58 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 10 / 58
Yayın Interactions of nonlinear acoustic waves in a fluid-filled elastic tube(Pergamon-Elsevier Science, 2001-03) Akgün, Güler; Demiray, HilmiIn 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.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 Head-on collision of the solitary waves in fluid-filled elastic tubes(Işık University Press, 2018-04-12) Özden, Ali Erinç; Demiray, HilmiIn the present work, by employing the field equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter epsilon and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite different from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.Yayın Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation(Pergamon-Elsevier Science Ltd, 2010-09) Demiray, HilmiIn 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.Yayın Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube(Pergamon-Elsevier Science, 2002-10) Demiray, HilmiIn 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.Yayın Higher order perturbation expansion of waves in water of variable depth(Elsevier Ltd, 2010-01) Demiray, HilmiIn 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 coordinateYayın Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid(Wit Press, 2002) Bakırtaş, İlkay; Demiray, HilmiIn 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 reductive perturbation technique, the amplitude modulation of weakly nonlinear waves is examined. It is shown that, the amplitude modulation of these waves is governed by a nonlinear Schrödinger (NLS) equation. The result is compared with some previous works on the same subject. The modulational instability of the monochromatic wave solution is discussed for some elastic materials and initial deformations. It is shown that the amplitude modulation of weakly nonlinear waves near the marginal state is governed by the Generalized Nonlinear Schrödinger equation (GNLS).Yayın Modulation of non-linear axial and transverse waves in a fluid-filled thin elastic tube(Pergamon-Elsevier Science, 2000-07) Akgün, Güler; Demiray, HilmiIn 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.Yayın On the derivation of some non-linear evolution equations and their progressive wave solutions(Pergamon-Elsevier Science, 2003-06) Demiray, HilmiIn 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.Yayın Interactions of nonlinear waves in fluid-filled elastic tubes(Verlag Z Naturforsch, 2007-02) Demiray, HilmiIn this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincare-Lighthill-Kuo) perturbation method. The results show that up to O(k(3)), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.
