scholarly journals Nonlinear Closure Relations for Electron Transport in Hydrodynamical Models

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
A. Salhoumi
Keyword(s):  
Distribution Function ◽  
Fourth Order ◽  
Lagrange Multipliers ◽  
Hermite Polynomials ◽  
Boltzmann Distribution ◽  
Hydrodynamical Models ◽  
Calculation Results ◽  
Closure Relations ◽  
Theory Calculation

Closure relations problem of hydrodynamical models in semiconductors is considered by expressing third- and fourth-order closure relations for the moments of the distribution function in terms of second-order Lagrange multipliers using a generalized Maxwell-Boltzmann distribution function within information theory. Calculation results are commented and compared with others to justify the accuracy of the approach developed in this paper. The comparison involves, in the first part with good agreements, the closure relations results obtained within extended thermodynamics which were checked by means of Monte Carlo simulations, in the second part, the results obtained by Grad's method which expands the distribution function up to fourth-order in Hermite polynomials. It is seen that the latter method cannot give any restriction on closure relations for higher-order moments, within the same conditions proposed in our approach. The important role of Lagrange multipliers for the determination of all closure relations is asserted.

scholarly journals DETERMINATION OF EARTHQUAKE FOCUS COORDINATES USING THE CASSINI OVAL METHOD WITH SECOND- AND FOURTH-ORDER HYPERBOLA FIGURES

2020 ◽  
Vol 46 (4) ◽  
pp. 134-142
Author(s):  
B. I. Shakhtarin ◽  
T. G. Aslanov ◽  
U. R. Tetakaev
Keyword(s):  
Comparative Analysis ◽  
Fourth Order ◽  
Relative Position ◽  
Seismic Waves ◽  
Arrival Times ◽  
Earthquake Focus ◽  
Seismic Sensors ◽  
Calculation Results ◽  
The Difference

Objectives. To study the dependencies obtained when determining the coordinates of an earthquake hypocentre using the figures of fourth and second orders.Method. A comparative analysis of determining the coordinates of the earthquake focus using the Cassini oval method, both taking errors in the readings of seismic sensors into account the and ignoring them, is presented.Result. A new method is proposed for determining the coordinates of the earthquake hypocentre, which uses the fourth-order figure, the Cassini oval, in the calculations. A graph is obtained for the distribution of errors in determining the coordinates of the earthquake focus (using the Cassini oval) depending on the relative position of two seismic sensors with different values of their errors in determining the difference in travel times of seismic waves.Conclusion. Since the calculation results are independent of the error sign in determining the difference in the arrival times of seismic waves, the method is suitable for the initial determination of the coordinates of the earthquake hypocentre as well as for comparison with the results of other methods for identifying the error sign. 

scholarly journals Determination of Cumulative Distribution Function of the Crest Value of the Lightning Current Circulating Through Line Surge Arresters

2020 ◽  
Vol 69 (2) ◽  
pp. 11-18
Author(s):  
Goran Levačić ◽  
Alain Xémard ◽  
Miroslav Mesić
Keyword(s):  
Distribution Function ◽  
Transmission Line ◽  
Transmission Lines ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Lightning Strikes ◽  
Surge Arresters ◽  
Lightning Current ◽  
Calculation Results

For the selection and design of line surge arresters (LSA), it is essential to know the characteristics of the lightning current circulating through LSA. When lightning strikes a transmission line, only a part of the lightning current circulates through LSA.This part mostly depends on the point of impact, and the characteristic of the lightning stroke current. The determination of the cumulative distribution function of the lightning current circulating through arresters is presented in first part of the paper. It can be applied on transmission lines where LSAs will be installed to protect the line against the effect of atmospheric discharges.Second part of paper presents the calculation results of the cumulative distribution function of the lightning current circulating through arresters for particular 110 kV transmission line located in an area with high lightning activity.

scholarly journals Dependability of the Exemplary Technical System for Assumed Functions of Defect Density

2016 ◽  
Vol 39 (1) ◽  
pp. 151-161
Author(s):  
Sławomir Stępień ◽  
Justyna Grzesik
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Defect Density ◽  
Technical System ◽  
Cumulative Distribution ◽  
Distribution Shape ◽  
Calculation Results ◽  
Over Time

