46 research outputs found
Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps
We calculated, within the Gross-Pitaevskii formalism, the critical number of
atoms for Bose-Einstein condensates with two-body attractive interactions in
cylindrical traps with different frequency ratios. In particular, by using the
trap geometries considered by the JILA group [Phys. Rev. Lett. 86, 4211
(2001)], we show that the theoretical maximum critical numbers are given
approximately by . Our results also show that, by
exchanging the frequencies and , the geometry with
favors the condensation of larger number of particles.
We also simulate the time evolution of the condensate when changing the ground
state from to using a 200ms ramp. A conjecture on higher order
nonlinear effects is also added in our analysis with an experimental proposal
to determine its signal and strength.Comment: (4 pages, 2 figures) To appear in Physical Review
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and convergence are presented. Comparisons are made between the
present schemes in terms of accuracy and computational efficiency for solving
problems with severe internal and boundary gradients. The present study shows
that the fourth-order compact ADI scheme is stable and efficient