly improve the efficiency of environmental monitoring. Therefore, this study demonstrates the use of an open-source image analysis tool (ImageJ/Fiji) to quantify the aforementioned parameters to analyze the extent of damage caused by lethal concentration of > 2 mg/L of Cu2+ and > 6 mg/L of Zn2+ which disintegrates S. platensis cells into smaller fragments and subsequently affects their structural parameters in perimeter and cell distribution. In summary, this article demonstrates the use of an image analysis platform to quantify the geometric parameters of microbes for environmental monitoring.

Spatial overlap of wildfire and biodiversity in California highlights gap in non‐conifer fire research and management

AbstractAimGlobal change has spurred the escalation of megafires in California over the last 20 years throughout a variety of ecosystems. Here, we examine the spatial distribution of California wildfires and megafires from the last two decades (2000–2020) in relation to ecosystem types and biodiversity metrics. We offer insights into the prevalence of fire across vegetation types and its potential implications for biodiversity, and for fire and land management. These results challenge the prevailing discourse that wildfire in California is chiefly an issue of forest management.LocationCalifornia, United States of America.MethodsWe calculated burned area across vegetation types from 2000 to 2020 by integrating fire perimeter and land cover data and compared this to a content analysis of coverage of wildfires by media and scientific research across California. We then compared the distribution of fire perimeters across biodiversity metrics (richness and endemism) for five terrestrial taxonomic groups (birds, reptiles, plants, mammals and amphibians) and against the distribution of the wildland‐urban interface (WUI).ResultsTotal burned area from 2000 to 2020 was highest in shrubland ecosystems (38%), followed by conifer (36%), hardwood (17%) and grasslands (9%). In aggregate, ecosystems other than conifer make up the majority (64%) of the area burned in wildfires over the last 20 years. Fires most likely to impact endemic species, overlap areas of high species richness or burn within the WUI occurred predominantly in non‐conifer ecosystems.Main ConclusionsFires outside of forests have burned biodiverse areas critical to endemic species, but recent research and management in fire ecology continues to focus disproportionately on forests.Non‐conifer forested areas in California represent an important gap in fire research and management. As fire regimes shift dramatically in the state, other ecosystem types must be part of the wider conversation on fire management and policies to better protect people and biodiversity.

Multifractal analysis of glaciers in the Lombardy region of the Italian Alps

Glaciers are continuously monitored to detect their spatial extension and time evolution since they are the best witnesses of climate changes. There is a particular interest for Italian glaciers in the Alps as there is evidence that they are melting at a faster rate than those located in other regions of the globe. The determination of the perimeters of glaciers represents an effective method to evaluate the area covered by them. The availability of data for the perimeters encompassing several years suggests the opportunity of correlating the morphological variations in time with the properties of their shrinkage. In this work, we investigate the multifractal properties of the perimeters of the Lombardy glaciers in the Italian Alps. We characterize the area and perimeter distributions of the population of glaciers and we show that the distribution of perimeters exhibits a marked peak, not present in the distribution of areas. We analyze the area-perimeter relation, which is characterized by a power-law behavior that indicates a fractal structure of the perimeters with fractal dimension 1.2, independently from the size of the glaciers. We investigate the multifractal spectra of perimeters and we show that their features are strongly correlated with the area of the glaciers. Finally, we study the time evolution of the area and perimeter of glaciers and we detect the existence of a large class of glaciers whose perimeters increase while their areas decrease. We show that this behavior has a well definite counterpart in their multifractal spectra.

Variability in skeletal muscle fibre characteristics during repeated muscle biopsy sampling in human vastus lateralis.

The percutaneous muscle biopsy procedure is an invaluable tool for characterizing skeletal muscle and capillarization. Little is known about methodological or biological variation stemming from the technique in heterogeneous muscle. Five muscle biopsies were taken from the vastus lateralis of a group of young men (n = 29, 22 ± 1 years) over a 96-h period. We investigated the repeatability of fibre distribution, indices of muscle capillarization and perfusion, and myofibre characteristics. No differences between the biopsies were reported in myofibre type distribution, cross-sectional area (CSA), and perimeter. Capillary-to-fibre perimeter exchange index and individual capillary-fibre contacts were unchanged with respect to the location of the muscle biopsy and index of capillarization. The variability in the sampling distribution of fibre type specific muscle CSA increased when fewer than 150 muscle fibres were quantified. Variability in fibre type distribution increased when fewer than 150 muscle fibres were quantified. Myofibre characteristics and indices of capillarization are largely consistent throughout the vastus lateralis when assessed via the skeletal muscle biopsy technique. Novelty Markers of muscle capillarization and perfusion were unchanged across multiple sites of the human vastus lateralis. Myofibre characteristics such as muscle cross-sectional area, perimeter, and fibre type distribution were also unchanged. Variation of muscle CSA was higher when fewer than 150 muscle fibres were quantified.

