Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also
describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.

In-vitro investigation of out-of-field cell survival following the delivery of conformal, intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) plans

The aim of this work is to determine the out-of-field survival of cells irradiated with either the primary field or scattered radiation in the presence and absence of intercellular communication following delivery of conformal, IMRT and VMAT treatment plans. Single beam, conformal, IMRT and VMAT plans were created to deliver 3 Gy to half the area of a T80 flask containing either DU-145 or AGO-1522 cells allowing intercellular communication between the in-and out-of-field cell populations. The same plans were delivered to a similar custom made phantom used to hold two T25 culture flasks, one flask in-field and one out-of-field to allow comparison of cell survival responses when intercellular communication is physically inhibited. Plans were created for the delivery of 8 Gy to the more radio-resistant DU-145 cells only in the presence and absence of intercellular communication. Cell survival was determined by clonogenic assay. In both cell lines, the out-of-field survival was not statistically different between delivery techniques for either cell line or dose. There was however, a statistically significant difference between survival out-of-field when intercellular communication was intact (single T80 culture flask) or inhibited (multiple T25 culture flasks) to in-field for all plans. No statistically significant difference was observed in-field with or without cellular communication to out-of-field for all plans. These data demonstrate out-of-field effects as important determinants of cell survival following exposure to modulated irradiation fields when cellular communication between differentially irradiated cell populations is present. This data is further evidence that refinement of existing radiobiological models to include indirect cell killing effects is required.

Use of arc-length method for capturing mode jumping in postbuckling aerostructures

The arc-length method has become a widely established solution technique for studying nonlinear structural behavior. By augmenting the set of nonlinear equilibrium equations with a constraint equation, which is a function of both the displacements and load increment, it is capable of traversing limit points. Numerous investigations have shown that highly nonlinear behavior such as sharp "snap-backs" can still lead to numerical difficulties. Two practical examples are presented to assess the effectiveness of this solution technique in capturing secondary instabilities in postbuckling structures, which present themselves as abrupt mode jumps. Although the first example poses no special difficulties, in the second case the nonlinear procedure fails to converge. An improvement to the method's formulation is suggested, which accounts for the residual forces that are usually neglected, when proceeding to the next increment once convergence is reached on the current increment. The choice of a correct load increment at the first iteration, within a predictor-corrector scheme, is central to the method's effectiveness. Current strategies for a choice of this load increment are discussed and are shown to be no longer consistent with the modified formulation; therefore, a new approach is proposed.

Inverse planned constant dose rate volumetric modulated arc therapy (VMAT) as an efficient alternative to five-field intensity modulated radiation therapy (IMRT) for prostate

Purpose: The aim of this work was to determine if volumetric modulated arc therapy (VMAT) plans, created for constant dose-rate (cdrVMAT) delivery are a viable alternative to step and shoot five-field intensity modulated radiation therapy (IMRT). Materials and methods: The cdrVMAT plans, inverse planned on a treatment planning system with no solution to account for couch top or rails, were created for delivery on a linear accelerator with no variable dose rate control system. A series of five-field IMRT and cdrVMAT plans were created using dual partial arcs (gantry rotating between 260° and 100°) with 4° control points for ten prostate patients with the average rectal constraint incrementally increased. Pareto fronts were compared for the planning target volume homogeneity and average rectal dose between the two techniques for each patient. Also investigated were tumour control probability and normal tissue complication probability values for each technique. The delivery parameters [monitor units (MU) and time] and delivery accuracy of the IMRT and VMAT plans were also compared. Results: Pareto fronts showed that the dual partial arc plans were superior to the five-field IMRT plans, particularly for the clinically acceptable plans where average rectal doses were less for rotational plans (p = 0·009) with no statistical difference in target homogeneity. The cdrVMAT plans had significantly more MU (p = 0·005) but the average delivery time was significantly less than the IMRT plans by 42%. All clinically acceptable cdrVMAT plans were accurate in their delivery (gamma 99·2 ± 1·1%, 3%3 mm criteria). Conclusions Accurate delivery of dual partial arc cdrVMAT avoiding the couch top and rails has been demonstrated.

