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Erişim Hakkı: info:eu-repo/semantics/closedAccess × Konu: Elastic tubes ×

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Listeleniyor 1 - 10 / 26
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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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    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.
  • Küçük Resim Yok
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    Variable coefficient Korteweg-deVries equation in fluid-filled elastic tubes
    (Technical University Liberec, 2011-09-05) Demiray, Hilmi
    In the present work, treating the arteries as a prestressed thin elastic tube with a stenosis and the blood as an inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium by use of the reductive perturbation method and obtained the variable coefficient Korteweg-deVries (KdV) equation as the evolution equation. A progressive wave type of solution to this evolution equation, in the sense of distribution, is presented and the result is discussed.
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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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    Interactions of nonlinear waves in fluid-filled elastic tubes
    (Verlag Z Naturforsch, 2007-02) Demiray, Hilmi
    In 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.
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    Reflection and transmission of nonlinear waves from arterial branching
    (Elsevier Ltd, 2006-10) Demiray, Hilmi
    In this work, treating the arteries as a prestressed thin walled elastic tube and the blood as an inviscid fluid, we have studied the reflection and transmission of nonlinear waves from arterial branching, through the use of reductive perturbation method. The reflected and the transmitted waves at the bifurcation point are calculated in terms of the incident wave. The numerical results indicate that the reflected wave is comparatively small whereas the transmitted waves in branches are comparable with the incident wave. This result is quite consistent with the experimental measurements [N. Sergiopulos, M. Spiridon, F. Pythoud, J.J. Meister, On wave transmission and reflection properties of stenosis, J. Biomechanics 26 (1996) 31-38].
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    Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube
    (Pergamon-Elsevier Science Ltd, 2009-08-30) Demiray, Hilmi
    In this work, treating the arteries as a thin walled, prestressed elastic tube and the blood as an incompressible viscous fluid of variable viscosity, we have studied the interactions of two nonlinear waves, in the long wave approximation, through the use of extended PLK perturbation method, and the evolution equations are shown to be the Korteweg-deVries-Burgers equation. The results show that, Up to O(is an element of(3/2)), the head-on-collision of two nonlinear progressive waves is elastic and the nonlinear progressive waves preserve their original properties after the collision. The phase functions for each wave are derived explicitly and it is shown that they are not straight lines anymore, they are rather some curves.
  • Küçük Resim
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    On the contribution of higher order terms to solitary waves in fluid filled elastic tubes
    (Birkhauser Verlag, 2000-01) 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 scale 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 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. Mathematics Subject Classification (1991).
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    Non-linear waves in a fluid-filled inhomogeneous elastic tube with variable radius
    (Pergamon-Elsevier Scıence Ltd, 2008-05) Demiray, Hilmi
    In the present work, by employing the non-linear equations of motion of an incompressible, inhomogeneous, isotropic and prestressed thin elastic tube with variable radius and the approximate equations of an inviscid fluid, which is assumed to be a model for blood, we studied the propagation of non-linear waves in such a medium, in the longwave approximation. Utilizing the reductive perturbation method we obtained the variable coefficient Korteweg-de Vries (KdV) equation as the evolution equation. By seeking a progressive wave type of solution to this evolution equation, we observed that the wave speed decreases for increasing radius and shear modulus, while it increases for decreasing inner radius and the shear modulus.
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    Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube
    (Elsevier Science Inc, 2004-07-15) Bakırtaş, İlkay; Demiray, Hilmi
    In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible inviscid fluid the evolution equation is obtained as the nonlinear Schrodinger equation with variable coefficients. 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 decreases with distance for tubes with descending radius while it increases for tubes with ascending radius.