Conditions for Equality between Lyapunov and Morse Decompositions

Let $Q\rightarrow X$ be a continuous principal bundle whose group $G$ is reductive. A flow $\phi$ of automorphisms of $Q$ endowed with an ergodic probability measure on the compact base space $X$ induces two decompositions of the flag bundles associated to $Q$. A continuous one given by the finest Morse decomposition and a measurable one furnished by the Multiplicative Ergodic Theorem. The second is contained in the first. In this paper we find necessary and sufficient conditions so that they coincide. The equality between the two decompositions implies continuity of the Lyapunov spectra under pertubations leaving unchanged the flow on the base space

Petrography and petrology of the Hawaii Scientific Drilling Project lavas: Inferences from olivine phenocryst abundances and compositions

The Mauna Loa (ML) and Mauna Kea (MK) lavas recovered by the Hawaii Scientific Drilling Project (HSDP) include aphyric to highly olivine-phyric basalts. The average olivine phenocryst abundance in the reference suite of ML flows is 14.5 vol % (vesicle-free and weighted by the flow thickness), while the average abundances of olivine in the reference suites of the MK alkalic and tholeiitic basalts are 1.1 and 14.0 vol %, respectively. Plagioclase and augite phenocrysts are rare in the ML and MK tholeiites, but the MK alkalic basalts can have up to 4 vol % plagioclase phenocrysts. Strained olivine grains, thought to represent disaggregated dunite xenoliths from the cumulate pile within the magma chamber(s), are ubiquitous in the drill core lavas. These deformed grains can comprise up to 50 % of the modal olivine in a given rock. Olivine core compositions in the lavas span forsterite contents of 80.4–90.7 (median 88.8, ML tholeiites), 75.8–86.6 (median 85.8, MK alkalic basalts), and 76.3–90.5 (median 88.0 mol %, MK tholeiites). Olivines with core compositions in the range Fo_(89–90.5) are present in tholeiitic lavas with a wide range of whole-rock MgO contents (9–30 wt %). Strained and unstrained olivines completely overlap in composition as do the compositions of spinels (100*Cr/(Cr+Al) ∼59–72; Mg# = 100*Mg/(Mg+Fe^(2+)) ∼40–66) present as inclusions in the olivine phenocrysts. The presence of Fo_(90.5) olivine in the HSDP lavas requires magmas with ∼16 wt % MgO in the ML and MK plumbing systems. Rare dunite xenoliths are also present in the drill core lavas. While compositionally homogeneous within a given xenolith, the six xenoliths contain olivines that span a wide range of forsterite contents (78.3–89.2 mol %). Spinels in these xenoliths are chrome-rich, have Mg# between 31 and 66, and define two populations on the basis of TiO_2 contents. Whole-rock compositions for the ML and MK tholeiites define olivine control lines on MgO-oxide diagrams, and the relationship between whole-rock MgO and olivine phenocryst abundance in these lavas suggests that the lavas with >12 wt % MgO have accumulated olivine. Comparing the weighted bulk composition of all of the MK tholeiites in the drill core with a calculated parental magma suggests that, on average, the MK tholeiites entrained most of the olivine phenocrysts that crystallized from their parental liquids. Although deformed olivines in Hawaiian lavas are widely thought to represent disaggregated dunite xenoliths, none of the majoror minor-element data on the strained or unstrained olivine phenocrysts suggest that the strained olivines in the HSDP lavas are exotic. We suggest that most of the olivine phenocrysts in a given flow, whether strained or unstrained, are closely related to the evolved liquid that now forms the groundmass. This is consistent with observed correlations between isotopic systems measured on olivine separates (e.g., O, He) and isotopic systems dominated by groundmass (e.g., Nd, Pb)

It's a Gluino!

For a long time it has been known that the like-sign dilepton signature can help establish the existence of a gluino at the LHC. To unambiguously claim that we see a strongly interacting Majorana fermion -- which we could call a gluino -- we need to prove that the particle responsible for the like-sign dilepton events is indeed a fermion. Using only angular correlations in the same gluino decay cascade which is used to measure its mass, we show how to distinguish a universal extra dimensional interpretation with a bosonic heavy gluon from supersymmetry with a fermionic gluino. Assuming a supersymmetric interpretation, we show how the same angular correlations can be used to study the left--right nature of the sfermions appearing in the decay chain.Comment: 10 pages, 10 figures, version accepted for publication at Physical Review