On Berenstein-Douglas-Seiberg Duality

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed.Comment: 22 pages, LaTe

Nanoparticulate nickel sulfides formed in low temperature aqueous solutions

The nature of the nickel sulfides formed in low temperature aqueous solutions is not well-understood. The material has some intrinsic interest to mineralogy, geochemistry and materials science as well as to biogeochemisty, especially as a possible catalyst involved in the origin and early evolution of life. We synthesized Ni sulfide under anoxic conditions at 25 C: (1) chemically, by the addition of 50 mL of 0.1 M NiSO4Æ7H2O to 100 mL of 0.05M Na2SÆ9H2O; (2) electrochemically, with a Ni foil and H2S gas. At pH 6 5, millerite (b-NiS) was produced electrochemically and NiS mixtures, including heazlewoodite (Ni3S2) and polydymite (Ni3S4), were obtained chemically. At pH >11, a- NiS was obtained from the chemical reaction. At pH 6–9, the product produced only two broad peaks (d = ca. 2.7 and 1.8 ) with conventional and synchrotron XRPD which could be assigned to a number of Ni sulfides. It has previously been referred to as ‘‘amorphous NiS’’ Jeong and Manthiram, 2001. Eight SAED reflections were collected which identified the material as godlevskite, orthorhombic NiS. HRTEM shows that the godlevskite particles are ca. 30 nm in diameter and plate-like. SAXS analyses show that the material is 6–8.5 nm thick. Godlevskite is structurally related to makinawite, tetragonal FeS, and is found naturally in similar parageneses-associated with the monosulfide solid solution products of high temperature nickel ores. Mackinawite is the black FeS precipitate from the reaction between Fe(II) and S(-II) in aqueous solution. It appears that, geochemically, godlevskite is the Ni analogue of mackinawite

Mechanisms of deformation-induced trace element migration in zircon resolved by atom probe and correlative microscopy

The widespread use of zircon in geochemical and geochronological studies of crustal rocks is underpinned by an understanding of the processes that may modify its composition. Deformation during tectonic and impact related strain is known to modify zircon trace element compositions, but the mechanisms by which this occurs remain unresolved. Here we combine electron backscatter diffraction, transmission Kikuchi diffraction and atom probe microscopy to investigate trace element migration associated with a ~20 nm wide, 2° low-angle subgrain boundary formed in zircon during a single, high-strain rate, deformation associated with a bolide impact. The low-angle boundary shows elevated concentrations of both substitutional (Y) and interstitial (Al, Mg and Be) ions. The observed compositional variations reflect a dynamic process associated with the recovery of shock-induced vacancies and dislocations into lower energy low-angle boundaries. Y segregation is linked to the migration and localisation of oxygen vacancies, whilst the interstitial ions migrate in association with dislocations. These data represent the direct nanoscale observation of geologically-instantaneous, trace element migration associated with crystal plasticity of zircon and provide a framework for further understanding mass transfer processes in zircon

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

Torsion pairs and simple-minded systems in triangulated categories

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if its closure under extensions is all of T. We construct torsion pairs in T associated to any subset X of a simple-minded system S, and use these to define left and right mutations of S relative to X. When T has a Serre functor \nu, and S and X are invariant under \nu[1], we show that these mutations are again simple-minded systems. We are particularly interested in the case where T is the stable module category of a self-injective algebra \Lambda. In this case, our mutation procedure parallels that introduced by Koenig and Yang for simple-minded collections in the derived category of \Lambda. It follows that the mutation of the set of simple \Lambda-modules relative to X yields the images of the simple \Gamma-modules under a stable equivalence between \Gamma\ and \Lambda, where \Gamma\ is the tilting mutation of \Lambda\ relative to X.Comment: Minor corrections. To appear in Applied Categorical Structures. The final publication is available at springerlink.com: http://link.springer.com/article/10.1007%2Fs10485-014-9365-

