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1999 - 199932000 - 20044
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Konu: Incompressible flow × WoS Q: Q1 ×

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Listeleniyor 1 - 7 / 7
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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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    Solitary waves in elastic tubes filled with a layered fluid
    (Pergamon-Elsevier Science, 2001-04) Demiray, Hilmi
    In this work, we studied the propagation of weakly non-linear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is studied. The governing equation is shown to be the perturbed Korteweg-de Vries (KdV) equation. A travelling wave type of solution for this evolution equation is sought and it is shown that the amplitude of the solitary wave for the perturbed KdV equation decays slowly with time.
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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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    Weakly nonlinear waves in a prestressed thin elastic tube containing a viscous fluid
    (Pergamon-Elsevier Science Ltd, 1999-11) Antar, Nalan; Demiray, Hilmi
    In this work, we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible viscous fluid. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and sheer 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, is shown to be governed by the Korteweg-de Vries-Burgers (KdVB) equation. Due to dependence of coefficients of the governing equation on the initial deformation, the material and viscosity parameters, the profile of the travelling wave solution to the KdVB equation changes with these parameters. These variations are calculated numerically for some elastic materials and the effects of initial deformation and the viscosity parameter on the propagation characteristics are discussed.
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    On the existence of some evolution equations in fluid-filled elastic tubes and their progressive wave solutions
    (Pergamon-Elsevier Science Ltd., 2004-09) Demiray, Hilmi
    In the present work, by employing the nonlinear equations of motion of an incompressible, isotropic and prestressed thin elastic tube and the approximate equations of an incompressible inviscid fluid, we studied the existence of some possible evolution equations in the longwave approximation and their progressive wave solutions. It is shown that, depending on the set of values of the initial deformation, it might be possible to obtain the conventional Korteweg-deVries (KdV) and the modified KdV equations of various forms. Finally, a set of progressive wave solutions is presented for such evolution equations.
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    Solitary waves in fluid-filled elastic tubes: weakly dispersive case
    (Pergamon-Elsevier Science, 2001-03) 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, the propagation of weakly nonlinear waves, in such a medium is studied through the use of the modified multiple expansion method. It is shown that the evolution of the lowest order (first-order) term in the perturbation expansion may be described by the Korteweg-de Vries (KdV) equation. The governing equation for the second-order terms and the localized travelling wave solution for these equations are also obtained. The applicability of the present model to flow problems in arteries is discussed.
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    Propagation of weakly nonlinear waves in fluid-filled thick viscoelastic tubes
    (Elsevier Science Inc., 1999-10) Demiray, Hilmi
    In the present work, we studied the propagation of small-but-finite-amplitude waves in a prestressed thick walled viscoelastic tube filled with an incompressible inviscid fluid. In order to include the dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Korteweg-de Vries (KdV), Koteweg-de Vries-Burgers (KdVB) and the generalized Burgers' equations. By proper re-scaling of the perturbation parameter, the modified form of the evolution equations is also obtained. The variations of the travelling wave profile with initial deformation and the viscosity coefficients are numerically evaluated and the results are illustrated in some figures.