71,770 research outputs found
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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MHD-RLC discharge model and the efficiency characteristics of plasma synthetic jet actuator
Major factors affecting efficiency of plasma synthetic jet actuator (PSJA) are analyzed based on a new discharge model in the present paper. The model couples the magnetohydrodynamics (MHD) equations with the resistor–inductor–capacitor (RLC) equations, and is able to resolve the time-dependent voltage fall on the sheath region and arc region, which is critical in analyzing energy loss in the heating process. This model is integrated into the commercial CFD software by a two-equation method. Results show that in a typical capacitive discharge at microsecond scale, the maximum energy loss is the sheath energy loss, which accounts for nearly half of the discharge energy, while the radiation loss is less than 5%. The discharge time is an important parameter for the PSJA efficiency. A short discharge time less than 1 μs will effectively reduce the sheath energy loss, while a longer discharge time will decrease the thermodynamic efficiency
On the nature of the lightest scalar resonances
We briefly review the recent progresses in the new unitarization approach
being developed by us. Especially we discuss the large
scatterings by making use of the partial wave matrix parametrization form.
We find that the pole may move to the negative real axis on the second
sheet of the complex plane, therefore it raises the interesting question
that this `' pole may be related to the in the linear
model.Comment: Talk presented by Zheng at ``Quark Confinement and Hadron
Spectroscopy VI'', 21--25 Sept. 2004, Cagliari, Italy. 3 pages with 2 figure
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Modeling and optimization of the multichannel spark discharge
This paper reports a novel analytic model of this multichannel spark discharge, considering the delay time in the breakdown process, the electric transforming of the discharge channel from a capacitor to a resistor induced by the air breakdown, and the varying plasma resistance in the discharge process. The good agreement between the experimental and the simulated results validated the accuracy of this model. Based on this model, the influence of the circuit parameters on the maximum discharge channel number (MDCN) is investigated. Both the input voltage amplitude and the breakdown voltage threshold of each discharge channel play a critical role. With the increase of the input voltage and the decrease of the breakdown voltage, the MCDN increases almost linearly. With the increase of the discharge capacitance, the MDCN first rises and then remains almost constant. With the increase of the circuit inductance, the MDCN increases slowly but decreases quickly when the inductance increases over a certain value. There is an optimal value of the capacitor connected to the discharge channel corresponding to the MDCN. Finally, based on these results, to shorten the discharge time, a modified multichannel discharge circuit is developed and validated by the experiment. With only 6-kV input voltage, 31-channels discharge is achieved. The breakdown voltage of each electrode gap is larger than 3 kV. The modified discharge circuit is certain to be widely used in the PSJA flow control field
The origins of electromechanical indentation size effect in ferroelectrics
Metals exhibit a size-dependent hardening when subject to indentation.
Mechanisms for this phenomenon have been intensely researched in recent times.
Does such a size-effect also exist in the electromechanical behavior of
ferroelectrics?--if yes, what are the operative mechanisms? Our experiments on
BaTiO3 indeed suggest an electromechanical size-effect. We argue, through
theoretical calculations and differential experiments on another
non-ferroelectric piezoelectric (Quartz), that the phenomenon of
flexoelectricity(as opposed to dislocation activity) is responsible for our
observations. Flexoelectricity is the coupling of strain gradients to
polarization and exists in both ordinary and piezoelectric dielectrics. In
particular, ferroelectrics exhibit an unusually large flexoelectric response.Comment: in revie
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