Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

Spin precession and alternating spin polarization in spin-3/2 hole systems

The spin density matrix for spin-3/2 hole systems can be decomposed into a sequence of multipoles which has important higher-order contributions beyond the ones known for electron systems [R. Winkler, Phys. Rev. B \textbf{70}, 125301 (2004)]. We show here that the hole spin polarization and the higher-order multipoles can precess due to the spin-orbit coupling in the valence band, yet in the absence of external or effective magnetic fields. Hole spin precession is important in the context of spin relaxation and offers the possibility of new device applications. We discuss this precession in the context of recent experiments and suggest a related experimental setup in which hole spin precession gives rise to an alternating spin polarization.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

Magma mixing and high fountaining during the 1959 K īlauea Iki eruption, Hawai'i

The 1959 Kīlauea Iki eruption provides a unique opportunity to investigate the process of shallow magma mixing, its impact on the magmatic volatile budget and its role in triggering and driving episodes of Hawaiian fountaining. Melt inclusions hosted by olivine record a continuous decrease in H2O concentration through the 17 episodes of the eruption, while CO2 concentrations correlate with the degree of post-entrapment crystallization of olivine on the inclusion walls. Geochemical data, when combined with the magma budget and with contemporaneous eruption observations, show complex mixing between episodes involving hot, geochemically heterogeneous melts from depth, likely carrying exsolved vapour, and melts which had erupted at the surface, degassed and drained-back into the vent. The drained-back melts acted as a coolant, inducing rapid cooling of the more primitive melts and their olivines at shallow depths and inducing crystallization and vesiculation and triggering renewed fountaining. A consequence of the mixing is that the melts became vapor-undersaturated, so equilibration pressures cannot be inferred from them using saturation models. After the melt inclusions were trapped, continued growth of vapor bubbles, caused by enhanced post-entrapment crystallization, sequestered a large fraction of CO2 from the melt within the inclusions. This study, while cautioning against accepting melt inclusion CO2 concentrations “as measured” in mixed magmas, also illustrates that careful analysis and interpretation of post-entrapment modifications can turn this apparent challenge into a way to yield novel useful insights into the geochemical controls on eruption intensity.IS was supported by a NERC-funded studentship and a USGS Jack Kleinman Grant for Volcano Research. ME acknowledges NERC ion probe grant IMF376/0509. BH’s participation was funded by NSF EAR-1145159. We acknowledge the NERC Edinburgh Ion Microprobe facility, where we undertook the SIMS analyses.This version is the author accepted manuscript and will be under embargo until the 6th of June 2015. The final version has been published by Elsevier in Earth and Planetary Science Letters here: http://www.sciencedirect.com/science/article/pii/S0012821X14003264

Isoscalar short-range current in the deuteron induced by an intermediate dibaryon

A new model for short-range isoscalar currents in the deuteron and in the NN system is developed; it is based on the generation of an intermediate dibaryon which is the basic ingredient for the medium- and short-range NN interaction which was proposed recently by the present authors.This new current model can very well describe the experimental data for the three basic deuteron observables of isoscalar magnetic type, viz. the magnetic moment, the circular polarization of the photon in the $np\to d\gamma$ process at thermal neutron energies and the structure function B up to Q$^2$=60 fm$^{-2}$.Comment: LaTex, 22 pages with 8 figure

Multi-year satellite observations of sulfur dioxide gas emissions and lava extrusion at bagana volcano, papua new guinea

Bagana, arguably the most active volcano in Papua New Guinea, has been in a state of near-continuous eruption for over 150 years, with activity dominated by sluggish extrusion of thick blocky lava flows. If current extrusion rates are representative, the entire edifice may have been constructed in only 300–500 years. Bagana exhibits a remarkably high gas flux to the atmosphere, with persistent sulfur dioxide (SO2) emissions of several thousand tons per day. This combination of apparent youth and high outgassing fluxes is considered unusual among persistently active volcanoes worldwide. We have used satellite observations of SO2 emissions and thermal infrared radiant flux to explore the coupling of lava extrusion and gas emission at Bagana. The highest gas emissions (up to 10 kt/day) occur during co-extrusive intervals, suggesting a degree of coupling between lava and gas, but gas emissions remain relatively high (~2,500 t/d) during inter-eruptive pauses. These passive emissions, which clearly persist for decades if not centuries, require a large volume of degassing but non-erupting magma beneath the volcano with a substantial exsolved volatile phase to feed the remarkable SO2 outgassing: an additional ~1.7–2 km3 basaltic andesite would be required to supply the excess SO2 emissions we observe in our study interval (2005 to present). That this volatile phase can ascend freely to the surface under most conditions is likely to be key to Bagana's largely effusive style of activity, in contrast with other persistently active silicic volcanoes where explosive and effusive eruptive styles alternate

