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Yayın Head-on collision of the solitary waves in fluid-filled elastic tubes(Işık University Press, 2018-04-12) Özden, Ali Erinç; Demiray, HilmiIn the present work, by employing the field equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter epsilon and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite different from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.Yayın On progressive wave solution for non-planar KDV equation in a plasma with q-nonextensive electrons and two oppositely charged ions(Işık University Press, 2020) Demiray, Hilmi; El-Zahar, Essam Roshdy; Shan, Shaukat AliIn this paper, the ion-acoustic wave is investigated in a plasma with q-nonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.Yayın Modulational instability of three dimensional waves in a plasma with vortex electron distribution(Işık University Press, 2019-02-10) Demiray, HilmiIn the present work, employing the three dimensional equations 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 an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the three dimensional form of the modified nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. The modulational instability of the homogeneous harmonic solution is investigated and the criteria for the instability is discussed as a function of the obliqueness angle. The numerical calculations show that the critical value of the wave number of the envelop wave increases with the wave number k of the carrier wave and the obliqueness angle gamma.Yayın An investigation of the certain class of multivalent harmonic mappings(Eudoxus Press, 2016-03) Özkan Uçar, Hatice Esra; Polatoğlu, Yaşar; Aydoğan, Seher MelikeThe main purpose of the present paper is to investigate some properties of the certain class of sense-preserving p-valent harmonic mappings in the open unit disc D = {z is an element of C parallel to z vertical bar < 1}.Yayın Notes on harmonic functions for which the second dilatation is α - spiral(Eudoxus Press, 2015-06) Aydoğan, Seher MelikeIn this study, we consider, f = h + (g) over bar harmonic functions in the unit disc D. By applying S. S. Miller and P. M. Mocanu result, we obtain a new subclass of harmonic functions, such as S-HPST*(alpha, beta) We introduce this new class as defined in the following form, S-HPST*(alpha, beta) = {f = h(z) + <(g(z))over bar>vertical bar f is an element of S-H, h(z) is an element of S* , Re (e(i alpha)g '(z)/h '(z)) > beta,vertical bar alpha vertical bar < pi/2,0 <= beta < (0.1), We also use subordination principle, study on distortion theorems, some numerical examples and coefficient inequalities of this class.Yayın A note on the cylindrical waves with transverse distortion in a plasma with vortex electron distribution(Işık University Press, 2020-01-20) Demiray, HilmiIn the present work, employing the conventional reductive perturbation method and the nonlinear field equations of a plasma consisting of a cold electron uid, hot electrons obeying a non-isothermal (trapped/vortex-like) distribution and station-ary ions with transverse distortion, we studied the propagation of nonlinear waves in such a plasma medium and obtained the modified CKP equation. Seeking a progressive wave solution to this evolution equation we obtained the exact analytical solution. It is observed that the speed of the solitary wave is directional dependent and the wave front is not circularly cylindrical surface any more.Yayın A certain class of harmonic mappings related to functions of bounded boundary rotation(Eudoxus Press, 2014-05) Polatoğlu, Yaşar; Yavuz Duman, Emel; Aydoğan, Seher MelikeLet V(k) be the class of functions with bounded boundary rotation and let S-H be the class of sense-preserving harmonic mappings. In the present paper we investigate a certain class of harmonic mappings related to the function of bounded boundary rotation.Yayın Some notes on spectra of cographs(Charles Babbage Res Ctr, 2011-07) Bıyıkoğlu, Türker; Simic, Slobodan K.; Stanic, ZoranA cograph is a P-4-free graph. We first give a short proof of the fact that 0 (-1) belongs to the spectrum of a connected cograph (with at least two vertices) if and only if it contains duplicate (resp. coduplicate) vertices. As a consequence, we next prove that the polynomial reconstruction of graphs whose vertex-deleted subgraphs have the second largest eigenvalue not exceeding root 5-1/2 is unique.Yayın Higher order perturbation expansion for ion-acoustic solitary waves with q-nonextensive nonthermal velocity distribution(Işık University Press, 2018-09-11) Demiray, HilmiThe basic nonlinear equations describing the dynamics of a two component plasma consisting of cold positive ions and electrons obeying hybrid q-nonextensive nonthermal velocity distribution are examined through the use of modified PLK formalism and the reductive perturbation method and obtained the KdV equation for the lowest order term in the perturbation expansion. The method is further extended to include the contribution of higher order terms in the expansion; the evolution equation for the second order term is found to be the degenerate(linearized) KdV equation with non-homogeneous term. Seekink the localized travelling wave solution (solitons) to these evolution equations we obtained the speed correction terms and the wave profiles. Numerical results for the set of suitable parameters( Williams et. al. [23]) are shown inb the form of some graphs. The combined effect of nonextensive parameter (q) and the nonthermal parameter (alpha) on the soliton dynamics has also been studied.Yayın Quasiconformal harmonic mappings related to starlike functions(Eudoxus Press, 2014-07) Polatoğlu, Yaşar; Duman, Emel Yavuz; Kahramaner, Yasemin; Aydoğan, Seher MelikeLet f = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the unit disc D = {z is an element of C parallel to z vertical bar < 1}. If f satisfies the condition vertical bar w(z)vertical bar = vertical bar g'(z)/h'(z)vertical bar < k, (0 <= k < 1), then f is called k-quasiconformal harmonic mapping in D.The aim of this paper is to investigate a subclass of k-quasiconformal harmonic mappings.
