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Yayın Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case(Pergamon-Elsevier Science, 2003-07) Demiray, HilmiIn 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.Yayın “International conference on vibration problems” ICOVP-2007 and a short history(Springer Science and Business Media, LLC, 2008) İnan, Esin[No abstract available]Yayın Interactions of nonlinear acoustic waves in a fluid-filled elastic tube(Pergamon-Elsevier Science, 2001-03) Akgün, Güler; Demiray, HilmiIn 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.Yayın Standing waves for a generalized Davey-Stewartson system(IOP Publishing, 2006-10-27) Eden, Osman Alp; Erbay, SaadetIn this paper, we establish the existence of non-trivial solutions for a semi-linear elliptic partial differential equation with a non-local term. This result allows us to prove the existence of standing wave ( ground state) solutions for a generalized Davey-Stewartson system. A sharp upper bound is also obtained on the size of the initial values for which solutions exist globally.Yayın A function of direction in a Weyl subspace associated with a set of orthogonal vector fields(World Scientific Publ Co Pte Ltd, 2003) Özdeğer, AbdülkadirLet W-m be an m-dimensional subspace of an n-dimensional Weyl space W-n. Suppose that (1)v, (2)v,..., (m)v are mutually orthogonal smooth vector fields in W-m and that v is a non-tangential smooth vector field defined on W-m. Consider the (m + 1)-dimensional net delta defined by (1)v, (2)v, ..., (m)v, v. In this work, we obtain a function of direction associated with the net delta and define a class of curves on W-m in relation to this function of direction.Yayın A note on the exact travelling wave solution to the KdV-Burgers equation(Elsevier Science, 2003-10) Demiray, HilmiIn the present note, by use of the hyperbolic tangent method, a progressive wave solution to the Korteweg-de Vries-Burgers (KdVB) equation is presented. The solution we introduced here is less restrictive and comprises some solutions existing in the current literature (see [Wave Motion 11 (1989) 559; Wave Motion 14 (1991) 369]).Yayın Network synchronization: Spectral versus statistical properties(Elsevier B.V., 2006-12) Atay, Fatihcan Mehmet; Bıyıkoğlu, Türker; Jost, JürgenWe consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.Yayın Waves in an elastic tube filled with a heterogeneous fluid of variable viscosity(Pergamon-Elsevier Science Ltd, 2009-07) Demiray, HilmiBy 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.Yayın Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube(Pergamon-Elsevier Science, 2002-10) Demiray, HilmiIn 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.Yayın Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid(Wit Press, 2002) Bakırtaş, İlkay; Demiray, HilmiIn 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).
