L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields

The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to high order at the center point of their functional equation. The main application is that for every prime p and every integer g>0 there are absolutely simple abelian varieties of dimension g over Fp(t) for which the BSD conjecture holds and which have arbitrarily large rank.Comment: To appear in Inventiones Mathematica

STAR FORMATION ACTIVITY IN A YOUNG GALAXY CLUSTER AT Z=0.866

The galaxy cluster RX J1257+4738 at z = 0.866 is one of the highest redshift clusters with a richness of multi-wavelength data, and is thus a good target to study the star formation-density relation at early epochs. Using a sample of spectroscopically confirmed cluster members, we derive the star-formation rates (SFRs) of our galaxies using two methods: (1) the relation between SFR and total infrared luminosity extrapolated from the observed Spitzer Multiband Imaging Photometer for Spitzer 24 μm imaging data; and (2) spectral energy distribution fitting using the MAGPHYS code, including eight different bands. We show that, for this cluster, the SFR-density relation is very weak and seems to be dominated by the two central galaxies and the SFR presents a mild dependence on stellar mass, with more massive galaxies having higher SFR. However, the specific SFR (SSFR) decreases with stellar mass, meaning that more massive galaxies are forming fewer stars per unit of mass, and thus suggesting that the increase in star-forming members is driven by cluster assembly and infall. If the environment is somehow driving the star formation, one would expect a relation between the SSFR and the cluster centric distance, but that is not the case. A possible scenario to explain this lack of correlation is the contamination by infalling galaxies in the inner part of the cluster, which may be on their initial pass through the cluster center. As these galaxies have higher SFRs for their stellar mass, they enhance the mean SSFR in the center of the cluste

Controls on lithium concentration and diffusion in zircon

This study was supported by ETH Research Grants ETH-34 15-2 (JS), ETH-14 16-1 (FM) and by Swiss National Science Foundation research grant 200020-153112/1 (NK).Thermal annealing of zircons prior to uranium-lead dating by laser ablation inductively coupled plasma mass spectrometry is a commonly-implemented procedure which improves data accuracy and precision by partially repairing radiation damage from the decay of uranium and thorium. However, it also leads to significantly higher concentrations of lithium in the zircon lattice, which become positively correlated with trivalent yttrium and rare earth elements. Prior to such treatments, zircons typically contain lithium below detection limits (typically <0.55 μg g−1), unless correlated with lanthanum and aluminum (i.e., melt/mineral inclusion tracer elements). This suggests that lithium in zircon is primarily sequestered within inclusions, and is able to permeate the crystal lattice to couple with yttrium and rare earth elements during the thermal annealing procedure. This process occurs 2–3 orders of magnitude faster than diffusion experiments have previously determined, indicating that another diffusion mechanism may apply. A model is proposed, whereby: (i) charge compensation of stoichiometrically over-abundant trivalent cations under water-rich magmatic conditions is likely accomplished by hydrogen, given the incompatibility of lithium in zircon and the abundance of hydrogen. However, (ii) conditions that are high temperature and low pressure (characteristic of both thermal annealing and the syn-eruptive environment), drive silicate melt inclusions to exsolve water, generating a motive force for both hydrogen and lithium from inclusions to permeate the lattice in order to reestablish electrochemical equilibrium between the interior and exterior of the zircon. To test the pressure dependency of lithium migration in the zircon lattice, thermal annealing experiments were performed at 850 °C and 1 bar, 2 kbar and 6 kbar using zircons from the Fish Canyon Tuff. The experiments demonstrate that thermal annealing at 2 and 6 kbar inhibits lithium mobility, with zircons registering lithium concentrations below detection limits similar to controls. The experimental results suggest that lithium concentrations in zircon are vulnerable to rapid perturbation by decompression (concurrent with high temperatures), which further indicate that lithium-in-zircon diffusion data should be interpreted with caution.Publisher PDFPeer reviewe

Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

The well-known Bragg-Kleeman rule RCSDA = A dot E0p has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range RCSDA of approximately monoenergetic protons with initial energy E0 in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z (0 <= z <= RCSDA). A relativistic extension of the generalized Langevin equation yields the formula RCSDA = A dot (E0 +E02/2M dot c2)p. The initial energy of therapeutic protons satisfies E0 << 2M dot c2 (M dot c2 = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of RCSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations.Comment: 97 pages review pape

