Browsing by Subject "Numerical solution"

Now showing 1 - 5 of 5

Open Access
Bell solitons in ultra-cold atomic Fermi gas
(2013) Khan, A.; Panigrahi P.K.
We demonstrate the existence of supersonic bell solitons in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensate crossover regime. Starting from the extended Thomas-Fermi density functional theory of superfluid order parameter, a density transformation is used to map the hydrodynamic mean field equation to a Lienard-type equation. As a result, bell solitons are obtained as exact solutions, which is further verified by the numerical solution of the dynamical equation. The stability of the soliton is established and its behaviour in the entire crossover domain is obtained. It is found that, akin to the case of vortices, bell solitons yield highest contrast in the BEC regime. © 2013 IOP Publishing Ltd.
Open Access
Direct numerical solution of the Lippmann-Schwinger equation in coordinate space without partial-wave decomposition
(American Physical Society, 2016) Kuruoğlu, Z. C.
Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystrom method employing a direct-product quadrature rule for three variables. To reduce the computational burden of discretizing three variables, advantage is taken of the fact that, for central potentials, the azimuthal angle can be integrated out, leaving a two-variable reduced integral equation. A regularization method for the kernel of the two-variable integral equation is derived from the treatment of the singularity in the three-dimensional equation. A quadrature rule constructed as the direct product of single-variable quadrature rules for radial distance and polar angle is used to discretize the two-variable integral equation. These two- and three-variable methods are tested on the Hartree potential. The results show that the Nystrom method for the coordinate-space LS equation compares favorably in terms of its ease of implementation and effectiveness with the Nystrom method for the momentum-space version of the LS equation.
Open Access
On approximation sums by maximums and vice versa
(SAGE, 1994) Özaktaş, Haldun M.
We discuss the approximation max (x, y) ≈x+y for x, y >0, which is found to be useful in obtaining simple and transparent approximate solutions and interpretations for analytically complicated problems.
Open Access
Rigorous analysis of double-negative materials with the multilevel fast multipole algorithm
(Applied Computational Electromagnetics Society, Inc., 2012) Ergül, Özgür; Gürel, Levent
We present rigorous analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of numerical solutions are investigated when DNMs are formulated with two recently developed formulations, i.e., the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Simulation results on canonical objects are consistent with previous results in the literature on ordinary objects. MLFMA is also parallelized to solve extremely large electromagnetics problems involving DNMs.
Open Access
Study of junction and bias parameters in readout of phase qubits
(2012) Zandi H.; Safaei, S.; Khorasani, S.; Fardmanesh, M.
The exact numerical solution of the nonlinear Ginzburg-Landau equation for Josephson junctions is obtained, from which the precise nontrivial current density and effective potential of the Josephson junctions are found. Based on the resulting potential well, the tunneling probabilities of the associated bound states are computed which are in complete agreement with the reported experimental data. The effects of junction and bias parameters such as thickness of the insulating barrier, cross sectional area, bias current, and magnetic field are fully investigated using a successive perturbation approach. We define and compute figures of merit for achieving optimal operation of phase qubits and measurements of the corresponding states. Particularly, it is found that Josephson junctions with thicker barriers yield better performance in measurements of phase qubits. The variations of characteristic parameters such as life time of the states due to the above considered parameters are also studied and discussed to obtain the appropriate configuration setup.