scholarly journals Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

Physics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 352-367
Author(s):  
Slobodan Babic ◽  
Cevdet Akyel
Keyword(s):  
Cross Sections ◽  
Special Functions ◽  
Rectangular Cross Section ◽  
The Self ◽  
Thin Wall ◽  
Elementary Functions ◽  
Special Cases ◽  
Current Densities ◽  
New Formula ◽  
Azimuthal Current

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

scholarly journals The Fast and Accurate Calculation of the Self Inductance for the Circular Coils of the Rectangular Cross Section with the Radial and the Azimuthal Current Densities

2020 ◽  
Author(s):  
Slobodan Babic ◽  
Cevdet Akyel
Keyword(s):  
Cross Sections ◽  
Special Functions ◽  
Rectangular Cross Section ◽  
The Self ◽  
Thin Wall ◽  
Elementary Functions ◽  
Special Cases ◽  
Current Densities ◽  
New Formula ◽  
Azimuthal Current

In this paper we give the new formulas for calculating the self-inductance for the circular coils of the rectangular cross sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions we can obtain the special cases for the self-inductance of the thin disk pancake and the thin wall solenoid that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin wall solenoid is obtained for the first time in the literature. In this paper we do not use special functions such as the elliptical integrals of the first, second and third kind, Struve, and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in the excellent agreement. This is way we consider this approach as the novelty because of its simplicity in the self -inductance calculation of the previously mentioned configurations.

scholarly journals A family of Finch and Skea relativistic stars

2017 ◽  
Vol 26 (03) ◽  
pp. 1750014 ◽  
Author(s):  
S. D. Maharaj ◽  
D. Kileba Matondo ◽  
P. Mafa Takisa
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Graphical Analysis ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Relativistic Stars ◽  
Spacetime Geometry ◽  
Special Cases ◽  
Barotropic Equation ◽  
Charged Model

Several new families of exact solution to the Einstein–Maxwell system of differential equations are found for anisotropic charged matter. The spacetime geometry is that of Finch and Skea which satisfies all criteria for physical acceptability. The exact solutions can be expressed in terms of elementary functions, Bessel functions and modified Bessel functions. When a parameter is restricted to be an integer then the special functions reduce to simple elementary functions. The uncharged model of Finch and Skea [R. Finch and J. E. F. Skea, Class. Quantum Grav. 6 (1989) 467.] and the charged model of Hansraj and Maharaj [S. Hansraj and S. D. Maharaj, Int. J. Mod. Phys. D 15 (2006) 1311.] are regained as special cases. The solutions found admit a barotropic equation of state. A graphical analysis indicates that the matter and electric quantities are well behaved.

A Semi-Analytic Solution for Self-Healing Concrete Beams Through Stress Spectral Decomposition

2018 ◽  
Vol 10 (07) ◽  
pp. 1850077
Author(s):  
A. Kazemi ◽  
M. Baghani ◽  
H. Shahsavari ◽  
S. Sohrabpour
Keyword(s):  
Cross Section ◽  
Spectral Decomposition ◽  
Damage Mechanics ◽  
Concrete Beam ◽  
Rectangular Cross Section ◽  
Closed Form Solution ◽  
The Self ◽  
Continuum Damage ◽  
Self Healing ◽  
Damage Healing

Continuum damage-healing mechanics (CDHM) is used for phenomenological modeling of self-healing materials. Self-healing materials have a structural capability to recover a part of the damage for increasing materials life. In this paper, a semi-analytic modeling for self-healing concrete beam is performed. Along this purpose, an elastic damage-healing model through spectral decomposition technique is utilized to investigate an anisotropic behavior of concrete in tension and compression. We drive an analytical closed-form solution of the self-healing concrete beam. The verification of the solution is shown by solving an example for a simply supported beam having uniformly distributed the load. Finally, a result of a self-healing concrete beam is compared to elastic one to demonstrate the capability of the proposed analytical method in simulating concrete beam behavior. The results show that for the specific geometry, the self-healing concrete beam tolerates 21% more weight, and the deflection of the entire beam up to failure load is about 27% larger than elastic solution under ultimate elastic load for both I-beam and rectangular cross-section. Comparison of Continuum Damage Mechanics (CDM) solution with CDHM solution of beam shows that critical effective damage is decreased by 32.4% for a rectangular cross-section and by 24.2% for I-shape beam made of self-healing concrete.

scholarly journals Fusion cross-sections for inertial fusion energy

2004 ◽  
Vol 22 (4) ◽  
pp. 469-477 ◽  
Author(s):  
XING ZHONG LI ◽  
BIN LIU ◽  
SI CHEN ◽  
QING MING WEI ◽  
HEINRICH HORA
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Light Nucleus ◽  
Resonant Tunneling ◽  
Fusion Energy ◽  
Inertial Fusion ◽  
Inertial Fusion Energy ◽  
Fusion Reactions ◽  
Tunneling Model ◽  
New Formula

The application of selective resonant tunneling model is extended from d + t fusion to other light nucleus fusion reactions, such as d + d fusion and d + 3He. In contrast to traditional formulas, the new formula for the cross-section needs only a few parameters to fit the experimental data in the energy range of interest. The features of the astrophysical S-function are derived in terms of this model. The physics of resonant tunneling is discussed.