Source depletion and extent of melting in the Tongan sub-arc mantle

The fluid immobile High Field Strength Elements (HFSE) Nb and Ta can be used to distinguish between the effects of variable extents of melting and prior source depletion of the Tongan sub-arc mantle. Melting of spinel Iherzolite beneath the Lau Basin back-arc spreading centres has the ability to fractionate Nb from Ta due to the greater compatibility of the latter in clinopyroxene. The identified spatial variation in plate velocities and separation of melt extraction zones, combined with extremely depleted lavas make Tonga an ideal setting in which to test models for arc melt generation and the role of back-arc magmatism. We present new data acquired by laser ablation-ICPMS of fused sample glasses produced without the use of a melt fluxing agent. The results show an arc trend towards strongly sub-chondritic Nb/Ta (

Magma Evolution in the Primitive, Intra-oceanic Tonga Arc: Petrogenesis of Basaltic Andesites at Tofua Volcano

Tofua volcano is situated midway along the Tonga oceanic arc and has undergone two phases of ignimbrite-forming activity. The eruptive products are almost entirely basaltic andesites (52 center dot 5-57 wt % SiO2) with the exception of a volumetrically minor pre-caldera dacite. The suite displays a strong tholeiitic trend with K2O <1 wt %. Phenocryst assemblages typically comprise plagioclase + clinopyroxene +/- orthopyroxene with microlites of Ti-magnetite. Olivine (Fo(83-88)) is rare and believed to be dominantly antecrystic. An increase in the extent and frequency of reverse zoning in phenocrysts, sieve-textured plagioclase and the occurrence of antecrystic phases in post-caldera lavas record a shift to dynamic conditions, allowing the interaction of magma batches that were previously distinct. Pyroxene thermobarometry suggests crystallization at 950-1200 degrees C and 0 center dot 8-1 center dot 8 kbar. Volatile measurements of glassy melt inclusions indicate a maximum H2O content of 4 center dot 16 wt % H2O, and CO2-H2O saturation curves indicate that crystallization occurred at two levels, at depths of 4-5 center dot 5 km and 1 center dot 5-2 center dot 5 km. Major and trace element models suggest that the compositions of the majority of the samples represent a differentiation trend whereby the dacite was produced by 65% fractional crystallization of the most primitive basaltic andesite. Trace element models suggest that the sub-arc mantle source is the residuum of depleted Indian mid-ocean ridge basalt mantle (IDMM-1% melt), whereas radiogenic isotope data imply addition of 0 center dot 2% average Tongan sediment melt and a fluid component derived from the subducted altered Pacific oceanic crust. A horizontal array on the U-Th equiline diagram and Ra excesses of up to 500% suggest fluid addition to the mantle wedge within the last few thousand years. Time-integrated (Ra-226/Th-230) vs Sr/Th and Ba/Th fractionation models imply differentiation timescales of up to 4500 years for the dacitic magma compositions at Tofua.

Magma Evolution in the Primitive, Intra-oceanic Tonga Arc: Rapid Petrogenesis of Dacites at Fonualei Volcano

