9,516 research outputs found
Mathematical modelling and experimental validation of electrostatic sensors for rotational speed measurement
Recent research has demonstrated that electrostatic sensors can be applied to the measurement of rotational speed with excellent repeatability and accuracy under a range of conditions. However, the sensing mechanism and fundamental characteristics of the electrostatic sensors are still largely unknown and hence the design of the sensors is not optimised for rotational speed measurement. This paper presents the mathematical modelling of strip electrostatic sensors for rotational speed measurement and associated experimental studies for the validation of the modelling results. In the modelling, an ideal point charge on the surface of the rotating object is regarded as an impulse input to the sensing system. The fundamental characteristics of the sensor, including spatial sensitivity, spatial filtering length and signal bandwidth, are quantified from the developed model. The effects of the geometric dimensions of the electrode, the distance between the electrode and the rotor surface and the rotational speed being measured on the performance of the sensor are analyzed. A close agreement between the modelling results and experimental measurements has been observed under a range of conditions. Optimal design of the electrostatic sensor for a given rotor size is suggested and discussed in accordance with the modelling and experimental results
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Spin Polarisability of the Nucleon in the Heavy Baryon Effective Field Theory
We have constructed a heavy baryon effective field theory with photon as an
external field in accordance with the symmetry requirements similar to the
heavy quark effective field theory. By treating the heavy baryon and
anti-baryon equally on the same footing in the effective field theory, we have
calculated the spin polarisabilities of the nucleon at
third order and at fourth-order of the spin-dependent Compton scattering. At
leading order (LO), our results agree with the corresponding results of the
heavy baryon chiral perturbation theory, at the next-to-leading order(NLO) the
results show a large correction to the ones in the heavy baryon chiral
perturbation theory due to baryon-antibaryon coupling terms. The low energy
theorem is satisfied both at LO and at NLO. The contributions arising from the
heavy baryon-antibaryon vertex were found to be significant and the results of
the polarisabilities obtained from our theory is much closer to the
experimental data.Comment: 21pages, title changed, minimal correction
Neutrino oscillations in de Sitter space-time
We try to understand flavor oscillations and to develop the formulae for
describing neutrino oscillations in de Sitter space-time. First, the covariant
Dirac equation is investigated under the conformally flat coordinates of de
Sitter geometry. Then, we obtain the exact solutions of the Dirac equation and
indicate the explicit form of the phase of wave function. Next, the concise
formulae for calculating the neutrino oscillation probabilities in de Sitter
space-time are given. Finally, The difference between our formulae and the
standard result in Minkowski space-time is pointed out.Comment: 13 pages, no figure
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