Filtreler

Filtreleri Sıfırla

Ayarlar

Bölüm: Işık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü × Konu: Nonlinear equations ×

Arama Sonuçları

Listeleniyor 1 - 10 / 41
  • Küçük Resim
    Yayın
    Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case
    (Pergamon-Elsevier Science, 2003-07) 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 modified reductive perturbation technique presented by us [15] the amplitude modulation of weakly nonlinear waves is examined. It is shown that the first order term in the perturbation expansion is governed by a nonlinear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a nonhomogeneous term. In the longwave limit a travelling wave type of solution to these equations are also given.
  • Küçük Resim
    Yayın
    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.
  • Küçük Resim
    Yayın
    A note on the amplitude modulation of symmetric regularized long-wave equation with quartic nonlinearity
    (Springer, 2012-12) Demiray, Hilmi
    We study the amplitude modulation of a symmetric regularized long-wave equation with quartic nonlinearity through the use of the reductive perturbation method by introducing a new set of slow variables. The nonlinear Schrodinger (NLS) equation with seventh order nonlinearity is obtained as the evolution equation for the lowest order term in the perturbation expansion. It is also shown that the NLS equation with seventh order nonlinearity assumes an envelope type of solitary wave solution.
  • Küçük Resim
    Yayın
    Modulational instability of acoustic waves in a dusty plasma with nonthermal electrons and trapped ions
    (Pergamon-Elsevier Science Ltd, 2019-04) Demiray, Hilmi; Abdikian, Alireza
    In the present work, employing the nonlinear field equations of a hot dusty plasma in the presence of nonthermal electrons and trapped ions, we studied the amplitude modulation of nonlinear waves in such a plasma medium by use of the reductive perturbation method and obtained the modified nonlinear Schrodinger equation. The modulational instability (MI) was investigated and the effects of the proportion of the fast electrons (alpha), the trapping parameter (b) and the plasma parameters such as the dust-ion temperature ratio (sigma(d)), the partial unperturbed electron to dust density (delta), and the ion-electron temperature ratio (sigma(i)) on it was discussed. For the investigation of modulational instability problems three parameters P/Q,K-max and Gamma(max) play the central role. The variations of these parameters with the wave number k and the other physical parameters are discussed and the possibility of occurence of modulational instability is indicated.
  • 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
    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
    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
    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.
  • 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.