Complete curvature homogeneous pseudo-Riemannian manifolds

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.Comment: Update paper to fix misprints in original versio

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

A rapid mechanism to remobilize and homogenize highly crystalline magma bodies

International audienceThe largest products of magmatic activity on Earth, the great bodies of granite and their corresponding large eruptions, have a dual nature: homogeneity at the large scale and spatial and temporal heterogeneity at the small scale1-4. This duality calls for amechanism that selectively removes the large-scale heterogeneities associated with the incremental assembly4 of these magmatic systems and yet occurs rapidly despite crystal-rich, viscous conditions seemingly resistant to mixing2,5. Here we show that a simple dynamic template can unify a wide range of apparently contradictory observations from both large plutonic bodies and volcanic systems by a mechanism of rapid remobilization (unzipping) of highly viscous crystalrich mushes. We demonstrate that this remobilization can lead to rapid overturn and produce the observed juxtaposition ofmagmatic materials with very disparate ages and complex chemical zoning. What distinguishes our model is the recognition that the process has two stages. Initially, a stiff mushy magma is reheated from below, producing a reduction in crystallinity that leads to the growth of a subjacent buoyant mobile layer. When the thickening mobile layer becomes sufficiently buoyant, it penetrates the overlying viscous mushy magma. This second stage rapidly exports homogenized material from the lower mobile layer to the top of the system, and leads to partial overturn within the viscous mush itself as an additional mechanism of mixing. Model outputs illustrate that unzipping can rapidly produce large amounts of mobile magma available for eruption. The agreement between calculated and observed unzipping rates for historical eruptions at Pinatubo and at Montserrat demonstrates the general applicability of the model. This mechanism furthers our understanding of both the formation of periodically homogenized plutons (crust building) and of ignimbrites by large eruptions

Timescales of Quartz Crystallization and the Longevity of the Bishop Giant Magma Body

Supereruptions violently transfer huge amounts (100 s–1000 s km3) of magma to the surface in a matter of days and testify to the existence of giant pools of magma at depth. The longevity of these giant magma bodies is of significant scientific and societal interest. Radiometric data on whole rocks, glasses, feldspar and zircon crystals have been used to suggest that the Bishop Tuff giant magma body, which erupted ∼760,000 years ago and created the Long Valley caldera (California), was long-lived (>100,000 years) and evolved rather slowly. In this work, we present four lines of evidence to constrain the timescales of crystallization of the Bishop magma body: (1) quartz residence times based on diffusional relaxation of Ti profiles, (2) quartz residence times based on the kinetics of faceting of melt inclusions, (3) quartz and feldspar crystallization times derived using quartz+feldspar crystal size distributions, and (4) timescales of cooling and crystallization based on thermodynamic and heat flow modeling. All of our estimates suggest quartz crystallization on timescales of <10,000 years, more typically within 500–3,000 years before eruption. We conclude that large-volume, crystal-poor magma bodies are ephemeral features that, once established, evolve on millennial timescales. We also suggest that zircon crystals, rather than recording the timescales of crystallization of a large pool of crystal-poor magma, record the extended periods of time necessary for maturation of the crust and establishment of these giant magma bodies

The Costs of VAT: A Review of the Literature

This paper reviews the published literature on the definition and measurement of the administrative and compliance costs of taxation, with special reference to VAT (including evasion and fraud) in the European Union