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Yazar: Demiray, Hilmi × Scopus Q: Q1 ×

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  • Küçük Resim
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    Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case
    (Pergamon-Elsevier Science, 2003-07) Demiray, Hilmi
    In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, and then utilizing the modified reductive perturbation technique presented by us [15] the amplitude modulation of weakly nonlinear waves is examined. It is shown that the first order term in the perturbation expansion is governed by a nonlinear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a nonhomogeneous term. In the longwave limit a travelling wave type of solution to these equations are also given.
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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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    Waves in an elastic tube filled with a heterogeneous fluid of variable viscosity
    (Pergamon-Elsevier Science Ltd, 2009-07) Demiray, Hilmi
    By treating the artery as a prestressed thin elastic tube and the blood as an incompressible heterogeneous fluid with variable viscosity. we studied the propagation of weakly non-linear waves in such a composite medium through the use of reductive perturbation method. By assuming a variable density and a variable viscosity for blood in the radial direction we obtained the perturbed Korteweg-deVries equation as the evolution equation when the viscosity is of order of epsilon(3/2). We observed that the perturbed character is the combined result of the viscosity and the heterogeneity of the blood. A progressive wave type of solution is presented for the evolution equation and the result is discussed. The numerical results indicate that for a certain value of the density parameter sigma, the wave equation loses its dispersive character and the evolution equation degenerates. It is further shown that, for the perturbed KdV equation both the amplitude and the wave speed decay in the time parameter tau.
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    Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
    (Pergamon-Elsevier Science Ltd, 2010-09) Demiray, Hilmi
    In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly non-linear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg-de Vries (KdV) equation. A progressive wave type of solution, which satisfies the evolution equation in the integral sense but not point by point, is presented. The resulting solution is numerically evaluated for two selected bottom profile functions, and it is observed that the wave amplitude increases but the band width of the solitary wave decreases with increasing undulation of the bottom profile.
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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 viscous fluid contained in a tapered elastic tube
    (Pergamon-Elsevier Science, 2002-10) Demiray, Hilmi
    In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and the blood as a Newtonian fluid, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method. The governing evolution equation is obtained as the dissipative nonlinear Schrodinger equation with variable coefficients. It is shown that this type of equations admit solitary wave solutions with variable wave amplitude and speed. It is observed that, the wave speed increases with distance for tubes of descending radius while it decreases for tubes of ascending radius. The dissipative effects cause a decay in wave amplitude and wave speed.
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    Higher order perturbation expansion of waves in water of variable depth
    (Elsevier Ltd, 2010-01) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to long waves in water of variable depth and obtained a set of KdV equations as the governing equations. Seeking a localized travelling wave solution to these evolution equations we determine the scale function c(1)(tau) so as to remove the possible secularities that might occur. We showed that for waves in water of variable depth, the phase function is not linear anymore in the variables x and t. It is further shown that, due to the variable depth of the water, the speed of the propagation is also variable in the x coordinate
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    The boundary layer approximation and nonlinear waves in elastic tubes
    (Pergamon-Elsevier Science, 2000-09) Antar, Nalan; Demiray, Hilmi
    In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg-de Vries (KdV) and the Korteweg-de Vries-Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg-de Vries and viscous-Burgers equations.
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    Modulation of non-linear axial and transverse waves in a fluid-filled thin elastic tube
    (Pergamon-Elsevier Science, 2000-07) Akgün, Güler; Demiray, Hilmi
    In the present work, utilizing the non-linear equations of a pre-stressed thin elastic tube filled with an incompressible inviscid fluid the propagation of weakly non-linear 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 non-linear equations governing the motion of the tube in the radial and axial directions are obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly non-linear 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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    On the derivation of some non-linear evolution equations and their progressive wave solutions
    (Pergamon-Elsevier Science, 2003-06) Demiray, Hilmi
    In the present work, utilizing the reductive perturbation method, the non-linear equations of a prestressed viscoelastic thick tube filled with a viscous fluid are examined in the longwave approximation and some evolution equations and their modified forms are derived. The analytical solution of some of these equations are obtained and it is shown that for perturbed cases, the wave amplitude and the phase velocity decay in the time parameter.