Browsing by Subject "Equations"

Now showing 1 - 7 of 7

Open Access
Dynamical systems and Poisson structures
(American Institute of Physics, 2009) Gurses, M.; Guseinov, G. Sh.; Zheltukhin, K.
We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in ℝ3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in Rn are locally (n-1) -Hamiltonian. We give also an algorithm, similar to the case in ℝ3, to construct a rank two Poisson structure of dynamical systems in ℝn. We give a classification of the dynamical systems with respect to the invariant functions of the vector field X→ and show that all autonomous dynamical systems in ℝn are superintegrable. © 2009 American Institute of Physics.
Open Access
On the classification of Darboux integrable chains
(American Institute of Physics, 2008) Habibullin, I.; Zheltukhina, N.; Pekcan, A.
We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, { t (n+k,x) } k=-∞ ∞, {(dk /d xk) t (n,x) } k=1 ∞, such that Dx F=0 and DI=I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp (n) =p (n+1). Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function f is of the special form f (u,v,w) =w+g (u,v). © 2009 American Institute of Physics.
Open Access
Preconditioning large integral-equation problems involving complex targets
(IEEE, 2008-07) Malas, Tahir; Gürel, Levent
When the target problem is small in terms of the wavelength, simple preconditioners, such as BDP, may sufficiently accelerate the convergence. On the other hand, for large-scale problems, the matrix equations become much more difficult to solve, and therefore, the importance of preconditioning become more evident for both formulations. In this paper, we demonstrate the use of novel, strong, and efficient preconditioners for the solutions of large EFIE and CFIE problems.
Open Access
Radar cross-section study of cylindrical cavity-backed apertures with outer or inner material coating: the case of H-polarization
(Institute of Electrical and Electronics Engineers, 1995-05) Çolak, D.; Nosich, A. I.; Altıntaş, A.
A dual-series-based solution is obtained for the scattering of an H-polarized plane wave from a slitted infinite circular cylinder coated with absorbing material from inside or outside. For both cases, numerical results are presented for the radar cross section and comparisons are given for two different realistic absorbing materials. The radar cross-section dependencies are also given for the aspect angle of the scatterer and the thickness of the absorbing layer.
Open Access
Simulating a wavelength-size 2-D lens with an accurate numerical method
(IEEE, 2001) Boriskin, A. V.; Nosich, A. I.; Altıntaş, Ayhan
The effect of a localized light source directivity improvement due to an arbitrarily shaped dielectric cylinder taken as a 2-D model of a dielectric lens is studied. The source is simulated by the field of a complex source-point (CSP). An efficient algorithm for the solution of 2-D problem of wave scattering by a smooth dielectric cylinder is developed, based on the concept of analytical regularization. The basic properties of the algorithm are studied. Numerical results for the accuracy of the algorithm and sample far-field characteristics such as the total radiated power, directivity and radiation patterns for various lens parameters are presented.
Open Access
Transient analysis of nonlinear circuits by combining asymptotic waveform evaluation with volterra series
(Institute of Electrical and Electronics Engineers, 1995-08) Celik, M.; Atalar, Abdullah; Tan, M. A.
A new method is proposed for the transient analysis of circuits with large number of linear lumped elements and lossy coupled transmission lines, and with few mildly nonlinear terminations. The method combines the Volterra-series technique with Asymptotic Waveform Evaluation approach and corresponds to recursive analysis of a linear equivalent circuit.
Open Access
V(Z) of the surface acoustic wave focusing system
(IEEE, 1986-11) Atalar, Abdullah; Köymen, Hayrettin
It is possible to define a V(Z) function for the surface acoustic wave (SAW) focusing system for a class of reflectors similar to that defined in acoustic microscopy. In this case V(Z) is a function which relates the transducer output voltage to the distance between the focal point and the reflection line. It is possible to express V(Z) in an analytical expression using angular spectrum techniques. V(Z) is measured for straight edge reflectors forming various angles with the surface. V(2) of straight step reflectors are investigated. These curves show a dependence on the type of reflector. The experiments are performed at 1.5 MHz in conjunction with a computerized data acquisition system. The phase information is also recorded in all these measurements in addition to the amplitude. It is possible to get an inversion of V(Z) to get the SAW reflection coefficient at a straight discontinuity.