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Yayın A note on the amplitude modulation of symmetric regularized long-wave equation with quartic nonlinearity(Springer, 2012-12) Demiray, HilmiWe study the amplitude modulation of a symmetric regularized long-wave equation with quartic nonlinearity through the use of the reductive perturbation method by introducing a new set of slow variables. The nonlinear Schrodinger (NLS) equation with seventh order nonlinearity is obtained as the evolution equation for the lowest order term in the perturbation expansion. It is also shown that the NLS equation with seventh order nonlinearity assumes an envelope type of solitary wave solution.Yayın Adaptive identification and equalization of magnetic recording channels(Wiley-Blackwell, 1998-03) Özden, Mehmet Tahir; Kayran, Ahmet Hamdi; Panayırcı, ErdalA new RLS adaptive Volterra filter is presented. The nonlinear filtering problem is transformed into an equivalent multichannel, but linear, filtering problem. The multichannel input signal is completely orthogonalized using sequential processing multichannel lattice stages. Thus, a fast convergent, highly modular and, simple filter with good numerical properties is designed. In the identification of magnetic recording channels, the filter identifies the channels directly and parameters for the channel nonlinearity are quantified simultaneously. In the equalization of magnetic channels, the most effective equalizer length can be assigned dynamically.Yayın Variable coefficient modified KdV equation in fluid-filled elastic tubes with stenosis: Solitary waves(Pergamon-Elsevier Science Ltd, 2009-10-15) Demiray, HilmiIn the present work, treating the arteries as a thin walled prestressed elastic tube with variable radius, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube, by employing the reductive perturbation method. By considering the blood as an incompressible non-viscous fluid, the evolution equation is obtained as variable coefficients Korteweg-de Vries equation. Noticing that for a set of initial deformations, the coefficient characterizing the nonlinearity vanish, by re-scaling the stretched coordinates we obtained the variable coefficient modified KdV equation. Progressive wave solution is sought for this evolution equation and it is found that the speed of the wave is variable along the tube axis.Yayın Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution(Amer Inst Physics, 2018-04) Demiray, Hilmi; El-Zahar, Essam RoshdyWe consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.Yayın Modulation of cylindrical (spherical) waves in a plasma with vortex electron distribution(American Institute of Physics Inc., 2018-07-01) Demiray, HilmiIn the present work, employing cylindrically (spherically) symmetric field equations of a plasma consisting of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we studied the amplitude modulation of electron-acoustic waves. Due to the physical nature of the problem under investigation, the nonlinearity of the field equations is of order (3/2), which causes considerable difficulty in the analysis of modulation problems. To solve this difficulty, we expanded this nonlinear term into the Fourier cosine series of the phase function and obtained the modified cylindrical (spherical) nonlinear Schrodinger (NLS) equation. A consistent analysis for the modulational instability is presented and a criterion between the time parameter tau and the wave number K is established. In addition, motivated with the solitonic solution of modified NLS equation for planar case and utilizing the "weighted residual method," we proposed a harmonic wave of variable frequency with progressive wave amplitude to the evolution equation. It is found that the modified cylindrical (spherical) NLS equation assumes an envelope type of progressive wave solution in the sense weighted residual. The numerical results reveal that the amplitude of spherical wave is much larger than that of the cylindrical wave and that both amplitudes decrease with increasing time parameter tau. It is further observed that the wave profiles get distorted with progressing time.Yayın Adaptive backstepping approach for 2-DOF telescopes despite unknown wind disturbance(Institute of Electrical and Electronics Engineers Inc., 2019-07) Ünal, Ali Cem; Yılmaz, Cemal Tuğrul; Kararsız, Gökhan; Keskin, Onur; Yeşilyaprak, CahitSmall ground telescopes on the marked are widely used in many space observatories and scientific researches. There are three main problems in such telescopes; positioning of the focal point and the need of tuning for both different seasonal wind speeds and mass changes of the telescope arm. This study focuses on eliminating those problems for 2-DOF altazimuth configuration small telescopes. An adaptive controller is designed to create a set and forget system. The mathematical model of the telescope is derived based on RR type joint configuration. For a realistic approach, motor dynamics is considered in the mathematical model. The wind disturbance is modeled according to the Wind-Gust model which is a sum of sinusoidal with unknown amplitude, frequency and phase. The controller aims to cancel the effect of the disturbance on focal point of the telescope while positioning. The asymptotic stability is proven with the Lyapunov approach. The numerical study is illustrated to success of the proposed controller.Yayın A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution(Amer Inst Physics, 2015-09) Demiray, Hilmi; Bayındır, CihanIn the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg-de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.Yayın Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation(Springer Science and Business Media, LLC, 2008) Tay, Kim Gaik; Demiray, Hilmi; Tiong, Ong CheeIn the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By introducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the smallness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
