109,691 research outputs found
Onset of unsteady horizontal convection in rectangle tank at
The horizontal convection within a rectangle tank is numerically simulated.
The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf
bifurcation of from steady solutions to periodic solutions, and the
critical Rayleigh number is obtained as for the
middle plume forcing at , which is much larger than the formerly obtained
value. Besides, the unstable perturbations are always generated from the
central jet, which implies that the onset of instability is due to velocity
shear (shear instability) other than thermally dynamics (thermal instability).
Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses
about the destabilization of the flow is numerically proved, i.e. the middle
plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in
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Effective Magnetic Fields in Graphene Superlattices
We demonstrate that the electronic spectrum of graphene in a one-dimensional
periodic potential will develop a Landau level spectrum when the potential
magnitude varies slowly in space. The effect is related to extra Dirac points
generated by the potential whose positions are sensitive to its magnitude. We
develop an effective theory that exploits a chiral symmetry in the Dirac
Hamiltonian description with a superlattice potential, to show that the low
energy theory contains an effective magnetic field. Numerical diagonalization
of the Dirac equation confirms the presence of Landau levels. Possible
consequences for transport are discussed.Comment: 4 pages (+ 2 pages of supplementary material), 3 figure
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
The angular momentum of a magnetically trapped atomic condensate
For an atomic condensate in an axially symmetric magnetic trap, the sum of
the axial components of the orbital angular momentum and the hyperfine spin is
conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field)
is not axially symmetric, the difference of the two becomes surprisingly
conserved. In this paper we investigate the relationship between the values of
the sum/difference angular momentums for an atomic condensate inside a magnetic
trap and the associated gauge potential induced by the adiabatic approximation.
Our result provides significant new insight into the vorticity of magnetically
trapped atomic quantum gases.Comment: 4 pages, 1 figure
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