A weakly nonlinear analysis of the magnetorotational instability in a model channel flow

We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow in a thin channel gives rise to a real Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (${\cal P}_{\rm m}$), the saturation amplitude is $\propto \sqrt{{\cal P}_{\rm m}}$ and the resulting momentum transport scales as ${\cal R}^{-1}$, where $\cal R$ is the {\em hydrodynamic} Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with ${\cal P}_{\rm m} \ll 1$.Comment: Accepted to Physical Review Letters - Nov. 30, 2006. In final for

Revised research about chaotic dynamics in Manko et al. spacetime

A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.Comment: 6 pages, 5 figure

How much measurement independence is needed in order to demonstrate nonlocality?

If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We study the case where this assumption is weakened, so that measurement settings and local variables are at least partially correlated. As we show, there is a connection between this type of model and models which reproduce nonlocal correlations by allowing classical communication between the distant parties, and a connection with models that exploit the detection loophole. We show that even if Bob's choices are completely independent, all correlations obtained from projective measurements on a singlet can be reproduced, with the correlation (measured by mutual information) between Alice's choice and local variables less than or equal to a single bit.Comment: 5 pages, 1 figure. v2 Various improvements in presentation. Results unchange

Crash risk by driver age, gender, and time of day using a new exposure methodology

Introduction: Concerns have been raised that the nonlinear relation between crashes and travel exposure invalidates the conventional use of crash rates to control for exposure. A new metric of exposure that bears a linear association to crashes was used as basis for calculating unbiased crash risks. This study compared the two methods – conventional crash rates and new adjusted crash risk – for assessing the effect of driver age, gender, and time of day on the risk of crash involvement and crash fatality. Method: We used police reports of single-car and multi-car crashes with fatal and nonfatal driver injuries that occurred during 2002–2012 in Great Britain. Results: Conventional crash rates were highest in the youngest age group and declined steeply until age 60–69 years. The adjusted crash risk instead peaked at age 21–29 years and reduced gradually with age. The risk of nighttime driving, especially among teenage drivers, was much smaller when based on adjusted crash risks. Finally, the adjusted fatality risk incurred by elderly drivers remained constant across time of day, suggesting that their risk of sustaining a fatal injury due to a crash is more attributable to excess fragility than to crash seriousness. Conclusions: Our findings demonstrate a biasing effect of low travel exposure on conventional crash rates. This implies that conventional methods do not yield meaningful comparisons of crash risk between driver groups and driving conditions of varying exposure to risk. The excess crash rates typically associated with teenage and elderly drivers as well as nighttime driving are attributed in part to overestimation of risk at low travel exposure. Practical Applications: Greater attention should be directed toward crash involvement among drivers in their 20s and 30s as well as younger drivers. Countermeasures should focus on the role of physical vulnerability in fatality risk of elderly drivers

Effects of dissipation in an adiabatic quantum search algorithm

We consider the effect of two different environments on the performance of the quantum adiabatic search algorithm, a thermal bath at finite temperature, and a structured environment similar to the one encountered in systems coupled to the electromagnetic field that exists within a photonic crystal. While for all the parameter regimes explored here, the algorithm performance is worsened by the contact with a thermal environment, the picture appears to be different when considering a structured environment. In this case we show that, by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More particularly, we find that the imaginary part of the rates can not be neglected with the usual argument that it simply amounts to an energy shift, and in fact influences crucially the system dynamics.Comment: 18 pages, 9 figure

The Hall instability of thin weakly-ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.Comment: 13 pages, 7 figure

Tight hardness of the non-commutative Grothendieck problem

We prove that for any $\varepsilon > 0$ it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor $1/2 + \varepsilon$, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC'13). Our proof uses an embedding of $\ell_2$ into the space of matrices endowed with the trace norm with the property that the image of standard basis vectors is longer than that of unit vectors with no large coordinates