Bayesian Prediction in Hybrid Conjoint Analysis

2002 ◽  
Vol 39 (2) ◽  
pp. 253-261 ◽  
Author(s):  
Frenkel Ter Hofstede ◽  
Youngchan Kim ◽  
Michel Wedel
Keyword(s):  
Prior Information ◽  
Current Model ◽  
The Self ◽  
Attribute Importance ◽  
Individual Level ◽  
Special Cases ◽  
Full Profile ◽  
Credible Intervals ◽  
Competing Models ◽  
The Individual

The authors propose a general model that includes the effects of discrete and continuous heterogeneity as well as self-stated and derived attribute importance in hybrid conjoint studies. Rather than use the self-stated importances as prior information, as has been done in several previous approaches, the authors consider them data and therefore include them in the formulation of the likelihood, which helps investigate the relationship of self-stated and derived importances at the individual level. The authors formulate several special cases of the model and estimate them using the Gibbs sampler. The authors reanalyze Srinivasan and Park's (1997) data and show that the current model predicts real choices better than competing models do. The posterior credible intervals of the predictions of models with the different heterogeneity specifications overlap, so there is no clear superior specification of heterogeneity. However, when different sources of data are used—that is, full profile evaluations, self-stated importances, or both—clear differences arise in the accuracy of predictions. Moreover, the authors find that including the self-stated importances in the likelihood leads to much better predictions than does considering them prior information.

Torsion of Noncylindrical Shafts of Circular Cross Section

1950 ◽  
Vol 17 (3) ◽  
pp. 275-282
Author(s):  
H. J. Reissner ◽  
G. J. Wennagel
Keyword(s):  
Cross Sections ◽  
Inverse Method ◽  
Direct Method ◽  
Circular Cross Section ◽  
Theory Of Elasticity ◽  
Elementary Functions ◽  
Single Term ◽  
Circumferential Displacement ◽  
Basic Differential Equation ◽  
Technical Interest

Abstract The theory of torsion of noncylindrical bodies of revolution, initiated by J. H. Michell and A. Föppl, is stated by a basic differential equation of the circumferential displacement and by a boundary condition of the shear stress along the generator surface. The solution of these two equations by the “direct” method of first assuming the boundary shape has not lent itself to closed solutions in terms of elementary functions, so that only approximation, infinite series, and experimental methods have been applied. A semi-inverse method analogous to Saint Venant’s semi-inverse method for cylindrical bodies has the disadvantage of the restriction to special boundary shapes but the advantage of exact solutions by means of elementary functions. By this method, bodies of conical, ellipsoidal, and hyperbolic boundary shapes have been obtained in a simple analysis. One class of integrals leading to other boundary shapes seems not to have been analyzed up to now, namely, the integrals in the form of a product of two functions of, respectively, axial (z) and radial (r) co-ordinates. A first suggestion of this possibility was given in Love’s treatise on the mathematical theory of elasticity. In the present paper, the classes of boundary shapes, displacements, and stress distributions are investigated analytically and numerically. The extent of the numerical investigation contains only the results of single-term integrals for full and hollow cross sections of technical interest. The detailed analysis of the boundary shapes, following from series integrals, presents essential mathematical obstacles. Overcoming these difficulties might lead to a multitude of solutions of interesting boundary shapes, and stress and strain distribution.

scholarly journals Dynamic modeling of tunnel survey spatiotemporal data

2014 ◽  
Vol 20 (2) ◽  
pp. 354-375
Author(s):  
Xiaolong Li ◽  
Jiansi Yang ◽  
Bingxuan Guo ◽  
Hua Liu ◽  
Jun Hua
Keyword(s):  
Survey Data ◽  
Cross Section ◽  
Cross Sections ◽  
3D Modeling ◽  
3D Model ◽  
Three Dimensional ◽  
Spatiotemporal Data ◽  
Excavation Process ◽  
Special Cases ◽  
Time Stamps

Currently, for tunnels, the design centerline and design cross-section with time stamps are used for dynamic three-dimensional (3D) modeling. However, this approach cannot correctly reflect some qualities of tunneling or some special cases, such as landslips. Therefore, a dynamic 3D model of a tunnel based on spatiotemporal data from survey cross-sections is proposed in this paper. This model can not only playback the excavation process but also reflect qualities of a project typically missed. In this paper, a new conceptual model for dynamic 3D modeling of tunneling survey data is introduced. Some specific solutions are proposed using key corresponding technologies for coordinate transformation of cross-sections from linear engineering coordinates to global projection coordinates, data structure of files and database, and dynamic 3D modeling. A 3D tunnel TIN model was proposed using the optimized minimum direction angle algorithm. The last section implements the construction of a survey data collection, acquisition, and dynamic simulation system, which verifies the feasibility and practicality of this modeling method.

scholarly journals Particle separation of a modified feed nozzle hydrocyclone under different operating parameters

2021 ◽  
Vol 11 (5) ◽  
pp. 159-170
Author(s):  
Zsolt Hegyes ◽  
Máté Petrik ◽  
L. Gábor Szepesi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Particle Separation ◽  
Baffle Plate ◽  
Important Data ◽  
Preliminary Research ◽  
All Speeds ◽  
Plate Solution

During the operation of the hydrocyclone the cut size diameter is the most important data. This is connected to feed rate, which is closely related to the feed cross section. Preliminary research has revealed that square cross-section is more effective than circular cross-section. The research compared 2 types of feed cross sections at 5 different feed rates. One is a standard rectangular cross-section and the other is a square cross-section that narrows with a baffle plate. Preliminary calculations for cut size diameter have shown that better particle separation at all speeds can be achieved with the baffle plate solution. In both types, the increased velocity created decreased cut size diameter. During the simulation, the baffle plate did not cause any abnormalities in the internal pressure and velocity distributions. The simulation revealed that the particles did not behave as previously calculated.

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