Browsing by Subject "Dynamical equation"

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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
Multi input dynamical modeling of heat flow with uncertain diffusivity parameter
(Taylor & Francis, 2003) Efe, M. Ö.; Özbay, Hitay
This paper focuses on the multi-input dynamical modeling of one-dimensional heat conduction process with uncertainty on thermal diffusivity parameter. Singular value decomposition is used to extract the most significant modes. The results of the spatiotemporal decomposition have been used in cooperation with Galerkin projection to obtain the set of ordinary differential equations, the solution of which synthesizes the temporal variables. The spatial properties have been generalized through a series of test cases and a low order model has been obtained. Since the value of the thermal diffusivity parameter is not known perfectly, the obtained model contains uncertainty. The paper describes how the uncertainty is modeled and how the boundary conditions are separated from the remaining terms of the dynamical equations. The results have been compared with those obtained through analytic solution. © Taylor and Francis Ltd.