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Transition of a vortex ring measured by 3D scanning Tomo-PIV
A vortex ring with piston-based Reynolds number Rep=4650 is studied experimentally by means of time-resolved scanning tomographic PIV. The present measurement technique provides the so-called 4D flow field, thus enables revealing the vortex ring’s transition from laminar to turbulent. The evolution of the ring torus as well as the generation of secondary vortex filaments in transition are first observed through 3D visualization. Analysis on the quantities of the vortex ring, such as circulation and vorticity components, defines the three evolution phases, namely laminar, transition and turbulent. The ring median plane is also examined to provide further insights on flow structure exhibited in transition. The axial vorticity component and radial velocity component are studied respectively and they are found to be organized in a multi-layer concentric-ring pattern. Spectrum analysis on the radial velocity component along the ring core and inner ring where secondary vortical activity happens reveals the dominate wavenumber in transition and broad band of wavenumbers in turbulent phase
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
Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits
We study the coherent control of microwave photons propagating in a
superconducting waveguide consisting of coupled transmission line resonators,
each of which is connected to a tunable charge qubit. While these coupled line
resonators form an artificial photonic crystal with an engineered photonic band
structure, the charge qubits collectively behave as spin waves in the low
excitation limit, which modify the band-gap structure to slow and stop the
microwave propagation. The conceptual exploration here suggests an
electromagnetically controlled quantum device based on the on-chip circuit QED
for the coherent manipulation of photons, such as the dynamic creation of
laser-like output from the waveguide by pumping the artificial atoms for
population inversion.Comment: 8 pages, 3 figure
Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei
We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its
renormalized theory to the structure calculations of finite nuclei. The
-matrix is calculated within the BHF basis, and the exact Pauli exclusion
operator is determined by the BHF spectrum. Self-consistent occupation
probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF).
Various systematics and convergences are studies. Good results are obtained for
the ground-state energy and radius. RBHF can give a more reasonable
single-particle spectrum and radius. We present a first benchmark calculation
with other {\it ab initio} methods using the same effective Hamiltonian. We
find that the BHF and RBHF results are in good agreement with other
methods
The Entanglement in Anisotropic Heisenberg XYZ Chain with inhomogeneous magnetic field
The thermal entanglement of a two-qubit anisotropic Heisenberg chain
under an inhomogeneous magnetic field b is studied. It is shown that when
inhomogeneity is increased to certain value, the entanglement can exhibit a
larger revival than that of less values of b. The property is both true for
zero temperature and a finite temperature. The results also show that the
entanglement and critical temperature can be increased by increasing
inhomogeneous exteral magnetic field
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