Morse matchings on polytopes

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes

Development of Optical Fibre Humidity Sensors for Assessing the Quality of Housing Insulation Materials

A fibre optic-based relative humidity (RH) sensing system has been developed for assessing the qualities of housing insulation materials, based on a Polyimide (PI)-coated Fibre Bragg Grating (FBG) device. This forms the key moisture sensitive element, allowing a carefully-designed and packaged sensor system to be fabricated, evaluated and calibrated, creating the robustness and reusability needed. Following calibration, the system performance evaluated on a range of commercial housing insulation materials shows excellent performance in establishing the key moisture-transport parameters of the materials routinely used by structural engineers. Cross-sensitivity issues are addressed allowing the RH sensor system to operate over a wide range of RH level experienced normally in this application. A sensitivity of 1.1 pm/%RH, with low hysteresis from a ruggedized sensor, is observed

The acceleration and propagation of solar flare energetic particles

Observations and theories of particle acceleration in solar flares are reviewed. The most direct signatures of particle acceleration in flares are gamma rays, X-rays and radio emissions produced by the energetic particles in the solar atmosphere and energetic particles detected in interplanetary space and in the Earth's atmosphere. The implication of these observations are discussed. Stochastic and shock acceleration as well as acceleration in direct electric fields are considered. Interplanetary particle propagation is discussed and an overview of the highlights of both current and promising future research is presented

X-ray Over-Luminous Elliptical Galaxies: A New Class of Mass Concentrations in the Universe?

We detect four isolated, X-ray over-luminous (Lx>2e43 [h/0.5]**-2 erg/s) elliptical galaxies (OLEGs) in our 160 square degree ROSAT PSPC survey. The extent of their X-ray emission, total X-ray luminosity, total mass, and mass of the hot gas in these systems correspond to poor clusters, and the optical luminosity of the central galaxies (M_R<-22.5 + 5 lg h) is comparable to that of cluster cDs. However, there are no detectable fainter galaxy concentrations around the central elliptical. The mass-to-light ratio within the radius of detectable X-ray emission is in the range 250-450 Msun/Lsun, which is 2-3 times higher than typically found in clusters or groups. These objects can be the result of galaxy merging within a group. However, their high M/L values are difficult to explain in this scenario. OLEGs must have been undisturbed for a very long time, which makes them the ultimate examples of systmes in hydrostatic equilibrium. The number density of OLEGs is n=2.4(+3.1-1.2}x10**-7 (h/0.5)**-3 Mpc**-3 at the 90% confidence. They comprise 20% of all clusters and groups of comparable X-ray luminosity, and nearly all galaxies brighter than M_R=-22.5. The estimated contirubution of OLEGs to the total mass density in the Universe is close to that of T>7 keV clusters.Comment: 4 pages, 2 figures, uses emulateapj.sty, submitted to ApJ Letter

Dynamics of Triangulations

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law $d^{-4}$

Complex diffuse radio emission in the merging PLANCK ESZ cluster Abell 3411

We present VLA radio and Chandra X-ray observations of the merging galaxy cluster Abell 3411. For the cluster, we find an overall temperature of 6.4 keV and an X-ray luminosity of 2.8 x 10^{44} erg s^{-1} between 0.5 and 2.0 keV. The Chandra observation reveals the cluster to be undergoing a merger event. The VLA observations show the presence of large-scale diffuse emission in the central region of the cluster, which we classify as a 0.9 Mpc size radio halo. In addition, a complex region of diffuse, polarized emission is found in the southeastern outskirts of the cluster, along the projected merger axis of the system. We classify this region of diffuse emission as a radio relic. The total extent of this radio relic is 1.9 Mpc. For the combined emission in the cluster region, we find a radio spectral index of -1.0 \pm 0.1 between 74 MHz and 1.4 GHz. The morphology of the radio relic is peculiar, as the relic is broken up into five fragments. This suggests that the shock responsible for the relic has been broken up due to interaction with a large-scale galaxy filament connected to the cluster or other substructures in the ICM. Alternatively, the complex morphology reflects the presence of electrons in fossil radio bubbles that are re-accelerated by a shock.Comment: Accepted for publication in ApJ, 8 pages, 5 figure

