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1999 - 199932000 - 200938
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Bitiş tarihi: 2009 × Konu: Water waves ×

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Listeleniyor 1 - 10 / 41
  • Küçük Resim
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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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    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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    Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid
    (Wit Press, 2002) Bakırtaş, İlkay; 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 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).
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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.
  • Küçük Resim
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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.
  • Küçük Resim
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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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    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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    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.
  • Küçük Resim
    Yayın
    Solitary waves in a tapered prestressed fluid-filled elastic tube
    (Birkhauser Verlag AG, 2004-03) Demiray, Hilmi
    In 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.
  • Küçük Resim
    Yayın
    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.