Special cases: cut-off cross sections andresonance frequencies

2011 ◽  
pp. 98-138
Keyword(s):  
Cross Sections ◽  
Special Cases

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 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.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

scholarly journals Modeling and Simulation of stochastically deformed Waveguides using Schelkunoff's Method

2018 ◽  
Vol 16 ◽  
pp. 35-41
Author(s):  
Hoang Duc Pham ◽  
Soeren Ploennigs ◽  
Wolfgang Mathis
Keyword(s):  
Cross Sections ◽  
Electromagnetic Waves ◽  
Analytic Solution ◽  
Propagation Constant ◽  
Circular Waveguide ◽  
Transverse Field ◽  
Field Pattern ◽  
Coupled Mode ◽  
Special Cases ◽  
Cylindrical Waveguides

Abstract. This paper deals with the propagation of electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections. The general theory of electromagnetic waves is of high interest because of its practical use as a transmission medium. But only in a few special cases, an analytic solution of Maxwell's equations and the appropriate boundary conditions can be found (Spencer, 1951). The coupled-mode theory, also known as Schelkunoff's method, is a semi-numerical method for computing electromagnetic waves in hollow and cylindrical waveguides bounded by perfect electric walls (Saad, 1985). It allows to calculate the transverse field pattern and the propagation constant. The aim of this paper is to derive the so-called generalized telegraphist's equations for irregular deformed waveguides. Subsequently, the method's application will be used on a circular waveguide as an illustrating example.

scholarly journals Monte Carlo simulation of γ and fission transfer reactions using extended ℛ-matrix theory

2020 ◽  
Vol 239 ◽  
pp. 03013
Author(s):  
Olivier Bouland
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Matrix Theory ◽  
Transfer Reactions ◽  
Test Case ◽  
Compound System ◽  
Reaction Method ◽  
Average Cross Section ◽  
Special Cases ◽  
Induced Fission

This paper comes back on the accuracy of the surrogate-reaction method (SRM) historically used for neutron-induced average partial cross sections inference from measured surrogate-reaction probabilities. The SRM level of performance is examined in relation to a reasonably accurate reference calculation performed with the 𝒜𝒱𝒳𝒮ℱ-ℒ𝒩𝒢 code [1] through a challenging test case : the 240Pu* compound system. This paper argues on some ingredients of the reference calculation [2] and returns some hints about the failure now well-known of the neutron-induced γ average cross section inference. It shows also that in some special cases, the SRM can be poorly accurate also in terms of neutron-induced fission average cross section inference.

Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

1966 ◽  
Vol 33 (4) ◽  
pp. 881-887 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Thermoelastic Stress ◽  
Cross Sectional ◽  
Special Cases ◽  
End Conditions ◽  
Instantaneous Temperature ◽  
The Cross ◽  
Sectional Shape

It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ′αLΔT, where kδ and kδ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ′ = 1/8.

A new technique for studying propagation and scattering for mixed paths with discontinuities

1987 ◽  
Vol 412 (1842) ◽  
pp. 125-167 ◽  
Keyword(s):  
Electric Field ◽  
Field Intensity ◽  
Cross Sections ◽  
Plane Surface ◽  
Current Source ◽  
Exciting Field ◽  
Analytical Technique ◽  
Radar Cross Sections ◽  
Special Cases ◽  
A New Technique

A new general formulation of the problem of determining the electromagnetic field resulting from a finite electric-current source located above a plane is presented. The plane surface is assumed to have electrical properties that vary in one direction only. The analytical technique used has the following properties: (1) the source or exciting field is arbitrary; (2) the resulting equations directly relate the unknown electric field intensity and the source field intensity; and (3) the boundary conditions evolve directly from the formulation as auxiliary equations. Solutions of the problem for the electric surface field are given for the following special cases: (1) a surface with one simple discontinuity; (2) a surface with two simple discontinuities; and (3) a surface with a discontinuity involving a finite region. Expressions for the electric field in all regions of the surface are given in each case, and these expressions are used to develop radar-range equations and radar cross sections for ground-wave radars.

Slender-body expressions for the wave load on offshore structures

1995 ◽  
Vol 450 (1939) ◽  
pp. 391-416 ◽  
Keyword(s):  
Cross Sections ◽  
General Result ◽  
Offshore Structures ◽  
Slender Body ◽  
Structural Members ◽  
Wave Load ◽  
Offshore Structure ◽  
Complete Structure ◽  
Special Cases ◽  
Surface Intersections

Expressions for the wave load on an offshore structure have recently been derived by several authors, by applying the classical slender-body approach to individual structural members. This paper shows that they are all special cases of a more general result, which covers a complete structure, including the effect of non-circular member cross-sections, joints between members, and surface intersections. This more general result cannot readily be derived by the methods adopted by the earlier authors; it relies on an energy argument.

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 Matrix Elements of the Boltzmann Collision Operator in a Basis Determined by an Anisotropic Maxwellian Weight Function including Drift

1980 ◽  
Vol 33 (2) ◽  
pp. 449 ◽  
Author(s):  
Kailash Kumar
Keyword(s):  
Weight Function ◽  
Cross Sections ◽  
Collision Operator ◽  
Weight Functions ◽  
Anisotropic Pressure ◽  
Matrix Elements ◽  
Methods Of Calculation ◽  
Special Cases ◽  
The Matrix ◽  
Boltzmann Collision Operator

The matrix elements of the linear Boltzmann collision operator are calculated in a Burnett-function basis determined by a weight function which itself describes a velocity distribution with a net drift and an anisotropic pressure (or temperature) tensor. Three different methods of calculation are described, leading to three different types of formulae. Two of these involve infinite summations, while the third involves only finite sums, but at the cost of greater complications in the summands and the integrals over cross sections. Both elastic and inelastic collisions are treated. Special cases arising from particular choices of the parameters in the weight functions are pointed out. The structure of the formulae is illustrated by means of diagrams. The work is a contribution towards establishing efficient methods of calculation based upon a better understanding of the matrix elements in such bases.

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