scholarly journals The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect

2017 ◽  
Vol 6 (2) ◽  
pp. 77
Author(s):  
H. A. Aebischer ◽  
B. Aebischer
Keyword(s):  
Cross Section ◽  
Skin Effect ◽  
Unit Length ◽  
Geometric Mean ◽  
Analytical Approximation ◽  
Elementary Functions ◽  
Exact Relation ◽  
Measurement Results ◽  
Definition Of ◽  
Analytical Expressions

The GMD method (geometric mean distance) to calculate inductance offers undoubted advantages over other methods. But so far it seemed to be limited to the case where the current is uniformly distributed over the cross section of the conductor, i.e. to DC (direct current). In this paper, the definition of the GMD is extended to include cases of nonuniform distribution observed at higher frequencies as the result of skin effect. An exact relation between the GMD and the internal inductance per unit length for infinitely long conductors of circularly symmetric cross section is derived. It enables much simpler derivations of Maxwell’s analytical expressions for the GMD of circular and annular disks than were known before. Its salient application, however, is the derivation of exact expressions for the GMD of infinitely long round wires and tubular conductors with skin effect. These expressions are then used to verify the consistency of the extended definition of the GMD. Further, approximate formulae for the GMD of round wires with skin effect based on elementary functions are discussed. Total inductances calculated with the help of the derived formulae for the GMD with and without skin effect are compared to measurement results from the literature. For conductors of square cross section, an analytical approximation for the GMD with skin effect based on elementary functions is presented. It is shown that it allows to calculate the total inductance of such conductors for frequencies from DC up to 25 GHz to a precision of better than 1 %.

scholarly journals Longitudinal oscillations of the sugar beet root crop body at vibrational digging up from soil

2012 ◽  
Vol 51 (No. 3) ◽  
pp. 99-104
Author(s):  
V. Bulgakov ◽  
I. Holovach ◽  
M. Berezovyy
Keyword(s):  
Sugar Beet ◽  
Cross Section ◽  
Forced Oscillations ◽  
Oscillatory Process ◽  
Longitudinal Vibrations ◽  
Beet Root ◽  
Fundamental Frequencies ◽  
Sugar Beet Root ◽  
Definition Of ◽  
Analytical Expressions

The longitudinal vibrations theory of a continuous elastic body with one fixed extremity is designed. The Ostrogradskii–Hamilton principle of a stationary operation is applied. By Ritz’s method the Ritz’s equation of frequencies for viewed oscillatory process is obtained. In particular analytical expressions for definition of the first and second fundamental frequencies of body oscillations and forced oscillations amplitude of its any cross-section are obtained.

scholarly journals Scattering of quantum fields by a MOG black hole

2020 ◽  
Vol 35 (15) ◽  
pp. 2050121
Author(s):  
Ciprian A. Sporea
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cross Section ◽  
Free Parameter ◽  
Spherically Symmetric ◽  
Gravitational Theories ◽  
Partial Wave Method ◽  
Hole Geometry ◽  
Definition Of ◽  
Analytical Expressions

This paper aims to investigate the scattering of fermions by spherically symmetric MOG black holes, which are a type of black holes encountered in scalar–tensor–vector modified gravitational theories. After determining the scattering modes in this black hole geometry, we apply the partial wave method to compute analytical expressions for the phase shifts that enter into the definition of scattering amplitudes. An analysis of the influence of the MOG parameter [Formula: see text] on the differential scattering cross-section and the induced polarization is conducted. Also, a comparison with Schwarzschild scattering (for which [Formula: see text]) is performed. Furthermore, it is also shown that glory and spiral/orbiting scattering are more significant for higher values of the free parameter [Formula: see text].

scholarly journals Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Roman N. Lee ◽  
Alexey A. Lyubyakin ◽  
Vyacheslav A. Stotsky
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Elliptic Integral ◽  
High Energy ◽  
Calculation Methods ◽  
Complete Elliptic Integral ◽  
Total Cross Sections ◽  
Multiloop Calculation ◽  
The Cross ◽  
Analytical Expressions

Abstract Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ →$$ {e}^{-}X\overline{X} $$ e − X X ¯ with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

Analytical approximation of cross-section effects on charge exchange spectra observed in hot fusion plasmas

1995 ◽  
Vol 37 (2) ◽  
pp. 71-94 ◽  
Author(s):  
M von Hellermann ◽  
P Breger ◽  
J Frieling ◽  
R Konig ◽  
W Mandl ◽  
...  
Keyword(s):  
Cross Section ◽  
Charge Exchange ◽  
Analytical Approximation ◽  
Fusion Plasmas

scholarly journals Thermal conductivity of sandstones from Biot’s coefficient

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. D173-D185 ◽  
Author(s):  
Tobias Orlander ◽  
Eirini Adamopoulou ◽  
Janus Jerver Asmussen ◽  
Adam Andrzej Marczyński ◽  
Harald Milsch ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Geometric Mean ◽  
Well Log ◽  
Biot’S Coefficient ◽  
Model Predictions ◽  
The Cross ◽  
Rock Texture

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

scholarly journals Structure of the Balmer jump

2018 ◽  
Vol 613 ◽  
pp. A55
Author(s):  
F. Calvo ◽  
L. Belluzzi ◽  
O. Steiner
Keyword(s):  
Hydrogen Atom ◽  
Absorption Coefficient ◽  
Total Cross Section ◽  
Analytical Model ◽  
Cross Section ◽  
Quantum Structure ◽  
Balmer Series ◽  
Polarization Phenomena ◽  
Definition Of ◽  
Rapid Drop

Context.The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series.Aims.We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit.Methods.We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl’Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem.Results.We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a “Balmer jump” is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way.Conclusions.The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms.

scholarly journals On the Temperature Distribution Inside a Tree Under Fire Conditions

1991 ◽  
Vol 1 (2) ◽  
pp. 87 ◽  
Author(s):  
JJ Costa ◽  
LA Oliveira ◽  
DX Viegas ◽  
LP Neto
Keyword(s):  
Cross Section ◽  
Heat Conduction Equation ◽  
Numerical Scheme ◽  
Unit Length ◽  
Circular Cross Section ◽  
Time Dependent ◽  
Tree Trunk ◽  
Temperature Field Distribution ◽  
Ground Fire ◽  
Fire Conditions

A simple and efficient numerical scheme is presented for the prediction of temperature field distribution inside a tree trunk subjected to ground fire conditions. The trunk is modelled by a cylinder of circular cross section and unit length, through which the time-dependent heat conduction equation is numerically integrated. The model is partly validated in laboratory and then applied to the case of a prescribed ground fire inside a Pinus pinmter stand.

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