scholarly journals Topological Derivative for Imaging of Thin Electromagnetic Inhomogeneity: Least Condition of Incident Directions

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Won-Kwang Park
Keyword(s):  
Numerical Simulations ◽  
Theoretical Investigation ◽  
Infinite Series ◽  
Bessel Functions ◽  
Noisy Data ◽  
Mathematical Structure ◽  
Topological Derivative ◽  
Small Thickness ◽  
Integer Order ◽  
Data Support

It is well-known that using topological derivative is an effective noniterative technique for imaging of crack-like electromagnetic inhomogeneity with small thickness when small number of incident directions are applied. However, there is no theoretical investigation about the configuration of the range of incident directions. In this paper, we carefully explore the mathematical structure of topological derivative imaging functional by establishing a relationship with an infinite series of Bessel functions of integer order of the first kind. Based on this, we identify the condition of the range of incident directions and it is highly depending on the shape of unknown defect. Results of numerical simulations with noisy data support our identification.

Summation of Series over Bourget Functions

2008 ◽  
Vol 51 (4) ◽  
pp. 627-636
Author(s):  
Mirjana V. Vidanović ◽  
Slobodan B. Tričković ◽  
Miomir S. Stanković
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Bessel Functions ◽  
Integer Order ◽  
Summation Of Series ◽  
Finite Sums ◽  
Riemann Ζ Function

AbstractIn this paper we derive formulas for summation of series involving J. Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H. M. Srivastava. These series are expressed in terms of the Riemann ζ function and Dirichlet functions η, λ, β, and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.

scholarly journals Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Won-Kwang Park
Keyword(s):  
Numerical Simulations ◽  
Bessel Functions ◽  
Noisy Data ◽  
Detection Algorithm ◽  
Signal Classification ◽  
Music Algorithm ◽  
Order Zero ◽  
Scattering Problems ◽  
Multiple Signal Classification ◽  
Location Detection

AbstractMUltiple SIgnal Classification (MUSIC) is a well-known non-iterative location detection algorithm for small, perfectly conducting cracks in inverse scattering problems. However, when the applied wavenumbers are unknown, inaccurate locations of targets are extracted by MUSIC with inappropriate wavenumbers, a fact that has been confirmed by numerical simulations. To date, the reason behind this phenomenon has not been theoretically investigated. Motivated by this fact, we identify the structure of MUSIC-type imaging functionals with inappropriate wavenumbers by establishing a relationship with Bessel functions of order zero of the first kind. This result explains the reasons for inaccurate results. Various results of numerical simulations with noisy data support the identified structure of MUSIC.

scholarly journals A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

2015 ◽  
Vol 35 (3) ◽  
pp. 34-43
Author(s):  
Reynaldo Iracheta
Keyword(s):  
Infinite Series ◽  
Bessel Functions ◽  
Integration Method ◽  
Recursive Formula ◽  
Definite Integral ◽  
Mathematical Software ◽  
Font Size ◽  
Buried Cables ◽  
The Time Domain ◽  
Numerical Laplace Transform

<p class="Abstractandkeywordscontent"><span style="font-size: small;"><span style="font-family: Century Gothic;">This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable  configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT) to obtain accurate transient responses in the time domain.</span></span></p>

Binding and Non-Binding Contracts: A Theoretical Appraisal

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Elena D’Agostino ◽  
Maurizio Lisciandra
Keyword(s):  
Numerical Simulations ◽  
Theoretical Investigation ◽  
Legal System ◽  
Equilibrium Conditions ◽  
Welfare Impact ◽  
Enforcement Mechanism

Abstract The article investigates the equilibrium conditions in the choice between legally binding contracts, which are costly to verify and enforce, and non-binding contracts, which simply rely on trust as an enforcement mechanism, in both one-shot and repeated interactions. The returns to effort appear to have an important effect on reputational behavior. The theoretical investigation is accompanied by numerical simulations of the welfare impact of the introduction of a legal system that allows for binding contracts. We find that contract-enforcing institutions mainly produce benefits when effort is particularly valuable, but turn out to be less effective otherwise and even detrimental for a subset of parameters. Finally, reputation unleashes its welfare-enhancing properties especially if non-binding agreements take place when the counterparty’s reliability is very unpredictable.

scholarly journals Legendre polynomials in irrationality proofs

1980 ◽  
Vol 22 (3) ◽  
pp. 431-438 ◽  
Author(s):  
F. Beukers
Keyword(s):  
Legendre Polynomials ◽  
Bessel Functions ◽  
Integer Order ◽  
Zeros Of Bessel Functions

It is shown that a simple trick involving Legendre polynomials readily yields the irrationality of ea, , π2, and of the zeros of Bessel functions of integer order. Generalisation of this idea yields the irrationality of ζ(3).

scholarly journals Motion of a non-axisymmetric particle in viscous shear flow

2019 ◽  
Vol 872 ◽  
pp. 532-559 ◽  
Author(s):  
Ian R. Thorp ◽  
John R. Lister
Keyword(s):  
Reynolds Number ◽  
Dynamical Systems ◽  
Shear Flow ◽  
Numerical Simulations ◽  
Rotational Motion ◽  
Kam Theory ◽  
Mathematical Structure ◽  
Viscous Shear ◽  
Viscous Shear Flow ◽  
Number Of Particles

We examine the motion in a shear flow at zero Reynolds number of particles with two planes of symmetry. We show that in most cases the rotational motion is qualitatively similar to that of a non-axisymmetric ellipsoid, and characterised by a combination of chaotic and quasiperiodic orbits. We use Kolmogorov–Arnold–Moser (KAM) theory and related ideas in dynamical systems to elucidate the underlying mathematical structure of the motion and thence to explain why such a large class of particles all rotate in essentially the same manner. Numerical simulations are presented for curved spheroids of varying centreline curvature, which are found to drift persistently across the streamlines of the flow for certain initial orientations. We explain the origin of this migration as the result of a lack of symmetries of the particle’s orientation orbit.

scholarly journals THE REPRODUCING KERNEL ALGORITHM FOR NUMERICAL SOLUTION OF VAN DER POL DAMPING MODEL IN VIEW OF THE ATANGANA–BALEANU FRACTIONAL APPROACH

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040010 ◽  
Author(s):  
SHAHER MOMANI ◽  
BANAN MAAYAH ◽  
OMAR ABU ARQUB
Keyword(s):  
Numerical Simulations ◽  
Numerical Solution ◽  
Reproducing Kernel ◽  
Computational Algorithm ◽  
Mathematical Structure ◽  
The Other ◽  
Modern Trend ◽  
Van Der Pol ◽  
New Approach ◽  
Damping Model

The aim of this paper is to propose the Atangana–Baleanu fractional methodology for fathoming the Van der Pol damping model by using the reproducing kernel algorithm. To this end, we discuss the mathematical structure of this new approach and some other numerical properties of solutions. Furthermore, all needed requirements for characterizing solutions by applying the reproducing kernel algorithm are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate Atangana–Baleanu fractional solutions are proposed. Finally, numerical simulations in fractional emotion is constructed one next to the other with tabulated data and graphical portrayals.

The Bessel Functions J n (x) of Integer Order

2008 ◽  
pp. 537-552
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Bessel Functions ◽  
Integer Order
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