2426. An Oscillation Problem Involving Elliptic Integrals of the First and Second Kinds

1954 ◽  
Vol 38 (324) ◽  
pp. 141
Author(s):  
N. W. McLachlan
Keyword(s):  
Elliptic Integrals ◽  
Oscillation Problem

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

Haar Wavelet Solution Analysis of Compound Pendulum-based Computational Electromagnetic Damping Oscillation Problem

2021 ◽  
pp. 1-9
Author(s):  
Arun Kumar ◽  
Mohammad Shabi Hashmi ◽  
Abdul Quaiyum Ansari ◽  
Sultangali Arzykulov
Keyword(s):  
Haar Wavelet ◽  
Electromagnetic Damping ◽  
Oscillation Problem

scholarly journals Improved FAST Device for Inherent Safety of Oxide-Fueled Sodium-Cooled Fast Reactors

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4610
Author(s):  
Ahmed Amin E. Abdelhameed ◽  
Chihyung Kim ◽  
Yonghee Kim
Keyword(s):  
Operating Temperature ◽  
Reactor Core ◽  
Coolant Temperature ◽  
Inherent Safety ◽  
Oxide Fuel ◽  
Fast Reactors ◽  
Power Oscillation ◽  
Negative Reactivity ◽  
Oscillation Problem ◽  
Reactivity Coefficient

The floating absorber for safety at transient (FAST) was proposed as a solution for the positive coolant temperature coefficient in sodium-cooled fast reactors (SFRs). It is designed to insert negative reactivity in the case of coolant temperature rise or coolant voiding in an inherently passive way. The use of the original FAST design showed effectiveness in protecting the reactor core during some anticipated transients without scram (ATWS) events. However, oscillation behaviors of power due to refloating of the absorber module in FAST were observed during other ATWS events. In this paper, we propose an improved FAST device (iFAST), in which a constraint is imposed on the sinking (insertion) limit of the absorber module in FAST. This provides a simple and effective solution to the power oscillation problem. Here, we focus on an oxide fuel-loaded SFR that is characterized by a more negative Doppler reactivity coefficient and higher operating temperature than the metallic-loaded SFR cores. The study is carried out for the 1000 MWth advanced burner reactor with an oxide fuel-loaded core during postulated ATWS events that are unprotected transient over power, unprotected loss of flow, and unprotected loss of the heat sink. It was found that the iFAST device has promising potentials for protecting the oxide SFR core during the various studied ATWS events.

scholarly journals OSCILLATION PROBLEM IN PITCH ANGLE CONTROL OF WINGED BODY

2005 ◽  
Vol 38 (1) ◽  
pp. 247-252
Author(s):  
Igor Ŝkrjanc ◽  
Marko Lepetić ◽  
SaŜo Blaziĉ ◽  
Yasuhiro Morita
Keyword(s):  
Pitch Angle ◽  
Oscillation Problem

Some Applications of Elliptic Integrals of First Kind

2013 ◽  
Vol 65 (1) ◽  
Author(s):  
Yasamin Barakat ◽  
Nor Haniza Sarmin
Keyword(s):  
Algebraic Function ◽  
High Accuracy ◽  
Elliptic Integrals ◽  
Definite Integrals ◽  
Engineering Mathematics ◽  
Optimal Values ◽  
Complete Elliptic Integrals

One of the most important applications of elliptic integrals in engineering mathematics is their usage to solve integrals of the form  (Eq. 1), where  is a rational algebraic function and  is a polynomial of degree  with no repeated roots. Nowadays, incomplete and complete elliptic integrals of first kind are estimated with high accuracy using advanced calculators.  In this paper, several techniques are discussed to show how definite integrals of the form (Eq. 1) can be converted to elliptic integrals of the first kind, and hence be estimated for optimal values. Indeed, related examples are provided in each step to help clarification.

Sign in / Sign up

Export Citation Format

Share Document