The airborne lava-seawater interaction plume at Kilauea Volcano, Hawaii

Petrology igneous metamorphic and volcanic studies; medm0

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

An exactly solvable limit of low energy QCD

Starting from the QCD Hamiltonian, we derive a schematic Hamiltonian for low energy quark dynamics with quarks restricted to the lowest s-level. The resulting eigenvalue problem can be solved analytically. Even though the Hamiltonian exhibits explicit chiral symmetry the severe restriction of the number of degrees of freedom breaks the pattern of chiral symmetry breaking for finite quark masses.Comment: 7 page

Reconstructing a Simple Polytope from its Graph

Blind and Mani (1987) proved that the entire combinatorial structure (the vertex-facet incidences) of a simple convex polytope is determined by its abstract graph. Their proof is not constructive. Kalai (1988) found a short, elegant, and algorithmic proof of that result. However, his algorithm has always exponential running time. We show that the problem to reconstruct the vertex-facet incidences of a simple polytope P from its graph can be formulated as a combinatorial optimization problem that is strongly dual to the problem of finding an abstract objective function on P (i.e., a shelling order of the facets of the dual polytope of P). Thereby, we derive polynomial certificates for both the vertex-facet incidences as well as for the abstract objective functions in terms of the graph of P. The paper is a variation on joint work with Michael Joswig and Friederike Koerner (2001).Comment: 14 page

Melt mixing causes negative correlation of trace element enrichment and CO<inf>2</inf> content prior to an Icelandic eruption

Major elements, trace elements and volatiles were measured in 110 olivine-hosted melt inclusions from the subglacial Skuggafjöll eruption in the Eastern Volcanic Zone of Iceland. Variations in melt inclusion trace element concentrations can be accounted for by incomplete mixing of diverse mantle parental melts accompanied by variable extents of fractional crystallisation. Binary mixing between an incompatible trace element-enriched and depleted melts provides a good fit to observed variations in trace element ratios such as Ce/Y. Surprisingly, the CO2 contents of melt inclusions correlate negatively with their degree of trace element enrichment. Depleted, low-Ce/Y inclusions with ∼1200 ppm CO2 have high CO2/Nb contents (∼400), suggesting that melts experienced little or no CO2 exsolution before inclusion entrapment. Enriched, high-Ce/Y inclusions contain ∼300 ppm CO2, have low CO2/Nb (contents 50–100) and melts are likely to have exsolved much of their original CO2 contents prior to inclusion entrapment. The negative correlation between CO2 content and trace element enrichment may arise either from the more efficient exsolution of CO2 from enriched melts, or from the intrusion of CO2-supersaturated depleted melts into enriched melts that had already exsolved much of their original CO2 contents. Some inclusions have lower CO2 contents than predicted from binary mixing models, which suggests that at least some CO2 exsolution occurred concurrently with mixing. Enriched inclusions record entrapment pressures of ∼0.5 kbar. These pressures probably correspond to the depth of mixing. Higher pressures recorded in depleted inclusions may have resulted from the development of CO2 supersaturation during ascent from storage at ≥1.5 kbar. The presence of CO2 supersaturation in melt inclusions has the potential to constrain timescales of melt inclusion entrapment.This work was supported by a Natural Environment Research Council studentship to D.A.N. (NE/1528277/1) and a Natural Environment Research Council Ion Microprobe Facility award (IMF461/0512).This is the final published version of the article, which can also be found online here: http://www.sciencedirect.com/science/article/pii/S0012821X14003604

Semi-relativistic description of quasielastic neutrino reactions and superscaling in a continuum shell model

The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(\nu_\mu,\mu^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(\nu_\mu,\mu^-)$ cross sections.Comment: 33 pages, 10 figures, to appear in PR

Reorientation Transition in Single-Domain (Ga,Mn)As

We demonstrate that the interplay of in-plane biaxial and uniaxial anisotropy fields in (Ga,Mn)As results in a magnetization reorientation transition and an anisotropic AC susceptibility which is fully consistent with a simple single domain model. The uniaxial and biaxial anisotropy constants vary respectively as the square and fourth power of the spontaneous magnetization across the whole temperature range up to T_C. The weakening of the anisotropy at the transition may be of technological importance for applications involving thermally-assisted magnetization switching.Comment: 4 pages, 4 figure