98,739 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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Fast entanglement of two charge-phase qubits through nonadiabatic coupling to a large junction
We propose a theoretical protocol for quantum logic gates between two
Josephson junction charge-phase qubits through the control of their coupling to
a large junction. In the low excitation limit of the large junction when
, it behaves effectively as a quantum data-bus mode of a
harmonic oscillator. Our protocol is efficient and fast. In addition, it does
not require the data-bus to stay adiabatically in its ground state, as such it
can be implemented over a wide parameter regime independent of the data-bus
quantum state.Comment: 5 pages, 1 figur
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
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