9,619 research outputs found
Stability of -orbital Bose-Einstein condensates in optical checkerboard and square lattices
We investigate -orbital Bose-Einstein condensates in both the square and
checkerboard lattice by numerically solving the Gross-Pitaevskii equation. The
periodic potential for the latter lattice is taken exactly from the recent
experiment [Nature Phys. 7, 147 (2011)]. It is confirmed that the staggered
orbital-current state is the lowest-energy state in the band. Our numerical
calculation further reveals that for both lattices the staggered -orbital
state suffers Landau instability but the situation is remarkably different for
dynamical instability. A dynamically stable parameter region is found for the
checkerboard lattice, but not for the square.Comment: 7 pages, 7 figure
A three-dimensional multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields
This paper extends the gas-kinetic scheme for one-dimensional inviscid
shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to
multidimensional gas dynamic equations under gravitational fields. Four
important issues in the construction of a well-balanced scheme for gas dynamic
equations are addressed. First, the inclusion of the gravitational source term
into the flux function is necessary. Second, to achieve second-order accuracy
of a well-balanced scheme, the Chapman-Enskog expansion of the Boltzmann
equation with the inclusion of the external force term is used. Third, to avoid
artificial heating in an isolated system under a gravitational field, the
source term treatment inside each cell has to be evaluated consistently with
the flux evaluation at the cell interface. Fourth, the multidimensional
approach with the inclusion of tangential gradients in two-dimensional and
three-dimensional cases becomes important in order to maintain the accuracy of
the scheme. Many numerical examples are used to validate the above issues,
which include the comparison between the solutions from the current scheme and
the Strang splitting method. The methodology developed in this paper can also
be applied to other systems, such as semi-conductor device simulations under
electric fields.Comment: The name of first author was misspelled as C.T.Tian in the published
paper. 35 pages,9 figure
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