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

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

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

Individualized early death and long-term survival prediction after stereotactic radiosurgery for brain metastases of non-small cell lung cancer:Two externally validated nomograms

Introduction Commonly used clinical models for survival prediction after stereotactic radiosurgery (SRS) for brain metastases (BMs) are limited by the lack of individual risk scores and disproportionate prognostic groups. In this study, two nomograms were developed to overcome these limitations. Methods 495 patients with BMs of NSCLC treated with SRS for a limited number of BMs in four Dutch radiation oncology centers were identified and divided in a training cohort (n = 214, patients treated in one hospital) and an external validation cohort n = 281, patients treated in three other hospitals). Using the training cohort, nomograms were developed for prediction of early death (<3 months) and long-term survival (>12 months) with prognostic factors for survival. Accuracy of prediction was defined as the area under the curve (AUC) by receiver operating characteristics analysis for prediction of early death and long term survival. The accuracy of the nomograms was also tested in the external validation cohort. Results Prognostic factors for survival were: WHO performance status, presence of extracranial metastases, age, GTV largest BM, and gender. Number of brain metastases and primary tumor control were not prognostic factors for survival. In the external validation cohort, the nomogram predicted early death statistically significantly better (p < 0.05) than the unfavorable groups of the RPA, DS-GPA, GGS, SIR, and Rades 2015 (AUC = 0.70 versus range AUCs = 0.51–0.60 respectively). With an AUC of 0.67, the other nomogram predicted 1 year survival statistically significantly better (p < 0.05) than the favorable groups of four models (range AUCs = 0.57–0.61), except for the SIR (AUC = 0.64, p = 0.34). The models are available on www.predictcancer.org. Conclusion The nomograms predicted early death and long-term survival more accurately than commonly used prognostic scores after SRS for a limited number of BMs of NSCLC. Moreover these nomograms enable individualized probability assessment and are easy into use in routine clinical practice

Geochemical stages at Jasper Seamount and the origin of intraplate volcanoes

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 19 (2009): Q02001, doi:10.1029/2008GC002236.Ocean intraplate volcanoes (OIVs) are formed in a sequence of stages, from large to small, that involve a systematic progression in mantle melting in terms of volumes and melt fractions with concomitant distinct mantle source signatures. The Hawaiian volcanoes are the best-known example of this type of evolution, even though they are extraordinarily large. We explore the Pb-Sr-Nd-Hf isotopic evolution of much smaller OIVs in the Fieberling-Guadalupe Seamount Trail (FGST) and small, near-ridge generated seamounts in the same region. In particular, we investigate whether we can extend the Hawaiian models to Jasper Seamount in the FGST, which displays three distinct volcanic stages. Each stage has characteristic variations in Pb-Sr-Nd-Hf isotopic composition and trace element enrichment that are remarkably similar to the systematics observed in Hawaii: (1) The most voluminous, basal “shield building” stage, the Flank Transitional Series (FTS), displays slightly isotopically enriched compositions compared to the common component C and the least enriched trace elements (143Nd/144Nd: 0.512866–0.512909, 206Pb/204Pb: 18.904–19.054; La/Sm: 3.71–4.82). (2) The younger and substantially less voluminous Flank Alkalic Series (FAS) is comparatively depleted in Sr, Nd, and Hf isotope compositions plotting on the side of C, near the least extreme values for the Austral Islands and St. Helena. Trace elements are highly enriched (143Nd/144Nd: 0.512912–0.512948, 206Pb/204Pb: 19.959–20.185; La/Sm: 9.24). (3) The Summit Alkalic Series (SAS) displays the most depleted Sr, Nd, and Hf isotope ratios and is very close in isotopic composition to the nearby near-ridge seamounts but with highly enriched trace elements (143Nd/144Nd: 0.512999–0.513050, 206Pb/204Pb: 19.080–19.237; La/Sm: 5.73–8.61). These data fit well with proposed multicomponent melting models for Hawaii, where source lithology controls melt productivity. We examine the effect of melting a source with dry peridotite, wet peridotite, and pyroxenite, calculating melt productivity functions with depth to evaluate the effect of potential temperature and lithospheric thickness. This type of melting model appears to explain the isotopic variation in a range of small to large OIVs, in particular for OIVs occurring far from the complicating effects of plate boundaries and continental crust, constraining their geodynamic origin.JBT acknowledges financial support from the French Institut National des Sciences de l’Univers. The isotope work at SDSU was made possible by NSF and Keck grants to BBH

How and when plume zonation appeared during the 132 Myr evolution of the Tristan Hotspot

Increasingly, spatial geochemical zonation, present as geographically distinct, subparallel trends, is observed along hotspot tracks, such as Hawaii and the Galapagos. The origin of this zonation is currently unclear. Recently zonation was found along the last B70 Myr of the Tristan-Gough hotspot track. Here we present new Sr–Nd–Pb–Hf isotope data from the older parts of this hotspot track (Walvis Ridge and Rio Grande Rise) and re-evaluate published data from the Etendeka and Parana flood basalts erupted at the initiation of the hotspot track. We show that only the enriched Gough, but not the less-enriched Tristan, component is present in the earlier (70–132 Ma) history of the hotspot. Here we present a model that can explain the temporal evolution and origin of plume zonation for both the Tristan-Gough and Hawaiian hotspots, two end member types of zoned plumes, through processes taking place in the plume sources at the base of the lower mantle

Deep storage of oceanic crust in a vigorously convecting mantle

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94626/1/jgrb15203.pd