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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, AlirezaIn 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.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 An essential approach to the architecture of diatomic molecules: 2. how are size, vibrational period of time, and mass interrelated?(Optical Soc Amer, 2004-11) Yarman, Nuh TolgaIn our previous article, we arrived at an essential relationship for T the classical vibrational period of a given diatomic molecule, at the total electronic energy E-, i.e., T = [4pi(2)/(rootn(1)n(2)h)] rootgM(0)m(e) R-2, where M-0 to is the reduced mass of the nuclei; m(3) is the mass of the electron; R is the internuclear distance: g is a dimensionless and relativistically invariant coefficient, roughly around unity; and n(1) and n(2) are the principal quantum numbers of electrons making up the bond(s) of the diatomic molecule, which, because of quantum defects. are not integer numbers. The above relationship holds generally. It essentially yields T similar to R 2 for the classical vibrational period versus the square of the internuclear distance in different electronic states of a given molecule. which happens to be an approximate relationship known since 1925 but not understood until now. For similarly configured electronic states, we determine n(1)n(2) to be R/R-0, where R is the internuclear distance in the given electronic state and R-0 is the internuclear distance in the ground state. Furthermore. from the analysis of H-2 spectroscopic data, we found out that the ambiguous states of this molecule are configured like alkali hydrides and Li-2. This suggests that, quantum mechanically, on the basis of an equivalent H-2 excited state. we can describe well, for example, the ground state of Li-2. On the basis of this interesting finding, herein we propose to associate the quantum numbers n(1) and n2 With the bond electrons of the ground state of any diatomic molecule belonging to a given chemical family in reference to the ground state of a diatomic molecule still belonging to this family but bearing, say, the lowest classical vibrational period, since g, depending only on the electronic configuration. will stay nearly constant throughout. This allows us to draw up a complete systematization of diatomic molecules given that g (appearing to be dependent purely on the electronic structure of the molecule) stays constant for chemically alike molecules and n(1)n(2) can be identified to be R-0/R-00 for diatomic molecules whose bonds are electronically configured in the same way, R-00 then being the internuclear distance of the ground state of the molecule chosen as the reference molecule within the chemical fan-Lily under consideration. Our approach discloses the simple architecture of diatomic molecules, otherwise hidden behind a much too cumbersome quantum-mechanical description. This architecture, telling how the vibrational period of Lime. size. and mass are determined, is Lorentz-invariant and can be considered as the mechanism of the behavior of the quantities in question in interrelation with each other when the molecule is brought into uniform translational motion or transplanted into a gravitational field or, in fact, any field with which it can interact.Yayın Bifurcation of drift shells near the dayside magnetopause(Amer Geophysical Union, 2007-07-10) Öztürk, Mehmet Kaan; Wolf, Richard A.Close to the dayside magnetopause, there is a region of space where each field line has two magnetic field minima, one near each cusp. That region is located around local noon, and extends about 1-2 R-e from the magnetopause. Particles that enter this region with equatorial pitch angles sufficiently close to 90 degrees will cross the dayside not along an equatorial path, but along one of the two branches on either side of the equatorial plane. The two branches are joined again past local noon. This process of drift-shell bifurcation (DSB) is nonadiabatic even under static conditions. Two physical mechanisms can cause this nonadiabaticity: one that is operative for nearly all magnetospheric magnetic field configurations and another that depends on a particular combination of north-south and east-west asymmetry in the magnetic field. This paper deals only with the first mechanism. For configurations with north-south and east-west symmetry, DSB changes the second invariant I of the motion by a small amount that is of the order of the gyroradius (the first invariant is intact). For near-equatorial particles (I approximate to 0) the change can be significantly larger. Assuming north-south and dawn-dusk symmetry, we present general theoretical expressions for the second-invariant jump Delta I, which can be applied to a variety of magnetic field models. The results show that Delta I is sensitively dependent on the bounce phase of the particle at the bifurcation line. The RMS value of Delta I over a bounce-phase ensemble increases with decreasing mirror field and with increasing kinetic energy. We verify these results with test-particle simulations using model magnetic fields.Yayın Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution(Amer Inst Physics, 2018-04) Demiray, Hilmi; El-Zahar, Essam RoshdyWe consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.Yayın Modulation of cylindrical (spherical) waves in a plasma with vortex electron distribution(American Institute of Physics Inc., 2018-07-01) Demiray, HilmiIn the present work, employing cylindrically (spherically) symmetric field equations of a plasma consisting of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we studied the amplitude modulation of electron-acoustic waves. Due to the physical nature of the problem under investigation, the nonlinearity of the field equations is of order (3/2), which causes considerable difficulty in the analysis of modulation problems. To solve this difficulty, we expanded this nonlinear term into the Fourier cosine series of the phase function and obtained the modified cylindrical (spherical) nonlinear Schrodinger (NLS) equation. A consistent analysis for the modulational instability is presented and a criterion between the time parameter tau and the wave number K is established. In addition, motivated with the solitonic solution of modified NLS equation for planar case and utilizing the "weighted residual method," we proposed a harmonic wave of variable frequency with progressive wave amplitude to the evolution equation. It is found that the modified cylindrical (spherical) NLS equation assumes an envelope type of progressive wave solution in the sense weighted residual. The numerical results reveal that the amplitude of spherical wave is much larger than that of the cylindrical wave and that both amplitudes decrease with increasing time parameter tau. It is further observed that the wave profiles get distorted with progressing time.Yayın Tunneling rates of single electrons on liquid helium in an extracting field(Springer/Plenum Publishers, 2009-02) Karakurt, İsmailWe calculated the tunneling rates of single electrons from the quasi-stationary states on both liquid He-4 and He-3 in an extracting electric field. The rates were obtained from the widths of the resonance lineshapes of the asymptotic amplitude of the wave function for the electron. The calculations were carried out in the limit of strong tunneling which leads to tunneling rates of the order of 1 GHz, and is of recent interest in a proposed quantum-computer system using the electronic states of electrons on helium as qubits. We find that the resonances can, in general, be described by Fano lineshapes. Our results, in addition to presenting quantitative information involving the read-out operations of qubits, clarify that when tunneling is weak the resonances are sharp and more accurately Lorentzian and that the observed Fano lineshapes result from strong tunneling leading to fat resonances and hence asymmetry.Yayın Modulation of electron-acoustic waves in a plasma with kappa distribution(American Institute of Physics Inc., 2016-03) Demiray, HilmiIn the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying ? velocity 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 of such a plasma, we obtained the nonlinear Schrödinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers.Yayın Interactions of nonlinear electron-acoustic solitary waves with vortex electron distribution(American Institute of Physics Inc., 2015-02-01) Demiray, HilmiIn the present work, based on a one dimensional model, we consider the head-on-collision of nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The analysis is based on the use of extended Poincare, Lighthill-Kuo method [C. H. Su and R. M. Mirie, J. Fluid Mech. 98, 509 (1980); R. M. Mirie and C. H. Su, J. Fluid Mech. 115, 475 (1982)]. It is shown that, for the first order approximation, the waves propagating in opposite directions are characterized by modified Korteweg-de Vries equations. In contrary to the results of previous investigations on this subject, we showed that the phase shifts are functions of both amplitudes of the colliding waves. The numerical results indicate that the waves with larger amplitude experience smaller phase shifts. Such a result seems to be plausible from physical considerations.Yayın A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution(Amer Inst Physics, 2015-09) Demiray, Hilmi; Bayındır, CihanIn the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg-de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.