Abstract The analysis of structural dependability of technical system, especially determining the change in dependability over time, requires knowledge on density function or the understanding of cumulative distribution function of components belonging to the structure. Based on previously registered data concerning component defect, it is relatively easy to establish the average uptime of component as well as the standard deviation for this time. However, defining distribution shape gives rise to some difficulties. Usually, we do not have the sufficient number of data at our disposal to verify the hypothesis regarding the distribution shape. Due to this fact, it is a common practice, depending on the case under consideration, to apply the function of defect density. However, the question arises: Does the incorrect determination of types of distributions of components leads to the big error of estimation results of dependability and system durability? This article will not respond to this question in whole, but one will conduct a comparison of calculation results for a few cases. The calculations were conducted for the exemplary technical system.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution

DETERMINATION OF THE DISTRIBUTION FUNCTION OF THE TIME BETWEEN FAILURES OF A WEAPON MODEL WITHOUT TAKING INTO ACCOUNT THE ENEMY’S FIRE IMPACT

2019 ◽  
pp. 39-45
Author(s):  
M. Sliusarenko ◽  
O. Semenenko ◽  
T. Akinina ◽  
O. Zaritsky ◽  
V. Ivanov
Keyword(s):  
Distribution Function ◽  
Analytical Description ◽  
Time To Failure ◽  
Missile Defense ◽  
Incorrect Choice ◽  
Military Equipment ◽  
Time Between Failures ◽  
The Military ◽  
Fire Impact

In the article, based on the analysis of the requirements for the readiness of weapons and military equipment during combat use and the reliability of their operation in the course of combat operations, it was discovered that one of the reasons that causes a discrepancy between the declared failures and real ones may be the incorrect choice and justification of the time distribution function up to the refusal of military means. As a rule, during the development of these tools, the function of distribution of time to failure is chosen by analogy with similar patterns of weapons and military equipment. In the theory of reliability, special attention is given to choosing the function of time-breaking non-response (failures or failures). Therefore, the article deals with the questions of evaluating the effectiveness of functioning of complex systems and methods of modeling the processes of their functioning, taking into account the laws of the distribution of random variables. The discrepancy between the declared irregularity of the military apparatus and the fact that is actually observed in the troops can be explained by the incorrectly accepted hypothesis about the distribution of time to failure. Therefore, the article analyzes the order of the justification of such a function without taking into account the enemy's fire impact and the proposed variant of determining the function of distribution of the time of work until the refusal of the model of military equipment. The article also cites the reasons for the discrepancy between the claimed missile defense equipment and what is actually observed in the troops. The proposed mathematical model of faultlessness, which at stages of designing and design will allow to set requirements to the model of technology with the help of analytical description. The sequence of calculations of non-failure indexes based on the use of Weibull distribution is substantiated.

Determination of eigenvectors with Lagrange multipliers

2021 ◽  
Author(s):  
Wooyong Han ◽  
Dong-Won Jung ◽  
Jungil Lee ◽  
Chaehyun Yu
Keyword(s):  
Lagrange Multipliers

Determination of thermodynamic state variables of liquids from its microscopic structure using an artificial neural network

Soft Matter ◽  
2020 ◽  
Author(s):  
Ulices Que-Salinas ◽  
Pedro Ezequiel Ramirez-Gonzalez ◽  
Alexis Torres-Carbajal
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Artificial Neural Network ◽  
Distribution Function ◽  
Microscopic Structure ◽  
Machine Learning Method ◽  
Learning Method ◽  
State Variables ◽  
Thermodynamic State

In this work we implement a machine learning method to predict the thermodynamic state of a liquid using only its microscopic structure provided by the radial distribution function (RDF). The...

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

Optimization of a Specimen Size for the Determination of the Diffusible Hydrogen Content in Metals

2014 ◽  
Vol 698 ◽  
pp. 466-471
Author(s):  
Oleg V. Panchenko ◽  
Alexey M. Levchenko ◽  
Victor A. Karkhin
Keyword(s):  
Hydrogen Content ◽  
Calculation Method ◽  
Specimen Size ◽  
Experimental Results ◽  
Diffusible Hydrogen ◽  
Measuring Methods ◽  
Deposited Metal ◽  
Calculation Results

Specimens of various sizes are used to determine hydrogen content in deposited metals in such standards as ISO 3690, AWS A 4.3, and GOST 23338 while measuring methods are the same. It causes problems in comparison of experimental results and brings up the following question: what kind of specimen size is optimal to determine hydrogen content? An optimal specimen size was estimated using a calculation method. Experimental and calculation results obtained by using specimens with estimated dimensions were compared to the results obtained by using the specimen with dimensions of 100*25*8 mm to determine hydrogen content in a deposited metal.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

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