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In this paper, we present two efficient and spectrally accurate numerical methods for computing the ground and first excited states in Bose–Einstein condensates (BECs). We begin with a review on the gradient flow with discrete normaliza-tion (GFDN) for computing stationary states of a nonconvex minimization problem and show how to choose initial data(More)
In this paper we review our recent work on mathematical analysis and efficient numerical computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation (GPE) with applications in Bose-Einstein condensation and nonlinear optics. We begin with the time-independent GPE and show how to reformulate it into a singularly(More)
In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose–Einstein condensates (BECs) by using the normalized gradient flow or imaginary time method. The key idea is to find a third projection or normalization condition based on the relation between the chemical potentials so that the three projection(More)
We present a two-dimensional computational model of amoeboid cell migration characterised by cell shape changes due to the formation and extension of protrusions known as blebs. Using this model, we numerically study the deformation of the cell membrane during blebbing, as well as the effects of obstacles, such as protein fibres in the extracellular matrix,(More)
We propose efficient and accurate numerical methods for computing the ground-state solution of spin-1 Bose-Einstein condensates subjected to a uniform magnetic field. The key idea in designing the numerical method is based on the normalized gradient flow with the introduction of a third normalization condition, together with two physical constraints on the(More)
Due to the high performance of electronic components, the heat generated is increasing dramatically and cooling system for such components becomes one of the most important issues to dissipate heat that generated in electronic component. In the present analysis, a microchannel heat sink configuration is simulated by modelling the stacked microchannel heat(More)
In this article, we propose efficient and accurate numerical methods for computing the ground state solution of spin-1 Bose-Einstein condensates subject to uniform magnetic field. The key idea in designing the numerical method is based on the normalized gradient flow with the introduction of the third normalization condition, together with the two physical(More)
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