Browsing by Subject "Exact 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
Comparison of the formulations for a hub-and-spoke network design problem under congestion
(Elsevier, 2016) Kian, Ramer; Kargar, Kamyar
In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set. © 2016 Elsevier Ltd
Open Access
Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface
(Optical Society of America, 2011-02-04) Onural, L.
The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented.
Open Access
Scheduling beams with different priorities on a military surveillance radar
(Institute of Electrical and Electronics Engineers, 2012) Taner, M. R.; Karasan O. E.; Yavuzturk, E.
The problem of scheduling the searching, verification, and tracking tasks of a ground based, three-dimensional military surveillance radar is studied. Although the radar is mechanically steered in the sense that a servomechanism rotates the antenna at a constant turn rate, it has limited electronic steering capability in azimuth. The scheduling problem arises within a planning period during which the antenna scans a given physical range. A task/job corresponds to sending a transmission beam to hit a particular target. Targets are allowed to be hit with an angular deviation up to a predetermined magnitude. The steering mechanism of the radar helps alter these deviations by imposing a scan-off angle from broadside on the transmission beam. A list of jobs along with their priority weights, processing times, and ideal beam positions are given during a predetermined planning period. The ideal beam position for a given job allows hitting the corresponding target with zero deviation. Each job also has a set of available scan-off angles. It is possible to map the antennas physical position, beam positions, scan-off angles, and angular deviations to a time scale. The goal is to select the subset of jobs to be processed during the given planning period and determining the starting time and scan-off angle for each selected job. The objectives are to simultaneously minimize the weighted number of unprocessed jobs and the total weighted deviation. An integer programming model and two versions of a heuristic mechanism that relies on the exact solution of a special case are proposed. Results of a computational study are presented.
Open Access
Solving school bus routing problems through integer programming
(Palgrave Macmillan Ltd., 2007) Bektaş, T.; Elmastaş, S.
In this paper, an exact solution approach is described for solving a real-life school bus routing problem (SBRP) for transporting the students of an elementary school throughout central Ankara, Turkey. The problem is modelled as a capacitated and distance constrained open vehicle routing problem and an associated integer linear program is presented. The integer program borrows some well-known inequalities from the vehicle routing problem, which are also shown to be valid for the SBRP under consideration. The optimal solution of the problem is computed using the proposed formulation, resulting in a saving of up to 28.6 in total travelling cost as compared to the current implementation. © 2007 Operational Research Society Ltd. All rights reserved.