Filtreler

Filtreleri Sıfırla

Ayarlar

Konu: Nonlinear waves ×

Arama Sonuçları

Listeleniyor 1 - 10 / 24
  • Küçük Resim
    Yayın
    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
    Yayın
    Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
    (Pergamon-Elsevier Science Ltd, 2010-09) Demiray, Hilmi
    In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly non-linear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg-de Vries (KdV) equation. A progressive wave type of solution, which satisfies the evolution equation in the integral sense but not point by point, is presented. The resulting solution is numerically evaluated for two selected bottom profile functions, and it is observed that the wave amplitude increases but the band width of the solitary wave decreases with increasing undulation of the bottom profile.
  • Küçük Resim
    Yayın
    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.
  • Küçük Resim
    Yayın
    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.
  • Küçük Resim
    Yayın
    Weakly nonlinear waves in a fluid with variable viscosity contained in a prestressed thin elastic tube
    (Pergamon-Elsevier Science Ltd, 2008-04) Demiray, Hilmi
    In this work, treating the artery as a prestressed thin elastic tube and the blood as an incompressible Newtonian fluid with variable viscosity which vanishes on the boundary of the tube, the propagation of nonlinear waves in such a fluid-filled elastic tube is studied, in the longwave approximation, through the use of reductive perturbation method and the evolution equation is obtained as the Korteweg-deVries-Burgers equation. A progressive wave type of solution is presented for this evolution equation and the result is discussed.
  • Küçük Resim
    Yayın
    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].
  • Küçük Resim
    Yayın
    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
    Yayın
    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.
  • Küçük Resim
    Yayın
    Head-on collisions of solitary waves
    (Işık Üniversitesi, 2015-12-11) Özden, Ali Erinç; Demiray, Hilmi; Işık Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Doktora Programı
    The interaction of solitary waves in various physical media is a long time studied subject in nonlinear wave theory. For overtaking collision between solitary waves, one can use the inverse scattering transform method to obtain the overtaking colliding effect of solitary waves. However, for the head-on collision between solitary waves, one must employ some kind of asymptotic expansion to solve the original field equations. This thesis addresses head-on collision problem between two solitary waves. The head-on collision of solitary waves in shallow water is re-examined upon discovering the wrongness of the statement about the secular terms in the pioneering work of Su and Mirie (J. Fluid Mech., 98:509-525, 1980). In the first part, based on the above argument, the head-on collision of two solitary waves propagating in shallow water is studied by introducing a set of stretched coordinates that includes some unknown trajectory functions which are to be determined so as to remove secularities that might occur in the solution. Expanding the field variables and trajectory functions into power series, a set of differential equations governing various terms in the perturbation expansion is obtained. By solving them under non-secularity condition, the evolution equations and also the expressions for phase shifts are determined. As opposed to the result of previous studies our calculation shows that the phase shifts depend on amplitudes of both colliding waves. In the second part, the head-on-collision of solitary waves in shallow water theory is examined through the use of extended Poincaré-Lighthill-Kuo(PLK) method. Following a similar procedure with the previous part, the speed correction terms and the trajectory functions are determined. The result obtained here is exactly same with that found in the first part. In the third part, the head-on collision of the solitary waves in fluid-filled elastic tubes is studied by employing the extended PLK method. Pursuing the procedure in the previous part, the speed correction terms and the trajectory functions are obtained. The results of our calculation show that both the evolution equations and the phase shifts are quite different from those of Xue (Phys. Lett. A, 331:409-413, 2004). As opposed to the result of previous works on the same subject, the phase shifts depend on the amplitudes of both colliding waves.
  • Küçük Resim
    Yayın
    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.