The impact of degassing on the oxidation state of basaltic magmas: A case study of Kīlauea volcano

Volcanic emissions link the oxidation state of the Earth's mantle to the composition of the atmosphere. Whether the oxidation state of an ascending magma follows a redox buffer – hence preserving mantle conditions – or deviates as a consequence of degassing remains under debate. Thus, further progress is required before erupted basalts can be used to infer the redox state of the upper mantle or the composition of their co-emitted gases to the atmosphere. Here we present the results of X-ray absorption near-edge structure (XANES) spectroscopy at the iron K-edge carried out for a series of melt inclusions and matrix glasses from ejecta associated with three eruptions of Kīlauea volcano (Hawai‘i). We show that the oxidation state of these melts is strongly correlated with their volatile content, particularly in respect of water and sulfur contents. We argue that sulfur degassing has played a major role in the observed reduction of iron in the melt, while the degassing of H$_{2}$O and CO$_{2}$ appears to have had a negligible effect on the melt oxidation state under the conditions investigated. Using gas–melt equilibrium degassing models, we relate the oxidation state of the melt to the composition of the gases emitted at Kīlauea. Our measurements and modelling yield a lower constraint on the oxygen fugacity of the mantle source beneath Kīlauea volcano, which we infer to be near the nickel nickel-oxide (NNO) buffer. Our findings should be widely applicable to other basaltic systems and we predict that the oxidation state of the mantle underneath most hotspot volcanoes is more oxidised than that of the associated lavas. We also suggest that whether the oxidation states of a basalt (in particular MORB) reflects that of its source, is primarily determined by the extent of sulfur degassing.We thank the Diamond Light Source for access to beamline I18 (proposal number SP11497-1) that contributed to the results presented here and the invaluable support during our analytical sessions from Konstantin Ignatyev. The Smithsonian Institution National Museum of Natural History is thanked for their loan of NMNH 117393. We thank Don Swanson (HVO-USGS) for his help acquiring the samples. YM acknowledges support from the Scripps Institution of Oceanography Postdoctoral Fellowship program. We are grateful to Nicole Métrich and an anonymous reviewer for providing valuable comments improving the quality of the manuscript. ME and CO are supported by the Natural Environment Research Council via the Centre for Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET). NP is also funded by the Natural Environment Research Council (grant NE/N009312/1). NERC-funded studentship funded sample collection. ME acknowledges NERC ion probe grant IMF376/0509.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.epsl.2016.06.031

Radiative orbital electron capture by the atomic nucleus

The rate for the photon emission accompanying orbital 1S electron capture by the atomic nucleus is recalculated. While a photon can be emitted by the electron or by the nucleus, the use of the length gauge significantly suppresses the nuclear contribution. Our calculations resolve the long standing discrepancy of theoretical predictions with experimental data for $\Delta J=2$ forbidden transitions. We illustrate the results by comparison with the data established experimentally for the first forbidden unique decays of $^{41}$Ca and $^{204}$Tl.Comment: 18 pages, 2 figures, submitted to Phys. Rev.

Spin Orientation of Holes in Quantum Wells

This paper reviews the spin orientation of spin-3/2 holes in quantum wells. We discuss the Zeeman and Rashba spin splitting in hole systems that are qualitatively different from their counterparts in electron systems. We show how a systematic understanding of the unusual spin-dependent phenomena in hole systems can be gained using a multipole expansion of the spin density matrix. As an example we discuss spin precession in hole systems that can give rise to an alternating spin polarization. Finally, we discuss the qualitatively different regimes of hole spin polarization decay in clean and dirty samples.Comment: 14 pages, 8 figure