Webs of Lagrangian Tori in Projective Symplectic Manifolds

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.Comment: 18 pages, minor latex problem fixe

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Huddle test measurement of a near Johnson noise limited geophone

In this paper, the sensor noise of two geophone configurations (L-22D and L-4C geophones from Sercel with custom built amplifiers) was measured by performing two huddle tests. It is shown that the accuracy of the results can be significantly improved by performing the huddle test in a seismically quiet environment and by using a large number of reference sensors to remove the seismic foreground signal from the data. Using these two techniques, the measured sensor noise of the two geophone configurations matched the calculated predictions remarkably well in the bandwidth of interest (0.01 Hz–100 Hz). Low noise operational amplifiers OPA188 were utilized to amplify the L-4C geophone to give a sensor that was characterized to be near Johnson noise limited in the bandwidth of interest with a noise value of 10−11 m/Hz⎯⎯⎯⎯⎯√10−11 m/Hz at 1 Hz

Flow-to-fracture transition in a volcanic mush plug may govern normal eruptions at Stromboli

Stromboli is a model volcano for studying eruptions driven by degassing. The current paradigm posits that Strombolian eruptions represent the bursting of gas slugs ascending through melt‐filled conduits, but petrological observations show that magma at shallow depth is crystalline enough to form a three‐phase plug consisting of crystals, bubbles, and melt. We combine a 1‐D model of gas flushing a crystalline mush with a 3‐D stress model. Our results suggest that localized gas segregation establishes hot conduits of mobile magma within a stagnant plug. The plug is prone to tensile failure controlled by gas overpressure and tectonic stress, with failure most likely beneath the observed vent locations. We hence argue that Strombolian eruptions are related to plug failure rather than flow. Our proposed three‐phase model of the shallow plumbing system may provide a promising framework for integrating geophysical, petrological, and morphological observations at Stromboli and in open‐system volcanism more generally

Steiner t-designs for large t

One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial t-designs exist for all values of t, no non-trivial Steiner t-design with t > 5 has been constructed until now. Understandingly, the case t = 6 has received considerable attention. There has been recent progress concerning the existence of highly symmetric Steiner 6-designs: It is shown in [M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial flag-transitive Steiner 6-design can exist. In this paper, we announce that essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008, ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in Computer Scienc

Hadean geodynamics inferred from time-varying 142Nd/144Nd in the early Earth rock record

Tracking the secular evolution of 142Nd/144Nd anomalies is important towards understanding the crust-mantle dynamics in the early Earth. Excessive scatter in the published data, however, precludes identifying the fine structure of 142Nd/144Nd evolution as the expected variability is on the order of few parts per million. We report ultra-high precision 142Nd/144Nd data for Eoarchean and Palaeoarchean rocks from the Isua Supracrustal Belt (SW Greenland) that show a well-resolved 142Nd/144Nd temporal variability suggesting progressive convective homogenisation of the Hadean Isua depleted mantle. This temporally decreasing 142Nd/144Nd signal provides a direct measure of early mantle dynamics, defining a stirring timescale of <250 Myr consistent with vigorous convective stirring in the early mantle. The 142Nd/144Nd evolution suggests protracted crustal residence times of ~1000-2000 Myr, inconsistent with modern-style plate tectonics in the Archean. In contrast, a stagnant-lid regime punctuated by episodes of mantle overturns accounts for the long life-time estimated here for the Hadean proto-crust