scholarly journals Symbolic Computation Applied to Cauchy Type Singular Integrals

2021 ◽  
Vol 27 (1) ◽  
pp. 3
Author(s):  
Ana C. Conceição ◽  
Jéssica C. Pires
Keyword(s):  
Operator Theory ◽  
Electromagnetic Waves ◽  
Singular Integrals ◽  
Transport Theory ◽  
Source Code ◽  
Cauchy Type ◽  
Linear Differential ◽  
First Time ◽  
Linear Transport Theory ◽  
Mathematics And Physics

The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system Mathematica to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.

scholarly journals Some Aspects of Spinodal Decomposition in Spinel Solid Solutions

1995 ◽  
Vol 50 (6) ◽  
pp. 525-532
Author(s):  
N. Burkert ◽  
R. Grüne ◽  
H. Schmalzried ◽  
S. Rahman
Keyword(s):  
Spinodal Decomposition ◽  
Solid Solutions ◽  
Common Property ◽  
Transport Theory ◽  
Decomposition Reaction ◽  
Sufficient Evidence ◽  
Spinel Crystal ◽  
Linear Transport Theory ◽  
Spinel Solid Solutions ◽  
Quasi Binary System

Abstract Decomposition morphologies of supersaturated spinel solid solutions in the quasi-binary system Co2TiO4-CoAl2O4 at 973 K show all pertinent features of spinodal decomposition. Since the decomposition morphology may not be considered as sufficient evidence for a spinodal process, the thermodynamics of the spinel solid solutions and the linear transport theory of spinodal decomposition were combined to corroborate the experimental results of the early decomposition reaction.Simultaneous ordering, a common property of ternary and higher nonequilibrium solid solutions, was also observed. These ordering processes occur locally in distinct regions of the spinel crystal. Moreover, the spinodal wavelength λ increases in time according to λ ∞ t, which is unusual and will be discussed in the light of cation diffusion in semiconducting oxides with two cation sublattices.

scholarly journals DISTORTIONLESS SIGNALS TRANSFER THROUGH A WIRE MEDIA METASTRUCTURE

2018 ◽  
Vol 8 (1) ◽  
pp. 44-47 ◽  
Author(s):  
Dmytro Vovchuk ◽  
Serhii Haliuk ◽  
Leonid Politanskyy
Keyword(s):  
Electromagnetic Waves ◽  
Spectral Characteristics ◽  
Wide Frequency Range ◽  
Power Transfer ◽  
Fabry Perot ◽  
Signal Distortions ◽  
Metallic Wires ◽  
The Wire ◽  
Wire Media ◽  
First Time

In the paper the development of the components of communication means is considered based on the wire metastructures. This approach is novel and quite promising due to the metamaterials provides new opportunities for the radio engineering devices such as antennas, absorbers etc. First of all it makes possible decreasing of the dimensions of devices while the characteristics stay the same or better. Here the artificially created metastructure that consists of parallel metallic wires and characterizes by a negative electric permittivity was investigated. The possibility of broadband power transfer of electromagnetic waves was demonstrated. Also, at first time, the investigation of possible signal distortions due to wave propagation through the wire medium (WM) slab was performed via analyzing of spectral characteristics. The obtained results allow applying of WM to power transfer in wide frequency range (not only at frequencies of Fabry-Perot resonant) and enhancement of weak source propagation as well as to antennas constructions due to the absence of signal distortions. One of the promising applications of such structures is the possibility of realizing of flexible screens with nanometer thickness and high resolution.

Linear transport theory in a random medium

1986 ◽  
Vol 27 (10) ◽  
pp. 2526-2536 ◽  
Author(s):  
C. D. Levermore ◽  
G. C. Pomraning ◽  
D. L. Sanzo ◽  
J. Wong
Keyword(s):  
Transport Theory ◽  
Random Medium ◽  
Linear Transport ◽  
Linear Transport Theory

scholarly journals Heating of Ti3C2Tx MXene/polymer composites in response to Radio Frequency fields

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Touseef Habib ◽  
Nutan Patil ◽  
Xiaofei Zhao ◽  
Evan Prehn ◽  
Muhammad Anas ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Thermal Imaging ◽  
Electromagnetic Waves ◽  
Rapid Heating ◽  
Composite Films ◽  
Heating Rates ◽  
New Material ◽  
High Dielectric ◽  
First Time ◽  
Percolating Network

Abstract Here we report for the first time that Ti3C2Tx/polymer composite films rapidly heat when exposed to low-power radio frequency fields. Ti3C2Tx MXenes possess a high dielectric loss tangent, which is correlated with this rapid heating under electromagnetic fields. Thermal imaging confirms that these structures are capable of extraordinary heating rates (as high as 303 K/s) that are frequency- and concentration-dependent. At high loading (and high conductivity), Ti3C2Tx MXene composites do not heat under RF fields due to reflection of electromagnetic waves, whereas composites with low conductivity do not heat due to the lack of an electrical percolating network. Composites with an intermediate loading and a conductivity between 10–1000 S m−1 rapidly generate heat under RF fields. This finding unlocks a new property of Ti3C2Tx MXenes and a new material for potential RF-based applications.

scholarly journals Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 728 ◽  
Author(s):  
SAIRA ◽  
Shuhuang Xiang
Keyword(s):  
Singular Integrals ◽  
Oscillatory Integral ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Cauchy Kernel ◽  
Cauchy Type ◽  
Highly Oscillatory ◽  
Logarithmic Singularities ◽  
Highly Oscillatory Integrals ◽  
Modified Moments

In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, ⨍ − 1 1 f ( x ) log ( x − α ) e i k x x − t d x , t ∉ ( − 1 , 1 ) , α ∈ [ − 1 , 1 ] for a smooth function f ( x ) . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some examples.

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