Reduction of gear pair transmission error with tooth profile modification

The gear noise problem that widely occurs in power transmission systems is typically characterised by one or more high amplitude acoustic signals. The noise originates from the vibration of the gear pair system caused by transmission error excitation that arises from tooth profile errors, misalignment and tooth deflections. This paper aims to further research the effect of tooth profile modifications on the transmission error of gear pairs. A spur gear pair was modelled using finite elements, and the gear mesh was simulated and analysed under static conditions. The results obtained were used to study the effect of intentional tooth profile modifications on the transmission error of the gear pair. A detailed parametric study, involving development of an optimisation algorithm to design the tooth modifications, was performed to quantify the changes in the transmission error as a function of tooth profile modification parameters as compared to an unmodified gear pair baseline

Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]

The Relativistic Levinson Theorem in Two Dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts $\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$: $$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\ (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~ j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right.$$ \noindent The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email: [email protected], [email protected]

Neutrino Mass from Triplet and Doublet Scalars at the TeV Scale

If the minimal standard model of particle interactions is extended to include a scalar triplet with lepton number $L=-2$ and a scalar doublet with $L=-1$, neutrino masses $m_\nu \sim \mu_{12}^4 v^2/M^5 \sim 10^{-2}$ eV is possible, where $v \sim 10^2$ GeV is the electroweak symmetry breaking scale, $M \sim 1$ TeV is the typical mass of the new scalars, and $\mu_{12} \sim 1$ GeV is a soft lepton-number-violating parameter.Comment: 6 pages, no figur

Assessing Ageing Condition of Mineral Oil-Paper Insulation by Polarization/Depolarization Current

Accurately assessing the ageing status of oil-paper insulation in transformer is essential and important. Polarization and Depolarization Current (PDC) technique is effective in assessing the condition of oil-paper insulation system. Though the PDC behaviour of mineral oil-paper insulation has been widely investigated, there is no report about how to make the quantitative analysis of mineral oil-paper insulation ageing condition by PDC. The PDC characteristics of mineral oil-paper insulation samples were investigated over the ageing period at 110°C. A new method for assessing the ageing condition of mineral oil-paper insulation by calculating the depolarization charge quantity was proposed. Results show that the depolarization charge quantity of mineral oil-paper insulation sample is very sensitive to its ageing condition. The stable depolarization charge quantity could be used to predict the ageing condition of mineral oil-paper insulation

Does abortion reduce self-esteem and life satisfaction?

PurposeThis study aims to assess the effects of obtaining an abortion versus being denied an abortion on self-esteem and life satisfaction.MethodsWe present the first 2.5 years of a 5-year longitudinal telephone-interview study that follows 956 women who sought an abortion from 30 facilities across the USA. We examine the self-esteem and life satisfaction trajectories of women who sought and received abortions just under the facility's gestational age limit, of women who sought and received abortions in their first trimester of pregnancy, and of women who sought abortions just beyond the facility gestational limit and were denied an abortion. We use adjusted mixed effects linear regression analyses to assess whether the trajectories of women who sought and obtained an abortion differ from those who were denied one.ResultsWomen denied an abortion initially reported lower self-esteem and life satisfaction than women who sought and obtained an abortion. For all study groups, except those who obtained first trimester abortions, self-esteem and life satisfaction improved over time. The initially lower levels of self-esteem and life satisfaction among women denied an abortion improved more rapidly reaching similar levels as those obtaining abortions at 6 months to one year after abortion seeking. For women obtaining first trimester abortions, initially higher levels of life satisfaction remained steady over time.ConclusionsThere is no evidence that abortion harms women's self-esteem or life satisfaction in the short term