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Yazar: Demiray, Hilmi × search.filters.applied.f.publicationcategory: Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı ×

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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).
  • 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.
  • Küçük Resim
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    Travelling waves in a prestressed elastic tube filled with a fluid of variable viscosity
    (Springer, 2008) Demiray, Hilmi; Gaik, Tay Kim
    In this work, treating the artery as a prestressed thin elastic tube with variable radius and the blood as all incompressible Newtonian fluid with variable viscosity, the propagation of nonlinear waves ill Such a composite medium is studied, in the long wave approximation, through the use of the reductive perturbation method and the Forced Korteweg-de Vries-Burgers (FKdVB) equation with variable coefficients is obtained as the evolution equation. A progressive wave type of solution is presented for this evolution equation and the result is discussed.
  • Küçük Resim
    Yayın
    Nonlinear waves in fluid-filled elastic tubes: A model to large arteries
    (Springer, 2007) Demiray, Hilmi
    In the present work, by treating the arteries as a prestressed thin walled elastic tube of variable radius and the blood as an incompressible inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium through the use of long wave approximation and the reductive perturbation method. The KdV equation with variable coefficient is obtained as the evolution equation. By seeking a progressive wave type of solution to this equation, we observed that the wave speed decreases with increasing inner radius while it increases with decreasing inner radius of the tube. Such a result is to be expected from physical considerations.
  • Küçük Resim
    Yayın
    Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation
    (Springer Science and Business Media, LLC, 2008) Tay, Kim Gaik; Demiray, Hilmi; Tiong, Ong Chee
    In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By introducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the smallness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.