Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

Isotopic Composition of Solar Wind Calcium: First in Situ Measurement by CELIAS/MTOF on Board SOHO

We present first results on the Ca isotopic abundances derived from the high resolution Mass Time-of-Flight (MTOF) spectrometer of the charge, element, and isotope analysis system (CELIAS) experiment on board the Solar and Heliospheric Observatory (SOHO). We obtain isotopic ratios 40Ca/42Ca = (128+-47) and 40Ca/44Ca = (50+-8), consistent with terrestrial values. This is the first in situ determination of the solar wind calcium isotopic composition and is important for studies of stellar modeling and solar system formation since the present-day solar Ca isotopic abundances are unchanged from their original isotopic composition in the solar nebula.Comment: 14 pages, 3 figure

Dust in the Local Interstellar Wind

The gas-to-dust mass ratios found for interstellar dust within the Solar System, versus values determined astronomically for the cloud around the Solar System, suggest that large and small interstellar grains have separate histories, and that large interstellar grains preferentially detected by spacecraft are not formed exclusively by mass exchange with nearby interstellar gas. Observations by the Ulysses and Galileo satellites of the mass spectrum and flux rate of interstellar dust within the heliosphere are combined with information about the density, composition, and relative flow speed and direction of interstellar gas in the cloud surrounding the solar system to derive an in situ value for the gas-to-dust mass ratio, $R_{g/d} = 94^{+46}_{-38}$. Hubble observations of the cloud surrounding the solar system yield a gas-to-dust mass ratio of Rg/d=551+61-251 when B-star reference abundances are assumed. The exclusion of small dust grains from the heliosheath and heliosphere regions are modeled, increasing the discrepancy between interstellar and in situ observations. The shock destruction of interstellar grains is considered, and comparisons are made with interplanetary and presolar dust grains.Comment: 87 pages, 9 figures, 6 tables, accepted for publication in Astrophysical Journal. Uses AASTe

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

Interception of comet Hyakutake's ion tail at a distance of 500 million kilometres

Remote sensing observations(1-5) and the direct sampling of material(6-8) from a few comets have established the characteristic composition of cometary gas. This gas is ionized by solar ultraviolet radiation and the solar wind to form 'pick-up' ions(9-11), ions in a low ionization state that retain the same compositional signatures as the original gas. The pick-up ions are carried outward by the solar wind, and they could in principle be detected far from the coma. (Sampling of pick-up ions has also been used to study interplanetary dust(12,13), Venus' tail(14) and the interstellar medium(15,16).) Here we report the serendipitous detection of cometary pick-up ions, most probably associated with the tail of comet Hyakutake, at a distance of 3.4 AU from the nucleus. Previous observations have provided a wealth of physical and chemical information about a small sample of comets(6-9), but this detection suggests that remote sampling of comet compositions, and the discovery of otherwise invisible comets, may be possible.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62756/1/404576a0.pd

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

Stellar Pollution in the Solar Neighborhood

We study spectroscopically determined iron abundances of 642 solar-type stars to search for the signature of accreted iron-rich material. We find that the metallicity [Fe/H] of a subset of 466 main sequence stars, when plotted as a function of stellar mass, mimics the pattern seen in lithium abundances in open clusters. Using Monte Carlo models we find that, on average, these stars have accreted about 0.4 Earth masses of iron while on the main sequence. A much smaller sample of 19 stars in the Hertzsprung gap, which are slightly evolved and whose convection zones are significantly more massive, have lower average [Fe/H], and their metallicity shows no clear variation with stellar mass. These findings suggest that terrestrial-type material is common around solar type stars.Comment: 33 pages, 11 figures. Submitted to Ap

On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori $L^{\infty}$-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.Comment: 28 pages. Added DOI https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final publication, corrected typo (missing gamma) in example 4.1

Intermittent release of transients in the slow solar wind: 2. In situ evidence

In paper 1, we showed that the Heliospheric Imager (HI) instruments on the pair of NASA STEREO spacecraft can be used to image the streamer belt and, in particular, the variability of the slow solar wind which originates near helmet streamers. The observation of intense intermittent transient outflow by HI implies that the corresponding in situ observations of the slow solar wind and corotating interaction regions (CIRs) should contain many signatures of transients. In the present paper, we compare the HI observations with in situ measurements from the STEREO and ACE spacecraft. Analysis of the solar wind ion, magnetic field, and suprathermal electron flux measurements from the STEREO spacecraft reveals the presence of both closed and partially disconnected interplanetary magnetic field lines permeating the slow solar wind. We predict that one of the transients embedded within the second CIR (CIR‐D in paper 1) should impact the near‐Earth ACE spacecraft. ACE measurements confirm the presence of a transient at the time of CIR passage; the transient signature includes helical magnetic fields and bidirectional suprathermal electrons. On the same day, a strahl electron dropout is observed at STEREO‐B, correlated with the passage of a high plasma beta structure. Unlike ACE, STEREO‐B observes the transient a few hours ahead of the CIR. STEREO‐A, STEREO‐B, and ACE spacecraft observe very different slow solar wind properties ahead of and during the CIR analyzed in this paper, which we associate with the intermittent release of transients

Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of sources of uncertainties in the standard solar model, which must be understood before the helioseismic observations can be used as constraints on theory. We find that the largest uncertainty in the sound speed in the solar interior, namely, 3 parts in 1000, arises from uncertainties in the observed photospheric abundances of the elements; uncertainties of 1 part in 1000 arise from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion constants for the gravitational settling of helium, and (4) the 50% uncertainties in diffusion constants for the heavier elements. (Other investigators have shown that similar uncertainties arise from uncertainties in the interior equation of state and in rotation-induced turbulent mixing.) The predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an order of magnitude larger than that predicted by earlier models that neglected gravitational settling and used older opacities), and is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37 experiment and by 3% for the Ga-71 experiments (not including uncertainties in the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.Comment: LaTeX, 38 pages (including 8 figures); ApJ, in press. Added figures/color figurea available at http://www.cita.utoronto.ca/~boothroy/sun4.htm