A universal approach for drainage basins

Drainage basins are essential to Geohydrology and Biodiversity. Defining those regions in a simple, robust and efficient way is a constant challenge in Earth Science. Here, we introduce a model to delineate multiple drainage basins through an extension of the Invasion Percolation-Based Algorithm (IPBA). In order to prove the potential of our approach, we apply it to real and artificial datasets. We observe that the perimeter and area distributions of basins and anti-basins display long tails extending over several orders of magnitude and following approximately power-law behaviors. Moreover, the exponents of these power laws depend on spatial correlations and are invariant under the landscape orientation, not only for terrestrial, but lunar and martian landscapes. The terrestrial and martian results are statistically identical, which suggests that a hypothetical martian river would present similarity to the terrestrial rivers. Finally, we propose a theoretical value for the Hack’s exponent based on the fractal dimension of watersheds, γ = D/2. We measure γ = 0.54 ± 0.01 for Earth, which is close to our estimation of γ ≈ 0.55. Our study suggests that Hack’s law can have its origin purely in the maximum and minimum lines of the landscapes.

Influence of coke structure on coke quality using image analysis method

The quality of coke affects the performance of the blast furnace, factors affecting coke quality include coal properties, coal charge granulometry and carbonization conditions. The coke properties include the size analysis, cold strength (Micum Indices-M40, M10) and hot strength (Coke Reactivity Index-CRI, Coke Strength after Reaction-CSR) properties and structural properties such as coke structure and texture. Structural properties comprise the porosity, pore-cell wall thickness and pore sizes, while textures consist of the carbon forms in the coke. In present work, advanced method such as image analysis method was used to interpret coke microstructure. Conventional methods such as determination of coke porosity by measurement of real and apparent density and mercury porosimetry have a number of limitations. Coke size, magnification, number of image frames captured, process of pellet preparations and coke properties such as M40, M10, CRI and CSR (low, medium and high values) were taken as variables for experimental purposes. The coke structure parameters such as porosity, length, perimeter, breadth, roundness, pore-wall thickness and pore size distribution of the pores were determined by image analysis method. This method provided average porosity in addition to pore-wall thickness and pore-size distribution. The pore wall thickness measurement by image analysis method provided significant correlations with M40, CRI and CSR values. This explained the usability of image analysis for coke structure measurement.

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

Flocculation experiments were performed in a Taylor-Couette reactor in turbulent conditions characterized by the mean shear rate. A sequenced hydrodynamic protocol was applied which consists in low and high shear rates steps allowing to promote respectively aggregation and breakage processes. The particle size distribution and the 3D fractal dimension were determined on line by laser diffraction while morphological parameters were characterized off line using an automated microscope coupled with image processing. After a first aggregation-breakage cycle, the flocs formed by charge neutralization have smaller sizes than during the first aggregation step when the main aggregation mechanism is the charge neutralization whereas coarser but more resistant aggregates can be produced by bridging mechanism. During the flocculation process, high shear rates calibrate the flocs, creating small flocs having a size close to the Kolmogorov microscale. These small flocs serve as bricks to form larger flocs when lower shear rates are applied and a full reproducibility is observed after one or two cycles of the sequence depending on the aggregation mechanism. A clear correspondence was put in evidence between the shear rate conditions and the volume base mean size or fractal dimension of flocs. The morphological fractal dimension, as well as the fractal dimension derived from laser measurements, are in good agreement with the mean trend of the morphological data but cannot represent the whole diversity of floc sizes and shapes. The 3D surface base area and perimeter distributions appear as a promising tool allowing a deeper analysis of the impact of physico-chemical and shear conditions on aggregate properties during a flocculation process.

Thermodynamic Constraints on the Size Distributions of Tropical Clouds

AbstractTropical convective clouds evolve over a wide range of temporal and spatial scales, which makes them difficult to simulate numerically. Here we propose that cloud statistical properties can be derived within a simplified time‐independent coordinate system of cloud number n, saturated static energy h⋆, and cloud perimeter λ. Under the constraint that circulations around cloud edge compete with each other for total buoyant energy and air, we show that the product of cloud number and cloud perimeter nλ is invariant with λ and that cloud number follows a negative exponential with respect to cloud‐edge deviations of h⋆ with respect to the mean. Overall, the summed perimeter of all clouds scales as the square root of the atmospheric static stability. These theoretical results suggest that the complexity of cloud field structures can be viewed statistically as an emergent property of atmospheric bulk thermodynamics. Comparison with a detailed tropical cloud field simulation shows general agreement to within ≤13%. For the sake of developing hypotheses about cloud temporal evolution that are testable in high resolution simulations, the shapes of tropical cloud perimeter distributions are predicted to be invariant as climate warms, although with a modest increase in total cloud amount.

Global patterns of tropical forest fragmentation.

Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments-at maximum by a factor of 33 over 50 years-as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.

Contribution of image processing for analyzing the cellular structure of cork

AbstractThe alveolar structure of cork confers to this natural material specific physical properties such as low permeability to liquids and gases, advanced thermal and acoustic insulation, and high elasticity. In this paper, a morphological analysis of natural cork cells is presented including statistical distributions of structural quantities. These results were obtained from the study of scanning electron microscopy images of natural cork stoppers. After automation of the image processing analysis, the area and perimeter distributions were measured in different cork sections: axial, tangential, and radial. Perpendicular to the radial direction we also focused on growth rings, which are characterized by smaller cell sizes. This systematic image analysis offers new possibilities to investigate the material at the cell scale and provides useful statistical information about the cork structure.