VLA Radio Observations of the HST Frontier Fields Cluster Abell 2744: The Discovery of New Radio Relics

Cluster mergers leave distinct signatures in the ICM in the form of shocks and diffuse cluster radio sources that provide evidence for the acceleration of relativistic particles. However, the physics of particle acceleration in the ICM is still not fully understood. Here we present new 1-4 GHz Jansky Very Large Array (VLA) and archival Chandra observations of the HST Frontier Fields Cluster Abell 2744. In our new VLA images, we detect the previously known $\sim2.1$ Mpc radio halo and $\sim1.5$ Mpc radio relic. We carry out a radio spectral analysis from which we determine the relic's injection spectral index to be $\alpha_{\rm{inj}} = -1.12 \pm 0.19$. This corresponds to a shock Mach number of $\mathcal{M}$ = 2.05$^{+0.31}_{-0.19}$ under the assumption of diffusive shock acceleration. We also find evidence for spectral steepening in the post-shock region. We do not find evidence for a significant correlation between the radio halo's spectral index and ICM temperature. In addition, we observe three new polarized diffuse sources and determine two of these to be newly discovered giant radio relics. These two relics are located in the southeastern and northwestern outskirts of the cluster. The corresponding integrated spectral indices measure $-1.81 \pm 0.26$ and $-0.63 \pm 0.21$ for the SE and NW relics, respectively. From an X-ray surface brightness profile we also detect a possible density jump of $R=1.39^{+0.34}_{-0.22}$ co-located with the newly discovered SE relic. This density jump would correspond to a shock front Mach number of $\mathcal{M}=1.26^{+0.25}_{-0.15}$.Comment: accepted for publication in Ap

Hot Gas Structure in the Elliptical Galaxy NGC 4472

We present X-ray spectroscopic and morphological analyses using Chandra ACIS and ROSAT observations of the giant elliptical galaxy NGC 4472 in the Virgo cluster. We discuss previously unobserved X-ray structures within the extended galactic corona. In the inner 2' of the galaxy, we find X-ray holes or cavities with radii of ~2 kpc, corresponding to the position of radio lobes. These holes were produced during a period of nuclear activity that began 1.2 x 10^7 years ago and may be ongoing. We also find an asymmetrical edge in the galaxy X-ray emission 3' (14 kpc) northeast of the core and an ~8' tail (36 kpc) extending southwest of the galaxy. These two features probably result from the interaction of NGC 4472 gas with the Virgo gas, which produces compression in the direction of NGC 4472's infall and an extended tail from ram pressure stripping. Assuming the tail is in pressure equilibrium with the surrounding gas, we compute its angle to our line of sight and estimate that its true extent exceeds 100 kpc. Finally, in addition to emission from the nucleus (first detected by Soldatenkov, Vikhlinin & Pavlinsky), we detect two small extended sources within 10'' of the nucleus of the galaxy, both of which have luminosities of ~7 x 10^38 erg/s.Comment: 25 pages, 11 figures, accepted by Ap

The Semiclassical Limit for SU(2)SU(2) and SO(3)SO(3) Gauge Theory on the Torus

We prove that for $SU(2)$ and $SO(3)$ quantum gauge theory on a torus, holonomy expectation values with respect to the Yang-Mills measure d\mu_T(\o) =N_T^{-1}e^{-S_{YM}(\o)/T}[{\cal D}\o] converge, as $T\downarrow 0$, to integrals with respect to a symplectic volume measure $\mu_0$ on the moduli space of flat connections on the bundle. These moduli spaces and the symplectic structures are described explicitly.Comment: 18 page