Random Distribution Of Points Research Articles

Heterogeneity Modelling of Concrete Structures by Nonlocal Damage Models

The behavior of structural concrete is usually represented by considering the homogeneous material media and its macroscopic properties. The problem can be represented in more realistic models considering the material as a heterogeneous multiphase media. In representing heterogeneity, either a direct or indirect description of the phases can be considered. The direct approach considers the phases to be geometrically described in the discrete model. In the indirect approach, phases are represented by homogenizing their physical properties or by the random distribution of points in the domain with material parameters corresponding to each phase. In the physically nonlinear analysis using the Finite Element Method, a constitutive model capable of differentiating the response to tension and compression and computing the gradual cracking process of the concrete is necessary. Furthermore, these models must be coupled with regularization mechanisms to deal with numerically induced localization problems, such as the nonlocal approach. Given the above, this work proposes a model for representing the heterogeneity of concrete aiming at the physically nonlinear analysis of structures. Two phases will be considered to describe the heterogeneity: the cement matrix and the coarse aggregates, which will be incorporated into the discrete model using a hybrid method, which combines characteristics of direct and indirect methods. For material media degradation, a non-local damage model will be adopted with appropriate constitutive laws for each constituent material. Finally, numerical simulations will be presented to evaluate the model's characteristics.

Random sampling and polynomial-free interpolation by Generalized MultiQuadrics

We prove that interpolation matrices for Generalized MultiQuadrics (GMQ) of order greater than one are almost surely nonsingular without polynomial addition, in any dimension and with any continuous random distribution of sampling points. We also include a new class of generalized MultiQuadrics recently proposed by Buhmann and Ortmann.

Investigating cosmic homogeneity using multifractal analysis of the SDSS-IV eBOSS DR16 quasar catalogue

ABSTRACT We analyse the volume-limited subsamples extracted from the sixteenth data release of the Sloan Digital Sky Survey-IV (SDSS-IV) eBOSS quasar survey spanning a redshift interval of 0.8 < z < 2.2, to estimate the scale of transition to homogeneity in the Universe. The multifractal analysis used for this purpose considers the scaling behaviour of different moments of quasar distribution in different density environments. This analysis gives the spectrum of generalized dimension Dq, where positive values of q characterize the scaling behaviour in overdense regions and the negative ones in underdense regions. We expect fractal correlation dimension Dq(r) = 3, for a homogeneous, random point distribution in 3-Dimensions. The fractal correlation dimension Dq(r), corresponding to q = 2 obtained in our study stabilizes in the range (2.8–2.9) for scales r > 80 h−1 Mpc. The observed quasar distribution shows consistency with the simulated mock data and the random distribution of quasars within one sigma. Further, the generalized dimension spectrum Dq(r) also reveals transition to homogeneity beyond >110 h−1 Mpc, and the dominance of clustering at small scales r < 80 h−1 Mpc. Consequently, our study provides strong evidence for the homogeneity in SDSS quasar distribution, offering insights into large-scale structure properties and, thus can play a pivotal role in scrutinizing the clustering properties of quasars and its evolution in various upcoming surveys such as Dark Energy Spectroscopic Instrument and Extremely Large Telescope.

Thermal simulation of microelectrode machining process during block electrical discharge grinding

Electrical discharge machining is widely used in aerospace industries, semiconductor applications, micro-electromechanical systems, and other fields of the machining of micro-holes, micro-shafts, and micro-structures due to non-contact stress during the electrical discharge machining process. In the electrical discharge machining process, the machining precision of electrical discharge machining depends on the dimensional precision of the tool electrode, therefore, the machining process of microelectrode has attracted growing concern. In this study, a thermal model of the microelectrode machining process was proposed to simulate the formation process of microelectrode based on the temperature distribution during block electrical discharge grinding of the microelectrode process. According to the microelectrode machining process, the thermal model considers the main influential factors such as random distribution of discharge points, time-dependent discharge channel radius, Gauss heat source, phase transformation latent heat, etc. Through the thermal simulation analysis, the temperature distribution and the dynamic spark-erosion process of the microelectrode based on random repetitive spark discharges were obtained during block electrical discharge grinding of the microelectrode. Besides, it is found that the maximum temperature value and discharge crater volume of the electrode surface fluctuate and gradually decrease with the increase of discharge times. In addition, the effect of pulse width on the machining process of microelectrode was investigated by numerical simulation and block electrical discharge grinding of microelectrode experiment. The results indicated that the crater volume and the maximum temperature value on the surface of the microelectrode increased with the increase of pulse width. The formation process of microelectrode was considered a significant indicator to determine the machining precision and machining efficiency of the electrical discharge machining process.

Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows

In this work, a radial basis function differential quadrature-based physics-informed neural network (RBFDQ-PINN) is proposed to simulate steady incompressible flows. The conventional physics-informed neural network (PINN) makes use of the physical equation as a constraint to ensure that the solution satisfies the physical law and the automatic differentiation (AD) method to calculate derivatives at collocation points. Although the AD-PINN is expedient in evaluating derivatives at arbitrary points, it is time-consuming with higher-order derivatives and may lead to nonphysical solutions with sparse samples. Alternatively, the finite difference (FD) method can facilitate the calculation of derivatives, but the FD-PINN will increase the computational cost when handling random point distributions, especially with higher-order discretization schemes. To address these issues, the radial basis function differential quadrature (RBFDQ) method is incorporated into the PINN to replace the AD method for the calculation of derivatives. The RBFDQ method equips with high efficiency in the calculation of high-order derivatives as compared with the AD method and great flexibility in the distribution of mesh points as compared with the FD method. As a result, the proposed RBFDQ-PINN is not only more efficient and accurate but also applicable to irregular geometries. To demonstrate its effectiveness, the RBFDQ-PINN is tested in sample problems such as the lid-driven cavity flow, the channel flow over a backward-facing step, and the flow around a circular cylinder. Numerical results reveal that the RBFDQ-PINN achieves satisfactory accuracy without any labeled collocation points, whereas the AD-PINN struggles to solve some cases, especially for high Reynolds number flows.

Voronoi Diagrams Generated by the Archimedes Spiral: Fibonacci Numbers, Chirality and Aesthetic Appeal

Voronoi mosaics inspired by seed points placed on the Archimedes Spirals are reported. Voronoi (Shannon) entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi tessellations generated by the seeds located on the Archimedes spiral and separated by linearly growing radial distance demonstrate a switch in their chirality. Voronoi mosaics built from cells of equal size, which are of primary importance for the decorative arts, are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.

A spatial evaluation method for earthquake disaster using optimized BP neural network model

Rapid spatial evaluation of seismic disaster after earthquake occurrence is required in disaster emergency rescue management, because of its importance in decreasing casualties and property losses. Among many categories of seismic disaster, evaluation of earthquake-affected population is of great significance to clarify the severity of earthquake disaster. For simple classic regression model, it is difficult to describe the strong nonlinear relationship between multiple influencing factors and earthquake disasters. In present study, an optimized BP neural network model considering spatial characteristic of influencing factors is proposed to evaluate the population distribution affected by earthquake. The correlation between earthquake-affected population and influencing factors is analysed using data of 2013 Ms7.0 Lushan earthquake. Ten influencing factors including elevation, slope angle, population density, per capita GDP, distance to fault, distance to river, NDVI, PGA, PGV, and distance to the epicentre, were classified into environmental and seismic factors. Correlation analysis revealed that per capita GDP and PGA factor had a stronger correlation with the earthquake-affected population. The earthquake-affected population was evaluated using a BP neural network by optimizing training samples considering spatial characteristics of per capita GDP and PGA factors. Different numbers of sample points, instead of a random distribution of sample points, were generated in areas with different value intervals of the influencing factors. The optimized samples improved the convergence speed and generalization capability of neuron network compared to random samples. The trained network was applied to the 2017 Ms7.0 Jiuzhaigou earthquake to verify its prediction accuracy. The MAE of the estimated earthquake-affected populations of different counties under Jiuzhaigou earthquake were 1.276 people/km2 using network model from optimized samples, smaller than the results of network model from random samples and linear regression model. The results indicate that BP neural network, which considers correlation characteristics of factors, has capability to evaluate spatial earthquake disaster.

Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol’s Quasi-Random Sampling

The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit approximations can be used instead. The accuracy of such approximations should be evaluated only throughout the domain of interest in engineering practice where the number of test points can be chosen in many different ways, using uniform, quasi-uniform, random, and quasi-random patterns. To avoid picking points with undetected errors, a sufficient minimal number of such points should be chosen, and they should be distributed using proper patterns. A properly chosen pattern can minimize the required number of testing points that are sufficient to detect maximums of the error. The ability of the Sobol quasi-random vs. random distribution of testing points to capture the maximal relative error using a sufficiently small number of samples is evaluated. Sobol testing points that are quasi-randomly distributed can cover the domain of interest more evenly, avoiding large gaps. Sobol sequences are quasi-random and are always the same, which allows the exact repetition of scientific results.

