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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 Comments on "upper cutoff frequency of the bound wave and new leaky wave on the slotline"(IEEE-INST Electrical Electronics Engineers Inc, 1999-05) İdemen, Mehmet Mithat; Büyükaksoy, İbrahim Alinur[No abstract available]Yayın Re-visiting the head-on collision problem between two solitary waves in shallow water(Pergamon-Elsevier Science Ltd, 2015-03) Özden, Ali Erinç; Demiray, HilmiUpon discovering the wrongness of the statement "although this term does not cause any secularity for this order it will cause secularity at higher order expansion, therefore, that term must vanish" by Su and Mirie [4], in the present work, we studied the head-on collision of two solitary waves propagating in shallow water by introducing a set of stretched coordinates in which the trajectory functions are of order of epsilon(2), where epsilon is the smallness parameter measuring non-linearity. Expanding the field variables and trajectory functions into power series in epsilon, we obtained a set of differential equations governing various terms in the perturbation expansion. By solving them under non-secularity condition we obtained the evolution equations and also the expressions for phase functions. By seeking a progressive wave solution to these evolution equations we have determined the speed correction terms and the phase shifts. As opposed to the result of Su and Mine [4] and similar works, our calculations show that the phase shifts depend on both amplitudes of the colliding waves.Yayın A method for higher-order expansion in non-linear ion-acoustic waves(Pergamon-Elsevier Science, 2000-03) Demiray, HilmiThe basic equations describing the non-linear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified multiple-scale expansion method. Expanding the field quantities into a power series of the smallness parameter epsilon, a Set Of evolution equations is obtained for various terms in the perturbation expansion. To illustrate the present derivation, a localized travelling wave solution is studied for the derived field equations and the result is compared with those of Malfliet and Wieers (J. Plasma Phys. 56 (1996) 441-450), who employed the dressed solitary wave approach from the outset of their study.Yayın Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution(Springer Basel AG, 2014-12) Demiray, HilmiThe 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.Yayın Weakly non-linear waves in a fluid-filled elastic tube with variable prestretch(Pergamon-Elsevier Science Ltd, 2008-11) Demiray, HilmiIn the present work, by utilizing the non-linear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable prestretch both in the axial and the radial directions and the approximate equations of motion of an incompressible inviscid fluid, which is assumed to be a model for blood, we studied the propagation of weakly non-linear waves in such a medium, in the long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient KdV equation as the evolution equation. By seeking a travelling wave solution to this evolution equation, we observed that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations.