Fonualei is unusual amongst subaerial volcanoes in the Tonga arc because it has erupted dacitic vesicular lavas, tuffs and phreomagmatic deposits for the last 165 years. The total volume of dacite may approach 5 km(3) and overlies basal basaltic andesite and andesite lavas that are constrained to be less than a few millennia in age. All of the products are crystal-poor and formed from relatively low-viscosity magmas inferred to have had temperatures of 1100-1000 degrees C, 2-4 wt % H2O and oxygen fugacities 1-2 log units above the quartz-fayalite-magnetite buffer. Major and trace element data, along with Sr-Nd-Pb and U-Th-Ra isotope data, are used to assess competing models for the origin of the dacites. Positive correlations between Sc and Zr and Sr rule out evolution of the within-dacite compositional array by closed-system crystal fractionation of a single magma batch. An origin by partial melting of lower crustal amphibolites cannot reproduce these data trends or, arguably, any of the dacites either. Instead, we develop a model in which the dacites reflect mixing between two dacitic magmas, each the product of fractional crystallization of basaltic andesite magmas formed by different degrees of partial melting. Mixing was efficient because the two magmas had similar temperatures and viscosities. This is inferred to have occurred at shallow (2-6 km) depths beneath the volcano. U-Th-Ra disequilibria in the basaltic andesite and andesite indicate that the parental magmas had fluids added to their mantle source regions less than 8 kyr ago and that fractionation to the dacitic compositions took less than a few millennia. The 165 year eruption period for the dacites implies that mixing occurred on a similar timescale, possibly during ascent in conduits. The composition of the dacites renders them unsuitable candidates as contributors to average continental crust.

Rapid magmatic processes accompany arc-continent collision: the Western Bismarck arc, Papua New Guinea

New U-Th-Ra, major and trace element, and Sr-Nd-Pb isotope data are presented for young lavas from the New Britain and Western Bismarck arcs in Papua New Guinea. New Britain is an oceanic arc, whereas the latter is the site of an arc-continent collision. Building on a recent study of the Manus Basin, contrasts between the two arcs are used to evaluate the processes and timescales of magma generation accompanying arc-continent collision and possible slab detachment. All three suites share many attributes characteristic of arc lavas that can be ascribed to the addition of a regionally uniform subduction component derived from the subducting altered oceanic crust and sediment followed by dynamic melting of the modified mantle. However, the Western Bismarck arc lavas diverge from the Pb isotope mixing array formed by the New Britain and the Manus Basin lavas toward elevated Pb-208/Pb-204. We interpret this to reflect a second and subsequent addition of sediment melt at crustal depth during collision. U-238 and Ra-226 excesses are preserved in all of the lavas and are greatest in the Western Bismarck arc. High-Mg andesites with high Sr/Y ratios in the westernmost arc are attributed to recent shallow mantle flux melting at the slab edge. Data for two historical rhyolites are also presented. Although these rhyolites formed in quite different tectonic settings and display different geochemical and isotopic compositions, both formed from mafic parents within millennia.

Mantle flow, volatiles, slab-surface temperatures and melting dynamics in the north Tonga arc-Lau back-arc basin

The Fonualei Spreading Center affords an excellent opportunity to evaluate geochemical changes with increasing depth to the slab in the Lau back-arc basin. We present H2O and CO2 concentrations and Sr, Nd, Pb, Hf and U-Th-Ra isotope data for selected glasses as well as new Hf isotope data from boninites and seamounts to the north of the Tonga arc. The Pb and Hf isotope data are used to show that mantle flow is oriented to the southwest and that the tear in the northern end of the slab may not extend east as far as the boninite locality. Along the Fonualei Spreading Center, key geochemical parameters change smoothly with increasing distance from the arc front and increasing slab surface temperatures. The latter may range from 720 to 866 degrees C, based on decreasing H2O/Ce ratios. Consistent with experimental data, the geochemical trends are interpreted to reflect changes in the amount and composition of wet pelite melts or super-critical fluids and aqueous fluids derived from the slab. With one exception, all of the lavas preserve both U-238 excesses and Ra-226 excesses. We suggest that lavas from the Fonualei Spreading Center and Valu Fa Ridge are dominated by fluid-fluxed melting whereas those from the East and Central Lau Spreading Centers, where slab surface temperatures exceed similar to 850-900 degrees C, are largely derived through decompression. A similar observation is found for the Manus and East Scotia back-arc basins and may reflect the expiry of a key phase such as lawsonite in the subducted basaltic crust.