Elastic response of wire frame glasses. I. Two dimensional model.

We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length L. We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions, the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method to find the scaling of the elastic stress with concentration in these glassy systems. We apply this method to a simple 2D model system where a test particle is placed on a plane and constrained by a random distribution of points with number density ν. Two striking differences between wire frame and rod suspensions are found: (1) The linear elasticity per particle for wire frames is very large, scaling like ν2L4, whereas for rods, it is much smaller and independent of concentration. (2) Rods always shear thin but wire frames shear harden for concentrations less than ∼K/kBTL4, where K is the bending modulus of the particles. The deformation of wire frames is found to be important even for small strains, with the proportion of deformed particles at a particular strain, γ, being given by (νL2)2γ2. Our results agree well with simple numerical calculations for the 2D system.

Improving regional ionospheric TEC mapping based on RBF interpolation

Radial basis function (RBF) interpolation with multi-quadric is developed to perform ionospheric total electron content (TEC) mapping for the Chinese region between 15°N ~ 40°N and 100°E ~ 125°E. TEC measurements from the Centre for Orbit Determination in Europe (CODE) covering the solar maximum year 2011 are used to investigate the performance of the proposed RBF interpolation method. The differences between the RBF interpolated TEC and the CODE TEC are within 0.5 TECU and the root mean square error (RMSE) is very small when 49 data points are used. The maximum difference is ~5 TECU and the error is less than 1 TECU with 25 samples. Our study suggests that a random distribution of measurement points gives smaller RMSEs than a homogenous distribution when the number of sample points is low. The study indicates that RBF interpolation offers a powerful and reliable tool for ionospheric TEC mapping.

Virtual Forestry Generation: Evaluating Models for Tree Placement in Games

A handful of approaches have been previously proposed to generate procedurally virtual forestry for virtual worlds and computer games, including plant growth models and point distribution methods. However, there has been no evaluation to date which assesses how effective these algorithms are at modelling real-world phenomena. In this paper, we tackle this issue by evaluating three algorithms used in the generation of virtual forests—a randomly uniform point distribution method (control), a plant competition model, and an iterative random point distribution technique. Our results show that a plant competition model generated more believable content when viewed from an aerial perspective. Interestingly, however, we also found that a randomly uniform point distribution method produced forestry which was rated higher in playability and photorealism, when viewed from a first-person perspective. We conclude that the objective of the game designer is important to consider when selecting an algorithm to generate forestry, as the algorithms produce forestry that is perceived differently.

Stochastic compartmental model of HIV-1 infection

Stochastic model of the dynamics of HIV-1 infection describing the interaction of target cells and viral particles in the lymphatic nodes and their movement between the lymphatic nodes is constructed. The lymphatic system is represented as a graph, vertices of which are the lymphatic nodes and edges are the lymphatic vessels. The novelty of the model consists in the description of populations of cells and viral particles in terms of a multidimensional birth and death process with the random point-distributions. The random pointdistributions describe the duration of the transition of cells and viral particles between the lymph nodes and the duration of the stages of their development. The durations of transitions of viral particles and cells between the lymphatic nodes are not random and based on the rate of lymph flow. The durations of the developmental stages of infected target cells are assume to be constant. The graph theory for the formalization and compact representation of the model is used. An algorithm for modelling the dynamics of the studied populations is constructed basing on the Monte-Carlo method. The results of computational experiments for a system consisting of five lymphatic nodes are presented.

How Is the Confidentiality of Crime Locations Affected by Parameters in Kernel Density Estimation?

