A probability density function for polycrystalline two-dimensional materials

2020 ◽  
Author(s):  
Christopher Samuel DiMarco
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Two Dimensional ◽  
Two Dimensional Materials

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals The five-point non-coherent model of a distributed radar object providing the independent control of angle noise probability characteristics along two orthogonal coordinate axes

2021 ◽  
Vol 2134 (1) ◽  
pp. 012003
Author(s):  
A O Podkopayev ◽  
M A Stepanov
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Processes ◽  
Radar Target ◽  
Two Dimensional ◽  
Independent Control ◽  
Noise Parameters ◽  
Fixed Model

Abstract The two-dimensional five-point non-coherent model replacing a distributed radar target is explored in this work. Four fixed model points are set in corners of the square but the fifth movable point lies inside of this square. Model points are supplied by normal uncorrelated random processes. The possibilities of the five-point non-coherent model of a distributed radar object for independent control of the producing angle noise parameters along two orthogonal coordinate axes are explored. The disadvantage of this model is noted - the connection of parameters values of angle noise probability density function for two coordinate axes. The expression describing this connection is specified. Expressions determining the boundaries of the allowable coordinate values of the fifth movable point of the five-point non-coherent model, within which the model provides the set parameters of the angle noise probability density function, are defined. The arrived results are validated by program simulations.

scholarly journals AUTONOMOUS UNMANNED AERIAL VEHICLE FLIGHT ACCURACY EVALUATION FOR THREE DIFFERENT PATH-TRACKING ALGORITHMS

Transport ◽  
2019 ◽  
Vol 34 (6) ◽  
pp. 652-661
Author(s):  
Ramūnas Kikutis ◽  
Jonas Stankūnas ◽  
Darius Rudinskas
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Unmanned Aerial Vehicle ◽  
Dimensional Space ◽  
Flight Path ◽  
Accuracy Evaluation ◽  
Two Dimensional ◽  
Aerial Vehicle ◽  
Probability Density Function Pdf

This paper shows mathematical results of three methods, which can be used for Unmanned Aerial Vehicle (UAV) to make transition from one flight leg to another. In paper, we present general equations, which can be used for generating waypoint-switching methods when for experiment purpose mathematical UAV model is used. UAV is modelled as moving dot, which eliminates all of the aerodynamics factors and we can concentrate only on the navigation problems. Lots of attention is dedicated to show possible flight path error values with representation of modelled flight path trajectories and deviations from the flight mission path. All of the modelled flight missions are done in two-dimensional space and all the results are evaluated by looking at Probability Density Function (PDF) values, as we are mostly interested in the probability of the error.

scholarly journals Modelling of patterns and estimation of characteristic parameters

2012 ◽  
Vol 9 (1) ◽  
Author(s):  
Anamarija Borštnik Bračić ◽  
Igor Grabec ◽  
Edvard Govekar
Keyword(s):  
Probability Density Function ◽  
Production Process ◽  
Probability Density ◽  
Statistical Method ◽  
Density Function ◽  
Joint Probability ◽  
Joint Probability Density Function ◽  
Two Dimensional ◽  
Characteristic Parameters ◽  
Joint Probability Density

A two-dimensional pattern represents a fingerprint of the process that generated it. It is therefore expected that the information about the production process can be extracted from the pattern. In this paper, a non-parametric statistical method for modelling chaotic two-dimensional patterns and the estimation of the characteristic parameters is proposed. It is based on the joint probability density function of samples taken from known two-dimensional patterns representing a database. A new pattern with an unknown production process is reproduced by comparing parts of the new pattern with samples taken from the database. Because the samples in the database also include information about the production process, relevant parameters and the type of production process can be estimated simultaneously with the reproduction of patterns.

scholarly journals Two-dimensional effects on the interaction of a shock wave with a cloud of particles

2020 ◽  
pp. 207-224
Author(s):  
К.Н. Волков ◽  
В.Н. Емельянов ◽  
А.Г. Карпенко ◽  
И.В. Тетерина
Keyword(s):  
Shock Wave ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Equations Of Motion ◽  
Wave Structure ◽  
Langevin Equations ◽  
Dispersed Phase ◽  
Two Dimensional ◽  
Dimensional Effects

В рамках статистического подхода, основанного на кинетическом уравнении для функции плотности вероятности распределения скорости и температуры частиц, построена континуальная модель, описывающая псевдотурбулентные течения дисперсной фазы. Введение функции плотности вероятности позволяет получить статистическое описание ансамбля частиц вместо динамического описания отдельных частиц на основе уравнений движения и теплопереноса типа Ланжевена. На основе уравнений для первых и вторых моментов дисперсной фазы проводится численное моделирование нестационарного течения газовзвеси, возникающего при взаимодействии ударной волны с облаком частиц. Основные уравнения имеют гиперболический тип, записываются в консервативной форме и решаются с использованием численного метода типа Годунова повышенного порядка точности. Обсуждается влияние двумерных эффектов на формирование ударно-волновой структуры течения и пространственно-временн´ые зависимости концентрации частиц и других параметров потока. A statistical approach based on the kinetic equation for the probability density function of the distribution of particle velocity and temperature is used to develop a continuum model describing pseudoturbulent flows of the dispersed phase. The introduction of the probability density function allows one to obtain a statistical description of an ensemble of particles instead of a dynamic description of individual particles based on Langevin equations of motion and heat transfer. The equations for the first and second moments of the dispersed phase are derived and the numerical simulation of the unsteady gas–particle flow arising due to the interaction of a shock wave with a cloud of particles is performed. The governing equations are of the hyperbolic type and are written in a conservative form. They are solved by a Godunov numerical method of high order of accuracy. Two-dimensional effects on the formation of the shock-wave structure of the gasparticle flow and distributions of particle concentration and other flow quantities in time and space are discussed.

A Skewed Two-Dimensional Probability Density Function for Methane-Air Turbulent Diffusion Flames

2010 ◽  
Author(s):  
Mohsen Abou-Ellail ◽  
Ryo S. Amano ◽  
Samer Elhaw ◽  
Karam Beshay ◽  
Hatem Kayed
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Diffusion Flames ◽  
Mixture Fraction ◽  
Two Dimensional ◽  
Flamelet Model ◽  
The Mean

The present paper describes a mathematical model for turbulent methane-air jet diffusion flames. The mathematical model solves density-weighted governing equations for momentum, mass continuity, turbulent kinetic energy and its dissipation rate. The combustion model solves density-weighted transport equations for the mixture fraction “f”, its variance “g” and its skewness “s”. These variables are used to compute one part of the probability density function (PDF) in mixture fraction domain. The second part of the PDF is computed from the numerical solutions of the mixture fraction dissipation rate “χ” and its variance χ˜″2. The resulting two-dimensional PDF is defined in the mixture-fraction-scalar-dissipation-rate 2D space. The flamelet combustion sub-model is used to compute the mean flame temperature, density and species mass fractions. The flamelet model provides instantaneous state relationships for the stretched flamelets up to the extinction limit. The mean flame properties are computed through the integration of the stretched flamelet state relationships over the two-dimensional PDF. The present 2D probability density function model can predict rim-attached flames as well as unstable lifted flames. This is because the flamelet model provides information on the flame instability arising from the stretching effects of highspeed flowing gases. The new two-dimensional probability density function is used to predict the flame properties of a free jet methane-air flame for which experimental data exists.

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