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1

Compact Transverse Electric Silicon-on-Insulator Mode Converter for Mode-Division Multiplexer

Sharaf Mohamed H., El-Mashade Mohamed B., Emran Ahmed A.

International Journal of Electronics and Telecommunications

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2022

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Vol. 68, No. 2

275--280

EN

On-chip optical-interconnect technology emerges as an attractive approach due to its ultra-large bandwidth and ultra-low power consumption. Silicon-on-insulator (SOI) wire waveguides, on the other hand, have been identified to potentially replace copper wires for intra-chip communication. To take advantage of the wide bandwidth of SOI waveguides, wavelengthdivision multiplexing (WDM) has been implemented. However, WDM have inherent drawbacks. Mode-division multiplexing (MDM) is a viable alternative to WDM in MIMO photonic circuits on SOI as it requires only one carrier wavelength to operate. In this vein, mode converters are key components in on-chip MDM systems. The goal of this paper is to introduce a transverse electric mode converter. The suggested device can convert fundamental transverse electric modes to first-order transverse electric ones and vice versa. It is based on small material perturbation which introduces gradual coupling between different modes. This device is very simple and highly compact; the size of which is 3 μm². Mathematical expressions for both the insertion loss and crosstalk are derived and optimized for best performance. In addition, three-dimensional finite-difference time-domain (3D-FDTD) simulations are performed in order to verify the mathematical model of the device. Our numerical results reveal that the proposed device has an insertion loss of 1.2 dB and a crosstalk of 10.1 dB. The device’s insertion loss can be decreased to 0.95 dB by adding tapers to its material perturbation.

2

Perturbation theory, M-essential spectra of 2 x 2 operator matrices and application to transport operators

Jeribi Aref, Moalla Nedra, Yengui Sonia

Journal of Mathematics and Applications

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2021

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Vol. 44

35--55

EN

In this article we give some results on perturbation theory of 2 x 2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space Lp([-a, a] x [-1, 1]) x Lp([-a, a] x [-1, 1]), p ≥ 1 and a > 0.

3

Dynamic response of ladder track rested on stochastic foundation under oscillating moving load

Mohammadzadeh S., Mehrali M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

281--291

EN

The ladder track is a new type of an elastically supported vibration-reduction track system that has been applied to several urban railways. This paper is devoted to the investigation of dynamic behavior of a ladder track under an oscillating moving load. The track is represented by an infinite Timoshenko beam supported by a random elastic foundation. In this regard, equations of motion for the ladder track are developed in a moving frame of reference. In continuation, by employing perturbation theory and contour integration, the response of the ladder track is obtained analytically and its results are verified using the stochastic finite element method. Finally, using the verified model, a series of sensitivity analyses are accomplished on effecting parameters including velocity and load frequency.

4

Investigation of the electron capture process in semiclassical plasma

Seisembayeva M. M., Dzhumagulova K. N., Ramazanov T. S.

Nukleonika

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2016

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Vol. 61, No. 2

201--205

EN

In this work, the process of electron capture in partially ionized plasma is considered. Electron- -atom interaction was described by the effective interaction potential, which takes into account the screening effect at large distances and the diffraction effect at the small distances. The results of numerical calculations of the electron capture radius, differential cross-section for different values of the coupling and density parameters are presented. The differential cross-section was obtained on the basis of perturbation theory and also by solving of the equation of motion of the projectile electron.

5

On a continuity of characteristic exponents of linear discrete time-varying systems

Czornik A., Mokry P., Niezabitowski M.

Archives of Control Sciences

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2012

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Vol. 22, no. 1

17-27

EN

In this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.

6

Homotopy perturbation method in the heat conduction problems

Hetmaniok E., Nowak I., Słota D., Wituła R.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

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2011

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z. 1

109--120

EN

In this paper an application of the homotopy perturbation method for solving the steady state and unsteady state heat conduction problem is presented.

PL

W artykule przedstawiono zastosowanie homotopijnej metody perturbacyjnej do rozwiązania zagadnień ustalonego oraz nieustalonego przewodzenia ciepła.

7

On the perturbation of linear regular descriptor systems

Kalogeropoulos G. I., Karageorgos A. D., Pantelous A. A.