Kernel density estimation (KDE) is widely adopted to show the overall crime distribution and at the same time obscure exact crime locations due to the confidentiality of crime data in many countries. However, the confidential level of crime locational information in the KDE map has not been systematically investigated. This study aims to examine whether a kernel density map could be reverse-transformed to its original map with discrete crime locations. Using the Epanecknikov kernel function, a default setting in ArcGIS for density mapping, the transformation from a density map to a point map was conducted with various combinations of parameters to examine its impact on the deconvolution process (density to point location). Results indicate that if the bandwidth parameter (search radius) in the original convolution process (point to density) was known, the original point map could be fully recovered by a deconvolution process. Conversely, when the parameter was unknown, the deconvolution process would be unable to restore the original point map. Experiments on four different point maps—a random point distribution, a simulated monocentric point distribution, a simulated polycentric point distribution, and a real crime location map—show consistent results. Therefore, it can be concluded that the point location of crime events cannot be restored from crime density maps as long as parameters such as the search radius parameter in the density mapping process remain confidential.

INCREASING TRACKING ROBUSTNESS FOR LOW-COMPLEXITY REAL-TIME RECONSTRUCTIONS WITH HANDHELD OPTICAL SCANNERS

Abstract. By offering fast and flexible solutions to create 3D models, handheld scanners are currently under the focus of many research activities in various 3D data processing fields. The real-time constraint is still challenging to achieve especially when it comes with concurrent needs, such as level of accuracy in the data acquisition, easiness of recovering from scanning interruptions or loop closure abilities... Among them, object/scene tracking quality is one of the most critical. In this work, we describe two issues that affects its performance, focusing on the robustness of the process. Specifically, we encounter such issues at to two different steps while moving through the working pipeline of a prototype handheld scanner, i.e. (1) the data pre-processing before running a pairwise alignment between a frame and the model representation, called key-frame, and (2) the temporal and quality criteria that govern key-frame updates. Our approach simply consists in substituting the use of a rigid (uniform) pattern for sampling, with a random distribution of points. We then implement an adaptive statistical method to select suitable timing steps for key-frames refreshing, comparing this solution with a previous static one based on regular updating rate. We run experiments on a dataset created with our own scanner and we show that the adoption of such alternatives reduce the number of tracking failures, consequently increasing the robustness of the system, improving the quality of the alignments and preserving the real-time behavior of the device.

Multi-scale prediction of chemo-mechanical properties of concrete materials through asymptotic homogenization

In the present contribution, the effective mechanical, diffusive, and chemo-expansive properties of concrete are computed from a multi-scale and multi-physics approach. The distinctive features of the approach are that i) the mechanical and diffusive responses are modelled in a coupled fashion (instead of separately, as is usually done), and that ii) the multi-scale model considers three different scales of observation, which allows for including heterogeneous effects from both the micro- and meso-scales in the effective macro-scale properties of concrete. At the macro-scale, the concrete material is considered as homogeneous, whereas at the meso-scale it consists of particle aggregates embedded in a porous cement paste. At the micro-scale the porous cement paste is described as a two-phase material, composed of a solid cement phase and saturated capillary pores. Adopting a two-level asymptotic homogenization procedure, the effective meso-scale properties of the porous cement paste are computed first, using a unit cell that includes the cement paste and pore characteristics. Subsequently, the obtained meso-scale response of the porous cement paste, together with the aggregate characteristics, defines the material properties of a second unit cell, which is used for calculating the effective macro-scale response of concrete. The distributions of the pores and the aggregates within the unit cells are determined from a uniform, random distribution of points, and their radii are defined from a probability distribution function. The efficacy of the proposed framework is illustrated by studying the effective mesoscopic response of a porous cement paste, which demonstrates the influence of the micro-scale porosity and pore percolation. Next, the effective macroscopic response of concrete is analysed, by considering the influence of the aggregate volume fraction, the mismatches in elastic stiffnesses and diffusivity between the aggregate and the cement paste, and the porosity. The computed effective properties are compared with experimental data from the literature, showing a good agreement.

A Least Square Residual version of the Modified Finite Particle Method to solve saddle point problems: Application to stationary Stokes and Navier–Stokes equations

The Modified Finite Particle Method (MFPM) is a meshless method belonging to the class of meshless method. Given the absence of a pre-determined connectivity among nodes, such methods are mainly used in applications where large deformations are involved, such as fluid-dynamics.In the present work we combine the Modified Finite Particle Method with a Weighted Least Square Residual Method, and use the combined version of the method for the solution of saddle point problems, such as the Stokes and Navier–Stokes equations for incompressible fluid flow simulations. The use of MFPM derivative approximation techniques in the framework of Least Square Residual Method permits a simple handling of the numerical difficulties typical of incompressible fluid simulations, avoiding problems such as pressure spurious oscillations, and preserving the convergence properties of the Modified Finite Particle Method also in presence of random collocation point distributions.