Spectroscopic Observations of Optically Selected Clusters of Galaxies from the Palomar Distant Cluster Survey

We have conducted a redshift survey of sixteen cluster candidates from the Palomar Distant Cluster Survey (PDCS) to determine both the density of PDCS clusters and the accuracy of the estimated redshifts presented in the PDCS catalog (Postman et. al. 1996). We find that the matched-filter redshift estimate presented in the PDCS has an error sigma_z = 0.06 in the redshift range 0.1 < z < 0.35 based on eight cluster candidates with three or more concordant galaxy redshifts. We measure the low redshift (0.1 < z < 0.35) space density of PDCS clusters to be 31.3^{+30.5}_{-17.1} * E-06 h^3 Mpc^-3 (68% confidence limits for a Poisson distribution) for Richness Class 1 systems. We find a tentative space density of 10.4^{+23.4}_{-8.4}* E-06 h^3 Mpc^-3 for Richness Class 2 clusters. These densities compare favorably with those found for the whole of the PDCS and support the finding that the space density of clusters in the PDCS is a factor of ~5 above that of clusters in the Abell catalog (Abell 1958; Abell, Corwin, and Olowin 1989). These new space density measurements were derived as independently as possible from the original PDCS analysis and therefore, demonstrate the robustness of the original work. Based on our survey, we conclude that the PDCS matched-filter algorithm is successful in detecting real clusters and in estimating their true redshifts in the redshift range we surveyed.Comment: 23 pages with 4 figures and 3 seperate tables. To be published in the November Issue of the Astronomical Journa

The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Rendering an Account: An Open-State Archive in Postgraduate Supervision

The paper begins with a brief account of the transformation of research degree studies under the pressures of global capitalism and neo-liberal governmentality. A parallel transformation is occurring in the conduct of research through the use of information and communication technologies. Yet the potential of ICTs to shape practices of surveillance or to produce new student-supervisor relations and enhance the processes of developing the dissertation has received almost no critical attention. As doctoral supervisor and student, we then describe the features and uses of a web-based open state archive of the student's work-in-progress, developed by the student and accessible to his supervisor. Our intention was to encourage more open conversations between data and theorising, student and supervisor, and ultimately between the student and professional community. However, we recognise that relations of accountability, as these have developed within a contemporary "audit revolution" (Power, 1994, 1997) in universities, create particular "lines of visibility" (Munro, 1996). Thus while the open-state archive may help to redefine in less managerial terms notions of quality, transparency, flexibility and accountability, it might also make possible greater supervisory surveillance. How should we think about the panoptical potential of this archive? We argue that the diverse kinds of interactional patterns and pedagogical intervention it encourages help to create shifting subjectivities. Moreover, the archive itself is multiple, in bringing together an array of diverse materials that can be read in various ways, by following multiple paths. It therefore constitutes a collage, which we identify as a mode of cognition and of accounting distinct from but related to argument and narrative. As a more "open" text (Iser, 1978) it has an indeterminacy which may render it less open to abuse for the technologies of managerial accountability

Tidal Disruption of a Star By a Black Hole : Observational Signature

We have modeled the time-variable profiles of the Halpha emission line from the non-axisymmetric disk and debris tail created in the tidal disruption of a solar-type star by a million solar mass black hole. Two tidal disruption event simulations were carried out using a three dimensional relativistic smooth-particle hydrodynamic code, to describe the early evolution of the debris during the first fifty to ninety days. We have calculated the physical conditions and radiative processes in the debris using the photoionization code CLOUDY. We model the emission line profiles in the period immediately after the accretion rate onto the black hole became significant. We find that the line profiles at these very early stages of the evolution of the post-disruption debris do not resemble the double peaked profiles expected from a rotating disk since the debris has not yet settled into such a stable structure. As a result of the uneven distribution of the debris and the existence of a ``tidal tail'' (the stream of returning debris), the line profiles depend sensitively on the orientation of the tail relative to the line of sight. Moreover, the predicted line profiles vary on fairly short time scales (of order hours to days). Given the accretion rate onto the black hole we also model the Halpha light curve from the debris and the evolution of the Halpha line profiles in time.Comment: 20 pages, 9 figures, to appear in ApJ, 1 August 2004 issue; mpeg simulations of tidal disruption available at http://www.astro.psu.edu/users/tamarab/tdmovies.htm