scholarly journals On the tangent model for the density of lines and a Monte Carlo method for computing hypersurface area

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Khaldoun El Khaldi ◽  
Elias G. Saleeby
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Integral Geometry ◽  
Surface Areas ◽  
Geometric Objects ◽  
Crofton Formula

AbstractMethods to estimate surface areas of geometric objects in 3D are well known. A number of these methods are of Monte Carlo type, and some are based on the Cauchy–Crofton formula from integral geometry. Employing this formula requires the generation of sets of random lines that are uniformly distributed in 3D. One model to generate sets of random lines that are uniformly distributed in 3D is called the tangent model (see [

scholarly journals On the density of lines and Santalo’s formula for computing geometric size measures

2020 ◽  
Vol 26 (4) ◽  
pp. 315-323
Author(s):  
Khaldoun El Khaldi ◽  
Elias G. Saleeby
Keyword(s):  
Monte Carlo ◽  
Integral Geometry ◽  
Convex Sets ◽  
Geometric Probability ◽  
Monte Carlo Algorithm ◽  
Simultaneous Estimation ◽  
Compact Sets ◽  
Established Method ◽  
Surface Areas ◽  
Geometric Size

AbstractMethods from integral geometry and geometric probability allow us to estimate geometric size measures indirectly. In this article, a Monte Carlo algorithm for simultaneous estimation of hyper-volumes and hyper-surface areas of a class of compact sets in Euclidean space is developed. The algorithm is based on Santalo’s formula and the Hadwiger formula from integral geometry, and employs a comparison principle to assign geometric probabilities. An essential component of the method is to be able to generate uniform sets of random lines on the sphere. We utilize an empirically established method to generate these random chords, and we describe a geometric randomness model associated with it. We verify our results by computing measures for hyper-ellipsoids and certain non-convex sets.

scholarly journals A Method for Estimating the Cloud Adjacency Effect on the Ground Surface Reflectance Reconstruction from Passive Satellite Observations through Gaps in Cloud Fields

Atmosphere ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1512
Author(s):  
Mikhail V. Tarasenkov ◽  
Matvei N. Zonov ◽  
Marina V. Engel ◽  
Vladimir V. Belov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiation Transfer ◽  
Ground Surface ◽  
Interpolation Formula ◽  
Statistical Simulation ◽  
Satellite Observations ◽  
Surface Reflectance ◽  
Surface Areas ◽  
The Monte Carlo Method

A method for estimating the cloud adjacency effect on the reflectance of ground surface areas reconstructed from passive satellite observations through gaps in cloud fields is proposed. The method allows one to estimate gaps of cloud fields in which the cloud adjacency effect can be considered small (the increment of the reflectance Δrsurf≤ 0.005). The algorithm is based on statistical simulation by the Monte Carlo method of radiation transfer in stochastic broken cloudiness with a deterministic cylindrical gap. An interpolation formula is obtained for the radius of the cloud adjacency effect that can be used for the reconstruction the ground surface reflectance in real time without calculations by the Monte Carlo method.

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

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