Kajian Simulasi Perbandingan Interpolasi Tetangga Terdekat dan 2-Tetangga Terdekat pada Sebaran Titik Spasial

Spatial point distribution in an area has three types of pattern. They are random, regular, and cluster. A set of points in space is an information about the number of events in that particular space. Oftenly, the number of events in a space is difficult to obtain, thus number of events estimation is necessary in order to conduct analysis and generate the right conclusion. This research uses nearest neighbor and 2- nearest neighbors interpolation as an interpolation methods under the principle of the object location proximity. The accuracy measurements were used in both methods can be computed by the smallest MAE values. MAE is a measure to evaluate the level of accuracy by using the absolute mean of the observed and interpolation expected value difference. This research uses MAE to determine the best method. This research uses both simulated and real-life data regarding the number of Dengue Hemorrhagic Fever (DBD) patient in Central Java Province. Simulated data were generated from the Poisson, binomial, and negative binomial distribution which were set in the quadrant. The results show that the 2-nearest neighbors interpolation yield smaller MAE value than the nearest neighbor interpolation MAE either in the random, regular, or cluster spatial point distribution. The percentage of bias of the observation and estimation value of the two interpolation methods are relatively small or less than 20%. Meanwhile, in the real-life data, the 2-nearest neighbors interpolation also yield a smaller MAE value than the nearest neighbor interpolation.

A statistical approach to relationships between fluid emissions and faults: The Sea of Marmara case

The Sea of Marmara is traversed by the North Anatolian Fault system and also presents abundant emission sites of methane gas into the water column. In order to assess the spatial relationship between gas emissions and active faults, the distribution of distances between gas emission sites and the nearest fault is calculated and compared with the distribution of distances between a uniform random distribution of points (Poisson process representing the null hypothesis of an absence of relationship between gas emissions and faults) and the nearest fault. Interestingly, the distance distribution for the Poisson process is nearly exponential, indicating that the fault map does not have a characteristic scale other than that representing the intensity of the fault network. The distance distribution for the observed gas emissions is significantly narrower than that arising from the Poisson process, with a Kolmogorov distance of 0.25 ± 0.02. The crossing point between the two distributions defines the characteristic half-width of the swath of gas emission sites around the mapped active faults. For the whole Sea of Marmara data set a characteristic half-width of 900–1000 m is found which matches the half-width of the seafloor deformation zone observed around the main active fault. When the same analysis is applied to zones covering the Western High and the Central High it is found that the swath of gas emissions is wider on the Central High (2 km half-width), and not clearly related to the seafloor deformation zone there. This difference is put in perspective with recent work showing that creep is occurring on the western segment of the Main Marmara Fault (this also causing microseismicity) while the central Istanbul-Silivri segment may have remained locked since the 1766 magnitude 7+ earthquake. This suggests that aseismic slip (and not only earthquake occurrence) effectively maintains high permeability conduits in fault zones in sediments.

Correlation methods for the analysis of X-ray polarimetric signals

X-ray polarimetric measurements are based on studying the distribution of the directions of scattered photons or photoelectrons and on the search of a sinusoidal modulation with a period of π. We developed two tools for investigating these angular distributions based on the correlations between counts in phase bins separated by fixed phase distances. In one case we use the correlation between data separated by half of the bin number (one period) which is expected to give a linear pattern. In the other case, the scatter plot obtained by shifting by 1/8 of the bin number (1/4 of period) transforms the sinusoid in a circular pattern whose radius is equal to the amplitude of the modulation. For unpolarized radiation these plots are reduced to a random point distribution centred at the mean count level. This new methods provide direct visual and simple statistical tools for evaluating the quality of polarization measurements and for estimating the polarization parameters. Furthermore they are useful for investigating distortions due to systematic effects.

On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large Dimensions with Correlated Coordinates

In a recent paper the author proved a theorem to the effect that the matrix of normalized Euclidean distances on the set of specially distributed random points in the $n$-dimensional Euclidean space $\mathbb R^{n}$ with independent coordinates converges in probability as $n\rightarrow\infty$ to an ultrametric matrix, the latter being completely determined by the expectations of conditional variances of random coordinates of points. The main theorem of the present paper extends this result to the case of weakly correlated coordinates of random points. Prior to formulating and stating this result we give two illustrative examples describing particular algorithms of generation of such ultrametric spaces.