http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2401 JAEM 2017, Vol 7, No 2 koleksiyonunu içerir. 2026-04-14T21:29:38Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/6042 Rogue wavefunctions due to noisy quantum tunneling potentials Bayındır, Cihan In this paper, we study the effects of white-noised potentials on nonlinear quantum tunneling. We use a split-step scheme to numerically solve the nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider three different types of potentials, namely; the single rectangular barrier, double rectangular barrier, and triangular barrier. For all these three cases, we show that white-noise given to potentials do not trigger modulation instability for tunneling of the sech type soliton solutions of the NLSE. However, white-noised potentials trigger modulation instability for tunneling of the sinusoidal wavefunctions; thus, such a wavefield turns into a chaotic one with many apparent peaks. We argue that peaks of such a field may be in the form of rational rogue wave solutions of the NLSE. Our results can be used to examine the effects of noise on quantum tunneling. Since a rogue wavefunction means a higher probability of the tunneling particle to be at a given (x,t) coordinate, our results may also be used for developing the quantum science and technology with many possible applications including but are not limited to increasing the resolution and efficiency of scanning tunneling microscopes, enhancing proton tunneling for DNA mutation and enhancing superconducting properties of junctions. 2017-04-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2637 Dirichlet series and approximate analytical method for the solution of mhd boundary layer flow of casson fluid over a stretching/shrinking sheet Awati, Vishwanath B. The paper presents analytical and semi-numerical solution for magnetohydrodynamic (MHD) boundary layer flow of Casson fluid over a exponentially permeable shrinking sheet. The governing partial differential equations of momentum equations are reduced to ordinary differential equations by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use fast converging Dirichlet series and approximate analytical solution by the Method of stretching of variables for the solution of the nonlinear differential equation. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes. 2017-01-25T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2636 Nonholonomic frames for finsler space with deformed matsumoto metric Tripathi, Brijesh Kumar; Chaubey, Vinit Kumar The purpose of present paper is to find the nonholonomic frames for the deformed Matsumoto type metric which are given in the forms I. (?2/???)? =?3/??? II. (?2/???)? =?2?/??? where ?2 = aij (x)yi yj and ? = bi(x)yi. The first metric of the above deformation is obtained by the product of Matsumoto and Riemannian metric and second one is the product of Matsumoto and 1-form metric. 2017-01-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2635 Some results on total chromatic number of a graph Vaidya, Samir K.; Isaac, Rakhimol V. A total coloring of a graph is a proper coloring in which no two adjacent or incident graph elements receive the same color. The total chromatic number of a graph is the smallest positive integer for which the graph admits a total coloring. In this paper, we derive some results on total chromatic number of a graph. 2017-08-24T00:00:00Z