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  • Küçük Resim
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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.
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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.
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    Nonlinear waves in a viscous fluid contained in a viscoelastic tube
    (Birkhauser Verlag, 2001-11) Demiray, Hilmi
    In the present work the propagation of weakly nonlinear waves in a prestressed viscoelastic thin tube filled with a viscous fluid is studied. Using the reductive perturbation technique in analyzing the nonlinear equations of a viscoelastic tube and the approximate equations of a viscous fluid, the propagation of weakly nonlinear waves in the longwave approximation is studied. Depending on the order of viscous effects, various evolution equations like, Burgers', Korteweg-de Vries, Korteweg-de Vries-Burgers' equations and their perturbed forms are obtained. Ravelling wave type of solutions to some of these evolution equations are sought. Finally, utilizing the finite difference scheme, a numerical solution is presentede for the perturbed KdVB equation and the result is discussed.
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    Modulation of electron-acoustic waves in a plasma with vortex electron distribution
    (Walter De Gruyter GMBH, 2015-04) Demiray, Hilmi
    In the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.
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    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.
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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).
  • Küçük Resim
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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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    Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution
    (Springer Basel AG, 2014-12) Demiray, Hilmi
    The basic equations describing the nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions, in the long-wave limit, are re-examined through the use of the modified PLK method. Introducing the concept of strained coordinates and expanding the field variables into a power series of the smallness parameter epsilon, a set of evolution equations is obtained for various order terms in the perturbation expansion. The evolution equation for the lowest order term in the perturbation expansion is characterized by the conventional modified Korteweg-deVries (mKdV) equation, whereas the evolution equations for the higher order terms in the expansion are described by the degenerate(linearized) mKdV equation. By studying the localized traveling wave solution to the evolution equations, the strained coordinate for this order is determined so as to remove possible secularities that might occur in the solution. It is observed that the coefficient of the strained coordinate for this order corresponds to the correction term in the wave speed. The numerical results reveal that the contribution of second order term to the wave amplitude is about 20 %, which cannot be ignored.
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    Weakly non-linear waves in a tapered elastic tube filled with an inviscid fluid
    (Pergamon-Elsevier Science Ltd, 2005-07) Bakırtaş, İlkay; Demiray, Hilmi
    In the present work, treating the artery as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly non-linear 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 equation admits a solitary wave-type solution with variable wave speed. It is observed that, the wave speed decreases with distance for positive tapering while it increases for negative tapering. It is further observed that, the progressive wave profile for expanding tubes (a > 0) becomes more steepened whereas for narrowing tubes (a < 0) it becomes more flattened.
  • Küçük Resim
    Yayın
    Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section
    (Elsevier Ltd, 2006-04) Demiray, Hilmi
    In the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave solution with a variable wave speed. It is observed that, the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.