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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 Nonlinear waves in a viscous fluid contained in a viscoelastic tube(Birkhauser Verlag, 2001-11) Demiray, HilmiIn the present work the propagation of weakly nonlinear waves in a prestressed viscoelastic thin tube filled with a viscous fluid is studied. Using the reductive perturbation technique in analyzing the nonlinear equations of a viscoelastic tube and the approximate equations of a viscous fluid, the propagation of weakly nonlinear waves in the longwave approximation is studied. Depending on the order of viscous effects, various evolution equations like, Burgers', Korteweg-de Vries, Korteweg-de Vries-Burgers' equations and their perturbed forms are obtained. Ravelling wave type of solutions to some of these evolution equations are sought. Finally, utilizing the finite difference scheme, a numerical solution is presentede for the perturbed KdVB equation and the result is discussed.Yayın Solitary waves in a tapered prestressed fluid-filled elastic tube(Birkhauser Verlag AG, 2004-03) Demiray, HilmiIn the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube 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 inviscid fluid the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed increases with distance for positive tapering while it decreases for negative tapering.Yayın Weakly non-linear waves in a fluid-filled elastic tube with variable prestretch(Pergamon-Elsevier Science Ltd, 2008-11) Demiray, HilmiIn the present work, by utilizing the non-linear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable prestretch both in the axial and the radial directions and the approximate equations of motion of an incompressible inviscid fluid, which is assumed to be a model for blood, we studied the propagation of weakly non-linear waves in such a medium, in the long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient KdV equation as the evolution equation. By seeking a travelling wave solution to this evolution equation, we observed that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations.Yayın Weakly non-linear waves in a tapered elastic tube filled with an inviscid fluid(Pergamon-Elsevier Science Ltd, 2005-07) Bakırtaş, İlkay; Demiray, HilmiIn the present work, treating the artery as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly non-linear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid, the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equation admits a solitary wave-type solution with variable wave speed. It is observed that, the wave speed decreases with distance for positive tapering while it increases for negative tapering. It is further observed that, the progressive wave profile for expanding tubes (a > 0) becomes more steepened whereas for narrowing tubes (a < 0) it becomes more flattened.Yayın Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section(Elsevier Ltd, 2006-04) Demiray, HilmiIn 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.Yayın Modulation of non-linear waves in a viscous fluid contained in an elastic tube(Pergamon-Elsevier Science, 2001-06) Demiray, HilmiIn the present work, utilizing the non-linear equations of a prestressed thin elastic tube filled with an incompressible viscous 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 how, a finite-time-dependent displacement is added to this initial field, the non-linear equations governing the motion of the tube in the radial direction is obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly non-linear and dissipative but strongly dispersive waves is examined and the dissipative non-linear Schrodinger equation is obtained. Finally, the numerical solution of the evolution equation under the given initial condition is given and the stability condition of the solution is discussed.
