Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 11Citation - Scopus: 10A Stabilizing Subgrid for Convection-Diffusion Problem(World Scientific Publishing Co. Pte Ltd, 2006) Neslitürk, Ali İhsanA stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection-diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.Conference Object New Casimir Energy Calculations(World Scientific Publishing Co. Pte Ltd, 2007) Ahmedov, Hadji; Duru, İsmail HakkıNew Casimir energy results for massless scalar field in some 3 -dimensional cavities are presented. We attempted to discuss the correlation between the sign and the magnitude of the energy and the shape of the cavities. Sign of the Casimir energy known to be dependent on the dimension, topology and the shape of the geometry. In this note we present some new exact results for massless scalar fields in three dimensional cavities with the trivial topology. We then compare the known Casimir energy values for several three dimensional cavities. The conclusion we arrived is that the existence of the corners lowers the vacuum energy.Article Citation - WoS: 91Citation - Scopus: 91Resonance Solitons as Black Holes in Madelung Fluid(World Scientific Publishing Co. Pte Ltd, 2002) Pashaev, Oktay; Lee, Jyh HaoEnvelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For s < 1, the model is equivalent to the usual NLS with rescaled coupling constant, while for s > 1, to the reaction-diffusion system. The last one is related to the anti-de Sitter (AdS) space valued Heisenberg model, realizing a particular gauge fixing condition of the (1 + 1)-dimensional Jackiw-Teitelboim gravity. For this gravity model, by the Madelung fluid representation we derive the acoustic form of the space-time metric. The space-time points, where dispersion changes the sign, correspond to the event horizon, while the soliton solution to the AdS black hole. Moving with the above bounded velocity, it describes evolution on the one sheet hyperboloid with nontrivial winding number, and creates under collision, the resonance states which we study by the Hirota bilinear method.