Influence of Pore Characteristics on Electrochemical and Biological Behavior of Ti Foams

This study reports on titanium (Ti) foams produced using the powder metallurgy technique. During the investigation, the cross-sectional area and perimeter distributions of the pores within the foam were measured. Metallographic image processing analysis software combined with scanning electron microscopic images demonstrated that the pore size and circularity were affected by varying the volume percentage of the space-holder material. The corrosion resistance was investigated using electrochemical impedance spectroscopy and cyclic polarization tests. MG-63 osteoblast-like cells were used to study the biocompatibility and to evaluate the cell attachment, viability, and alkaline phosphatase activity. Analytical results indicated that 50 and 60 vol.% samples were suitable for biomedical applications. Because of the high degree of interconnectivity in the 60 and 70% porosity samples, the electrochemical parameters produced similar results. The corrosion rate of the porous samples showed that the amount of dissolved Ti was at an acceptable level that can be ejected by the body. Applying a fluoridated hydroxyapatite coating significantly increased the osteoblast cell functions on the porous surface.

Scaling properties of planar discrete Poisson-Voronoi tessellations with von Neumann neighborhoods constructed according to the nucleation and growth mechanism

In contrast to the conventional continual case, discrete Poisson-Voronoi tessellations resulting from the growth to impingement of random nuclei differ from tessellations constructed from the nearest tile loci. Previously studied tessellations were based directly on the notion of locus [A. Korobov, Phys. Rev. E 79, 031607 (2009); A. Korobov, Phys. Rev. E 87, 014401 (2013)]. This paper presents results for tessellations constructed by the growth of random nuclei. Their boundaries have a different structure and scaling properties are comparably more robust. One more scalable characteristic may be introduced for them, the perimeter distribution function, which is well approximated by the normal distribution function with the unit mean and the standard deviation equal to 0.25.

Lake shoreline in the contiguous United States: quantity, distribution and sensitivity to observation resolution

Summary Quantifying lake biogeochemical processing at broad spatial scales requires that we scale processes along with physical metrics. Past work has primarily scaled lentic processes using estimates of lake surface area. However, many processes important to lakes, such as material, energy and biological fluxes and biogeochemical cycling, scale with lake perimeter. We estimate the total lake perimeter for the contiguous United States (U.S.) and examine the sensitivity of this estimate to measurement resolution. At the original mapping resolution, lakes in the contiguous U.S. have a total perimeter of over 1.8 million km. The change in measured perimeter versus measurement resolution for the contiguous U.S. had a log‐log slope (also known as the fractal dimension) of −0.21, generally less than previously reported estimates. With changing observation resolution, total measured perimeter was most sensitive to the inclusion or exclusion of small lakes, not shoreline complexity. The total aquatic–terrestrial interface in lakes is less than one‐tenth that of streams and rivers, which collectively account for over 21 million km of shoreline in the contiguous U.S. This study further describes the distribution of lake perimeter and proposes a technique that can contribute to understanding continental‐scale processes.

School characteristics of mesopelagic fish at South Georgia

In this paper, we describe the variation in myctophid schools characteristics at South Georgia using multi-frequency acoustic data collected annually between November 2007 and January 2012. We studied the relationship between the proximity of land and the distribution and schooling characteristics of myctophid fish. We also examined patterns in schooling behaviour in relation to oceanographic data. Fish schools were identified using a dual-frequency dB identification method (Sv120−38kHz), where negative Sv120−38kHz is indicative of gas-bearing organisms, such as swimbladdered fish. Available net data were used to provide information on the meosopelagic fish community in the region. School morphometrics (e.g. length, thickness, area) data were extracted and pooled according to their distance from the shore (0–30km, 30–60km, 60–90km, 90–120km). A total of 578 schools were detected in the survey region and there was high variation in school backscattering strength (NASC), length, height, perimeter, depth and horizontal distribution between surveys, including distinct inter-annual variation in these parameters when surveys were conducted in the same season (2009–2012). Schools were distributed predominantly on-shelf (0–500m isobaths) during some summer surveys (2007 and 2012) and predominantly off-shelf on others (>500m isobaths; 2009, 2010 and 2011). There was also evidence of bathymetric separation in the horizontal distribution of schools. Schools observed in the late-season in 2008 had the greatest NASC, largest height and the deepest depth distribution. Most schools occurred at depths between ∼60 and 300m, but they did not occupy the same water masses during each survey. Schools became progressively thinner, shallower and acoustically weaker with increasing distance to land, whilst school length and perimeter increased correspondingly. The change in fish schooling behaviour between environments could be a response to a combination of local predatory threats over short spatial/temporal scales and differences in oceanographic conditions, such as current velocity. The trend could also be evidence of spatial habitat partitioning of myctophids, with different schooling species, or different life-stages, orientating along a bathymetric gradient at South Georgia.