A self-consistent, multivariate method for the determination of gas-phase rate coefficients, applied to reactions of atmospheric VOCs and the hydroxyl radical

Gas-phase rate coefficients are fundamental to understanding atmospheric chemistry, yet experimental data are not available for the oxidation reactions of many of the thousands of volatile organic compounds (VOCs) observed in the troposphere. Here, a new experimental method is reported for the simultaneous study of reactions between multiple different VOCs and OH, the most important daytime atmospheric radical oxidant. This technique is based upon established relative rate concepts but has the advantage of a much higher throughput of target VOCs. By evaluating multiple VOCs in each experiment, and through measurement of the depletion in each VOC after reaction with OH, the OH + VOC reaction rate coefficients can be derived. Results from experiments conducted under controlled laboratory conditions were in good agreement with the available literature for the reaction of 19 VOCs, prepared in synthetic gas mixtures, with OH. This approach was used to determine a rate coefficient for the reaction of OH with 2,3-dimethylpent-1-ene for the first time; k =  5.7 (±0.3)  ×  10⁻¹¹ cm³ molecule⁻¹ s⁻¹. In addition, a further seven VOCs had only two, or fewer, individual OH rate coefficient measurements available in the literature. The results from this work were in good agreement with those measurements. A similar dataset, at an elevated temperature of 323 (±10) K, was used to determine new OH rate coefficients for 12 aromatic, 5 alkane, 5 alkene and 3 monoterpene VOC + OH reactions. In OH relative reactivity experiments that used ambient air at the University of York, a large number of different VOCs were observed, of which 23 were positively identified. Due to difficulties with detection limits and fully resolving peaks, only 19 OH rate coefficients were derived from these ambient air samples, including 10 reactions for which data were previously unavailable at the elevated reaction temperature of T =  323 (±10) K

The earliest O-type eclipsing binary in the Small Magellanic Cloud, AzV 476: A comprehensive analysis reveals surprisingly low stellar masses

CONTEXT: Massive stars at low metallicity are among the main feedback agents in the early Universe and in present-day star forming galaxies. When in binaries, these stars are potential progenitors of gravitational-wave events. Knowledge of stellar masses is a prerequisite to understanding evolution and feedback of low-metallicity massive stars. AIMS: Using abundant spectroscopic and photometric measurements of an outstandingly bright eclipsing binary, we compare its dynamic, spectroscopic, and evolutionary mass estimates and develop a binary evolution scenario. METHODS: We comprehensively studied the eclipsing binary system, AzV 476, in the Small Magellanic Cloud (SMC). The light curve and radial velocities were analyzed to obtain the orbital parameters. The photometric and spectroscopic data in the UV and optical were analyzed using the Potsdam Wolf-Rayet (PoWR) model atmospheres. The obtained results are interpreted using detailed binaryevolution tracks including mass transfer. RESULTS: AzV 476 consists of an O4 IV-III((f))p primary and an O9.5: Vn secondary. Both components have similar current masses (20 M_{\odot} and 18 M_{\odot}) obtained consistently from both the orbital and spectroscopic analysis. The effective temperatures are 42 kK and 32 kK, respectively. The wind mass-loss rate of log(M˙ /(M_{\odot}yr^{-1})) = −6.2 of the primary is a factor of ten higher than a recent empirical prescription for single O stars in the SMC. Only close-binary evolution with mass transfer can reproduce the current stellar and orbital parameters, including orbital separation, eccentricity, and the rapid rotation of the secondary. The binary evolutionary model reveals that the primary has lost about half of its initial mass and is already core helium burning. CONCLUSIONS: Our comprehensive analysis of AzV 476 yields a consistent set of parameters and suggests previous case B mass transfer. The derived stellar masses agree within their uncertainties. The moderate masses of AzV 476 underline the scarcity of bright massive stars in the SMC. The core helium burning nature of the primary indicates that stripped stars might be hidden among OB-type populations

Support varieties for selfinjective algebras

Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true