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Yazar: Demiray, Hilmi × Konu: Modulation ×

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    Interactions of nonlinear acoustic waves in a fluid-filled elastic tube
    (Pergamon-Elsevier Science, 2001-03) Akgün, Güler; Demiray, Hilmi
    In the present work, the nonlinear interactions of two acoustical waves propagating in a fluid-filled elastic tube with different wave numbers, frequencies and group velocities are examined. Employing the multiple-scale expansion method, expanding the field quantities into asymptotic series of the smallness parameter and solving the resulting differential equations of various orders of the same parameter, we obtained two coupled nonlinear Schrodinger equations. The nonlinear plane wave solutions to these equations are also given for some special cases.
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    Modulational instability of acoustic waves in a dusty plasma with nonthermal electrons and trapped ions
    (Pergamon-Elsevier Science Ltd, 2019-04) Demiray, Hilmi; Abdikian, Alireza
    In the present work, employing the nonlinear field equations of a hot dusty plasma in the presence of nonthermal electrons and trapped ions, we studied the amplitude modulation of nonlinear waves in such a plasma medium by use of the reductive perturbation method and obtained the modified nonlinear Schrodinger equation. The modulational instability (MI) was investigated and the effects of the proportion of the fast electrons (alpha), the trapping parameter (b) and the plasma parameters such as the dust-ion temperature ratio (sigma(d)), the partial unperturbed electron to dust density (delta), and the ion-electron temperature ratio (sigma(i)) on it was discussed. For the investigation of modulational instability problems three parameters P/Q,K-max and Gamma(max) play the central role. The variations of these parameters with the wave number k and the other physical parameters are discussed and the possibility of occurence of modulational instability is indicated.
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    Modulation of nonlinear waves in a thin elastic tube filled with a viscous fluid
    (Pergamon-Elsevier Science Ltd, 1999-11) Demiray, Hilmi
    In the present work, utilizing the nonlinear equations of a prestressed thin elastic tube filled with an incompressible viscous fluid the propagation of weakly nonlinear waves in such a medium is studied. Considering that the arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch lambda(z) and, in the course of blood flow, a finite time dependent displacement is added to this initial field, the nonlinear equations governing the motion of the tube in the radial direction is obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly nonlinear and dissipative but strongly dispersive waves is examined. The localized travelling wave solution to the evolution equation is given and the stability condition is discussed.
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    Modulation of cylindrical (spherical) waves in a plasma with vortex electron distribution
    (American Institute of Physics Inc., 2018-07-01) Demiray, Hilmi
    In 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.
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    Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section
    (Elsevier Ltd, 2006-04) Demiray, Hilmi
    In the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave solution with a variable wave speed. It is observed that, the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.
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    Modulation of electron-acoustic waves in a plasma with kappa distribution
    (American Institute of Physics Inc., 2016-03) Demiray, Hilmi
    In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying ? velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear Schrödinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers.