Addendum to: Capillary floating and the billiard ball problem

We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38

Os Isotope Systematics in the Canary Islands and Madeira: Lithospheric Contamination and Mantle Plume Signatures

Osmium concentrations and isotopic signatures were measured in 28 primarily Holocene basalts (22 of which have been analyzed for Sr–Nd–Pb isotope composition), two carbonatites and two mantle xenoliths from the Canary Islands, Selvagen Grande and Madeira in the eastern North Atlantic. 187Os/188Os ratios in the basalts range from 0.129 to 0.183. The Os isotope systematics indicate that the basalts fall into three petrogenetic groups: (1) a ‘radiogenic’ group with high 187Os/188Os from 0.152 to 0.183; (2) an ‘unradiogenic’ group with low 187Os/188Os from 0.129 to 0.138; (3) an ‘intermediate’ group with 187Os/188Os between 0.139 and 0.151. The Os isotope systematics of the radiogenic group samples are consistent with minor contamination of the basalts by marine sediment. All samples in the unradiogenic group contain mantle xenoliths, and the unradiogenic Os can be explained by bulk assimilation of ≤ 5% mantle peridotite in the form of disaggregated xenoliths. The radiogenic and unradiogenic groups are also characterized by higher 87Sr/86Sr and 208Pb/204Pb but lower 143Nd/144Nd than samples with similar 206Pb/204Pb from the intermediate group, which is interpreted to reflect interaction of plume magmas with the lithospheric mantle. The intermediate group samples are believed to represent the isotopic signature of the mantle plume. The Os isotopic composition of the Canary plume is among the most radiogenic found in ocean island basalts, comparable with the endmember HIMU islands Mangaia and Tubuaii, but at significantly lower 206Pb/204Pb. The radiogenic Os and moderate 206Pb/204Pb signature of the Canary plume is consistent with a plume which contains 25–35% of relatively young (∼1.2 Ga) recycled oceanic crust. Variable degree of mixing of the Canary Island plume source with shallow depleted asthenosphere containing a component of Paleozoic oceanic crust produces the limited range in Os isotopic signatures observed in the Madeira and Canary Island basalts despite a large range in 206Pb/204Pb isotopic composition

Petrogenesis of Eocene Tamazert continental carbonatites (Central High Atlas, Morocco): implications for a common source for the Tamazert and Canary and Cape Verde Island carbonatites

The Tamazert Eocene alkaline complex of the Central High Atlas Range of Morocco hosts the largest outcropping occurrences of carbonatites in northern Africa. The complex consists of carbonatites and undersaturated ultramafic to syenitic alkaline to peralkaline silicate rocks. Mineralogically and geochemically the Tamazert carbonatites are classified as calciocarbonatites, magnesiocarbonatites and silicocarbonatites.They are enriched in light rare earth elements and large ion lithophile elements (Cs, Rb, Ba, U,Th), but depleted in high field strength elements (particularly, Ti, Nb and Ta). Stable and radiogenic isotope ratios vary in the range of δ13CPDB=-5·8 to 1·8 0/00, δ18OSMOW=6·9-23·5 0/00, initial 87Sr/86Sr=0·7031-0·7076, 143Nd/144Nd=0·5125-0·5129 and 206Pb/204Pb=18·29-19·89. Calciocarbonatites intruding Jurassic limestones have the highest δ13C and δ18O values and the most radiogenic initial 87Sr/86Sr, but least radiogenic 143Nd/144Nd, 206Pb/204Pb and 208Pb/204Pb isotope ratios, and are interpreted to have interacted with the limestones (crustal components). The magnesio- and silicocarbonatites have Sr, Nd and Pb isotope ratios that are nearly identical to those of low-87Sr/86Sr calciocarbonatites. The isotope signature of the high-Sr, low-87Sr/86Sr calciocarbonatites with mantle-type O and C isotopic compositions indicates the presence of HIMU- and EMI-type components in the mantle source of the Tamazert carbonatites, similar to what has been proposed for the Cape Verde and Canary Islands.The close similarity in carbonatite composition between the Cape Verde and Canary Islands and Tamazert suggests a common sublithospheric source for these carbonatites. We therefore propose that theTamazert carbonatites originated through melting of Canary plume material that may have flowed through a sub-lithospheric corridor extending from the Atlantic near the Canary Islands to the Middle Atlas, formed by the delamination of the subcontinental lithosphere in response to Africa-Europe collision at c. 42Ma. Seismic tomography data suggest that the common source may be within the lower mantle at depths >1000 km

Compositional characteristics and spatial distribution of enriched Icelandic mantle components

Author Posting. © The Authors, 2010. This is the author's version of the work. It is posted here by permission of Oxford University Press for personal use, not for redistribution. The definitive version was published in Journal of Petrology 51 (2010): 1447-1475, doi:10.1093/petrology/egq025.We present compositional data on a suite of 18 primitive neovolcanic alkali basalts from three flank zone regions in Iceland (Vestmannaeyjar in the south, Snæfell in the east, and Snæfellsnes in the west) that are peripheral to the main rift zones that are dominated by tholeiitic basalts. This study integrates He isotope data with radiogenic isotope data (Sr-Nd-Pb-Hf), stable isotope data (δ18O), and trace element data to characterise the compositional features of the trace-elementenriched components of the Icelandic mantle. We also present high-precision Pb isotope data on an additional 57 lava samples from the flank zones (including Öræfajökull in the south-east) and the Northern and Eastern rift zones. Most Icelandic lavas have negative Δ207Pb (–4 to –1), with higher values (–1 to +4) found only in samples from Öræfajökull, Snæfell, and parts of the Reykjanes Peninsula. At Snæfell, this EM1-type component is characterised by a low δ18Oolivine signature (+4.1‰ to +4.6‰), moderate 206Pb/204Pb values (18.4-18.6) and MORB-like 3He/4He (6.9-7.5 R/RA). Samples from Vestmannaeyjar and Snæfellsnes have mantle-like δ18Oolivine (+4.9‰ to +5.0‰), and radiogenic 206Pb/204Pb values (18.9-19.3) that fall on the NHRL for 208Pb/204Pb (Δ208Pb –5 to +5). Compared to the Vestmannaeyjar lavas, Snæfellsnes lavas have higher La/YbN (5-11 vs. 3-5), lower εNd (5.5-6.5 vs. 6.8-7.6) and lower 3He/4He (6.3-8.6 R/RA vs. 11.4-13.5 R/RA). Therefore, the most trace element enriched components in the Icelandic mantle are not the carriers of the high 3He/4He values (> 15 R/RA) found in some lavas on Iceland and the adjacent ridges, and instead are consistent with degassed, recycled components. Even after excluding the EM1-type high Δ207Pb samples, high-precision Pb isotope data produce a kinked array on an 206Pb/204Pb vs. 208Pb/204Pb plot, which is not consistent with simple binary mixing between two end-members. This requires significant lateral heterogeneity within the Icelandic mantle and the presence of more than just two compositionally-distinct local mixing end-member components. Samples from each of the main axial rift zones define different trends. Despite the tectonic continuity between the Northern Volcanic Zone and the Eastern Volcanic Zone, lavas from these two rift zones define separate sub-parallel linear arrays. Lavas from the adjacent Western Volcanic Zone and the Eastern Volcanic Zone define oblique linear arrays that converge on a common local end-member that is not involved in the magmatism of the Northern Volcanic Zone. Therefore, there is a distinct NE-SW compositional heterogeneity within the Icelandic mantle.work was funded primarily by the Danish National Research Foundation through a grant to the former Danish Lithosphere Centre, with additional funding from the University of Iowa for the oxygen isotope analyses

Evidence for the return of subducted continental crust

Author Posting. © Nature Publishing Group, 2007. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature 448 (2007): 684-687, doi:10.1038/nature06048.Substantial quantities of terrigenous sediments are known to enter the mantle at subduction zones, but little is known about their fate in the mantle. Subducted sediment may be entrained in buoyantly upwelling plumes and returned to the earth’s surface at hotspots, but the proportion of recycled sediment in the mantle is small and clear examples of recycled sediment in hotspot lavas are rare. We report here remarkably enriched 87Sr/86Sr and 143Nd/144Nd isotope signatures (up to 0.720830 and 0.512285, respectively) in Samoan lavas from three dredge locations on the underwater flanks of Savai’i island, Western Samoa. The submarine Savai’i lavas represent the most extreme 87Sr/86Sr isotope compositions reported for ocean island basalts (OIBs) to date. The data are consistent with the presence of a recycled sediment component (with a composition similar to upper continental crust, or UCC) in the Samoan mantle. Trace element data show similar affinities with UCC—including exceptionally low Ce/Pb and Nb/U ratios—that complement the enriched 87Sr/86Sr and 143Nd/144Nd isotope signatures. The geochemical evidence from the new Samoan lavas radically redefines the composition of the EM2 (enriched mantle 2) mantle endmember, and points to the presence of an ancient recycled UCC component in the Samoan plume

Practical robustness evaluation in radiotherapy - A photon and proton-proof alternative to PTV-based plan evaluation

Background and purpose: A planning target volume (PTV) in photon treatments aims to ensure that the clinical target volume (CTV) receives adequate dose despite treatment uncertainties. The underlying static dose cloud approximation (the assumption that the dose distribution is invariant to errors) is problematic in intensity modulated proton treatments where range errors should be taken into account as well. The purpose of this work is to introduce a robustness evaluation method that is applicable to photon and proton treatments and is consistent with (historic) PTV-based treatment plan evaluations. Materials and methods: The limitation of the static dose cloud approximation was solved in a multi-scenario simulation by explicitly calculating doses for various treatment scenarios that describe possible errors in the treatment course. Setup errors were the same as the CTV-PTV margin and the underlying theory of 3D probability density distributions was extended to 4D to include range errors, maintaining a 90% confidence level. Scenario dose distributions were reduced to voxel-wise minimum and maximum dose distributions; the first to evaluate CTV coverage and the second for hot spots. Acceptance criteria for CTV D98 and D2 were calibrated against PTV-based criteria from historic photon treatment plans. Results: CTV D98 in worst case scenario dose and voxel-wise minimum dose showed a very strong correlation with scenario average D98 (R-2 > 0.99). The voxel-wise minimum dose visualised CTV dose conformity and coverage in 3D in agreement with PTV-based evaluation in photon therapy. Criteria for CTV D98 and D2 of the voxel-wise minimum and maximum dose showed very strong correlations to PTV D98 and D2 (R-2 > 0.99) and on average needed corrections of -0.9% and +2.3%, respectively. Conclusions: A practical approach to robustness evaluation was provided and clinically implemented for PTV-less photon and proton treatment planning, consistent with PTV evaluations but without its static dose cloud approximation. (C) 2019 The Authors. Published by Elsevier B.V

Differences in the association of time to treatment initiation and survival according to various head and neck cancer sites in a nationwide cohort

Objectives: To assess whether there are differences in the effects of time to treatment interval (TTI) on patient survival for head and neck cancer (HNC) sites in order to provide evidence that can support decision-making regarding prioritizing treatment. Materials and methods: Patients in the Netherlands with a first primary HNC without distant metastasis between 2010 and 2014 were included for analysis (N = 10,486). TTI was defined as the time from pathologic diagnosis to the start of initial treatment. Overall survival (OS), cox regression analyses and cubic spline hazard models were calculated and visualized. Results: Overall, the hazard of dying was higher (HR = 1.003; 95 % CI 1.001–1.005) with each additional day until treatment initiation. The pattern, as visualized in cubic spline graphs, differed by site the hazard increased more steeply with increasing TTI for oral cavity cancer. For oropharyngeal and laryngeal cancer, a slight increase commenced after a longer TTI than for oral cavity cancer, while there was hardly an increase in hazard with increasing TTI for hypopharyngeal cancer. Conclusion: The relationship between longer TTI and decreased survival was confirmed, but slight variations in the pattern of the hazard of dying by TTI by tumour site were observed. These findings could support decisions on prioritizing treatment. However, other aspects such as extent of treatment and quality of life should be investigated further so this can also be included

Nicoya Peninsula, Costa Rica: A single suite of Caribbean oceanic plateau magmas

The pre‐Tertiary oceanic crust exposed on the west coast of Costa Rica has been broadly referred to as the Nicoya Complex. This study was designed to determine the age of the Nicoya Complex in the Nicoya Peninsula, Playa Jacó, and the Quepos Peninsula using 40Ar‐39Ar radiometric dating and to assess the petrologic relationships between the different localities using major element, trace element, and Sr, Nd, Pb isotopic data. Radiometric ages of basalts and diabases from the Nicoya Peninsula are 88–90 Ma (with a weighted mean of 88.5 Ma), and those of two intrusive rocks (a gabbro and plagiogranite) are both 83–84 Ma. The combined geochemical data indicate that the sampled Nicoya Peninsula rocks belong to a single suite related by fractional crystallization of similar parental magmas. Nd and Pb isotopic ratios indicate a common mantle source distinct from that of mid‐ocean ridge basalts. Both the age and composition of the Nicoya rocks are consistent with the idea that they are a part of the Caribbean Cretaceous oceanic plateau [Donnelly, 1994]. The Jacó lavas are geochemically similar to the Nicoya Peninsula suite, and a single age of 84 Ma is identical to the age of the Nicoya Peninsula intrusives. The one analyzed Quepos basalt has a radiometric age of ∼64 Ma, and it is enriched in incompatible elements relative to the Nicoya rocks. Similarities in Nd and Pb isotopic ratios indicate that the Quepos and Nicoya/Jacó lavas were derived from a similar mantle source to that which produced the Nicoya rocks, possibly the Galapagos plume