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search.filters.applied.f.publicationcategory: Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı × Konu: Solitary waves ×

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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.