U-duality in three and four dimensions

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references added; v3: further discussion added on the conformal factor of the generalised metric in section 2 and on the Wick-rotation used to construct examples in section

On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

The Pain of Performative Professionalism: Emotionally Embodying Business as Usual

This essay is the personal and professional perspective of the National Communication Association Organizational Communication Division's awards chair during the 2019 convention. It explores issues of emotion, work, professionalism, silence, embodiment, symbolic violence, and intersectional precarity from the vantage point of an outsider within the academy and the discipline of communication studies

Asymmetric supernova remnants generated by Galactic, massive runaway stars

After the death of a runaway massive star, its supernova shock wave interacts with the bow shocks produced by its defunct progenitor, and may lose energy, momentum, and its spherical symmetry before expanding into the local interstellar medium (ISM). We investigate whether the initial mass and space velocity of these progenitors can be associated with asymmetric supernova remnants. We run hydrodynamical models of supernovae exploding in the pre-shaped medium of moving Galactic core-collapse progenitors. We find that bow shocks that accumulate more than about 1.5 Mo generate asymmetric remnants. The shock wave first collides with these bow shocks 160-750 yr after the supernova, and the collision lasts until 830-4900 yr. The shock wave is then located 1.35-5 pc from the center of the explosion, and it expands freely into the ISM, whereas in the opposite direction it is channelled into the region of undisturbed wind material. This applies to an initially 20 Mo progenitor moving with velocity 20 km/s and to our initially 40 Mo progenitor. These remnants generate mixing of ISM gas, stellar wind and supernova ejecta that is particularly important upstream from the center of the explosion. Their lightcurves are dominated by emission from optically-thin cooling and by X-ray emission of the shocked ISM gas. We find that these remnants are likely to be observed in the [OIII] lambda 5007 spectral line emission or in the soft energy-band of X-rays. Finally, we discuss our results in the context of observed Galactic supernova remnants such as 3C391 and the Cygnus Loop.Comment: 21 pages, 16 figure

What measurable zero point fluctuations can(not) tell us about dark energy

We show that laboratory experiments cannot measure the absolute value of dark energy. All known experiments rely on electromagnetic interactions. They are thus insensitive to particles and fields that interact only weakly with ordinary matter. In addition, Josephson junction experiments only measure differences in vacuum energy similar to Casimir force measurements. Gravity, however, couples to the absolute value. Finally we note that Casimir force measurements have tested zero point fluctuations up to energies of ~10 eV, well above the dark energy scale of ~0.01 eV. Hence, the proposed cut-off in the fluctuation spectrum is ruled out experimentally.Comment: 4 page

On the stability of bow shocks generated by red supergiants: the case of IRC-10414

In this Letter, we explore the hypothesis that the smooth appearance of bow shocks around some red supergiants (RSGs) might be caused by the ionization of their winds by external sources of radiation. Our numerical simulations of the bow shock generated by IRC-10414 (the first-ever RSG with an optically detected bow shock) show that the ionization of the wind results in its acceleration by a factor of two, which reduces the difference between the wind and space velocities of the star and makes the contact discontinuity of the bow shock stable for a range of stellar space velocities and mass-loss rates. Our best fit model reproduces the overall shape and surface brightness of the observed bow shock and suggests that the space velocity and mass-loss rate of IRC-10414 are $\approx$50 ${\rm km} \, {\rm s}^{-1}$ and $\approx$$10^{-6}$ $M_\odot \, {\rm yr}^{-1}$, respectively, and that the number density of the local ISM is $\approx$3 ${\rm cm}^{-3}$. It also shows that the bow shock emission comes mainly from the shocked stellar wind. This naturally explains the enhanced nitrogen abundance in the line-emitting material, derived from the spectroscopy of the bow shock. We found that photoionized bow shocks are $\approx$15$-$50 times brighter in optical line emission than their neutral counterparts, from which we conclude that the bow shock of IRC-10414 must be photoionized.Comment: 5 pages, 5 figures. Accepted for publication in MNRAS Letter

Deterministic Brownian motion generated from differential delay equations

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.Comment: 15 pages, 13 figure

Smart Parking System Based on Bluetooth Low Energy Beacons with Particle Filtering

Urban centers and dense populations are expanding, hence, there is a growing demand for novel applications to aid in planning and optimization. In this work, a smart parking system that operates both indoor and outdoor is introduced. The system is based on Bluetooth Low Energy (BLE) beacons and uses particle filtering to improve its accuracy. Through simple BLE connectivity with smartphones, an intuitive parking system is designed and deployed. The proposed system pairs each spot with a unique BLE beacon, providing users with guidance to free parking spaces and a secure and automated payment scheme based on real-time usage of the parking space. Three sets of experiments were conducted to examine different aspects of the system. A particle filter is implemented in order to increase the system performance and improve the credence of the results. Through extensive experimentation in both indoor and outdoor parking spaces, the system was able to correctly predict which spot the user has parked in, as well as estimate the distance of the user from the beacon