Systems Science

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2009

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Vol. 35, no 4

5-13

EN

In the perturbation theory of linear descriptor systems, it is well known that the theory of eigenvalues and eigenvectors of regular homogeneous matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. Moreover, since there are applications such that the eigenvalues and eigenvectors do not disappear upon by arbitrarily small perturbations, expressions for the relative error of Fw and Gw, i.e., [wzór] are provided by using the Frobenius norm [wzór].

8

Comparison of thermodynamic functions calculated by means of various methods

Avsec J., Marcic M.

Journal of Technical Physics

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2002

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Vol. 43, no 3

309-321

EN

The paper deals with the Lennard-Jones fluid and presents the mathematical model of computating thermodynamic functions of state in the liquid and gas domain by means of statistical thermodynamics. To calculate the thermodynamic properties of a real fluid, we used the Johnson-Zollweg-Gubbins model based on the modified Benedict-Webb-Rubin equation of state, the Chunxi-Yigui-Jiufang equation of state based on the simple perturbation theory, and the complex Tang-Tong-Lu model based on the solution of the Ornstein-Zernike equation obtained by means of the perturbation theory. The analytical results are compared with the thermodynamical data, and with the results obtained from classical thermodynamics.

9

Gauge symmetry in models of high temperature superconductors

Przeszowski J.

Journal of Technical Physics

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2001

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Vol. 42, no 4

389-396

EN

Gauge symmetry which appears in the slave-mode approach to the t-J model of high temperature superconductivity is presented. The mean field analysis of these microscopic models lead to the continuum gauge field systems with infinitely strong coupling constant. The viability of the perturbative calculations (with finite coupling constant) are illustrated with a particularly simple field theory model. Exact resummation of the perturbation series is discussed for the Heisenberg model of strongly interacting spins in 1 + 1 dimensions which is approximated by the Schwinger model.

10

Theoretical studies on sulfur-containing radical ions

Carmichael I.

Nukleonika

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2000

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Vol. 45, nr 1

11-17

EN

Structures and properties are reported for pi-radical cations and for sigma-radical cations and anions, containing SS, SN and SO odd-electron bonds, from a variety of ab initio molecular orbital techniques and Density Functional Theory (DFT). Characteristic frequencies and absorption bands are determined to aid in the assignment of transient vibrational and optical spectra detected in pulse radiolysis experiments. Hyperfine coupling tensors are evaluated to facilitate the identification of these radicals by EPR spectroscopy. By comparison with predictions from accurate coupled-cluster based calculations in some simple model systems, DFT is shown to have difficulties in correctly describing the electronic structure of these radical ions. Useful linear relationships are uncovered between the computed lenght of the odd-electron bond and both the wavelenght of maximum optical absorption and the bond stretching frequency.

11

Radius of convergence of the Amos-Musher intermolcular perturbation theory for the hydrogen molecule ground state

Adams W.H.

Polish Journal of Chemistry

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1998

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Vol. 72, nr 7S

1421-1431

EN

We have approximately determined the radius of convergence of the Amos-Musher perturbation theory applied to the hydrogen molecule at nuclear separations ranging from 3 to 12 bohr. We have done this by approximately locating for the lowest eigenvalue of the Amos-Musher Hamiltonian those branch points which are closest to the center about which the perturbation expansion is developed. Using the same method and basis set we have also located the branch points of the Polarization Approximation applied to H2 and obtined results in good agreement with the accurate values found a few years ago by Cwiok, Jeziorski, Kołos, et al. We find that the radius of convergence of the Amos-Musher theory increases from 1.7 times as large as that of the Polarization Approximation at 3 bohr to twice as large at 8 to 12 bohr. This shows that the Amos Musher theory differs fumdamantally from the Polarization Approximation.

12

Spectra of approximating operators

Pokrzywa Andrzej

Matematyka Stosowana : matematyka dla społeczeństwa

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1995

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Nr 38

87--100

EN

This is an interesting expository article about the approximation of operators on a complex infinite-dimensional Hilbert space. Although the article does not include research published during the past twenty years or so, it provides a nice account of the stability of the spectrum under approximation (or perturbation). The reader interested in pursuing this area of research might refer to the bibliography in [D. A. Herrero, Approximation of Hilbert space operators. Vol. I, Pitman, Boston, MA, 1982; MR0676127] and the subsequent publications of those authors.