Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

Interstellar neutral helium in the heliosphere from Interstellar Boundary Explorer observations. III. Mach number of the flow, velocity vector, and temperature from the first six years of measurements

We analyzed observations of interstellar neutral helium (ISN He) obtained from the Interstellar Boundary Explorer (IBEX) satellite during its first six years of operation. We used a refined version of the ISN He simulation model, presented in the companion paper by Sokol et al. (2015b), along with a sophisticated data correlation and uncertainty system and parameter fitting method, described in the companion paper by Swaczyna et al. We analyzed the entire data set together and the yearly subsets, and found the temperature and velocity vector of ISN He in front of the heliosphere. As seen in the previous studies, the allowable parameters are highly correlated and form a four-dimensional tube in the parameter space. The inflow longitudes obtained from the yearly data subsets show a spread of similar to 6 degrees, with the other parameters varying accordingly along the parameter tube, and the minimum chi(2) value is larger than expected. We found, however, that the Mach number of the ISN He flow shows very little scatter and is thus very tightly constrained. It is in excellent agreement with the original analysis of ISN He observations from IBEX and recent reanalyses of observations from Ulysses. We identify a possible inaccuracy in the Warm Breeze parameters as the likely cause of the scatter in the ISN He parameters obtained from the yearly subsets, and we suppose that another component may exist in the signal or a process that is not accounted for in the current physical model of ISN He in front of the heliosphere. From our analysis, the inflow velocity vector, temperature, and Mach number of the flow are equal to lambda(ISNHe) = 255 degrees.8 +/- 0 degrees.5, beta(ISNHe) = 5 degrees.16 +/- 0 degrees.10, T-ISNHe = 7440 +/- 260 K, nu(SNHe) = 25.8 +/- 0.4 km s(-1), and M-ISNHe = 5.079 +/- 0.028, with uncertainties strongly correlated along the parameter tube.

Observations of the Sensitivity of Beam Attenuation to Particle Size in a Coastal Bottom Boundary Layer

The goal of this study was to test the hypothesis that the aggregated state of natural marine particles constrains the sensitivity of optical beam attenuation to particle size. An instrumented bottom tripod was deployed at the 12-m node of the Martha's Vineyard Coastal Observatory to monitor particle size distributions, particle size-versus-settling-velocity relationships, and the beam attenuation coefficient (c(p)) in the bottom boundary layer in September 2007. An automated in situ filtration system on the tripod collected 24 direct estimates of suspended particulate mass (SPM) during each of five deployments. On a sampling interval of 5 min, data from a Sequoia Scientific LISST 100x Type B were merged with data from a digital floc camera to generate suspended particle volume size distributions spanning diameters from approximately 2 mu m to 4 cm. Diameter-dependent densities were calculated from size-versus-settling-velocity data, allowing conversion of the volume size distributions to mass distributions, which were used to estimate SPM every 5 min. Estimated SPM and measured c(p) from the LISST 100x were linearly correlated throughout the experiment, despite wide variations in particle size. The slope of the line, which is the ratio of c(p) to SPM, was 0.22 g m(-2). Individual estimates of c(p):SPM were between 0.2 and 0.4 g m(-2) for volumetric median particle diameters ranging from 10 to 150 mu m. The wide range of values in c(p):SPM in the literature likely results from three factors capable of producing factor-of-two variability in the ratio: particle size, particle composition, and the finite acceptance angle of commercial beam-transmissometers.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Alexander’s Dictum and the Reality of Familiar Objects

Alexander's Dictum--"to be is to have causal powers"--appears to furnish an argument against the reality of familiar medium-sized objects. For every time a familiar object appears to cause a familiar macro-event, it sets up a rival claim by its component microparticles to have caused the complex swarm of microphysical events that composes into that macro-event. But this argument, argues this paper, wrongly assumes that even after familiar objects are removed from the picture, there is a phenomenon of joint causation which unites all and only the microparticles within each familiar object.

Kadesh-Barnea : its importance and probable site, with the story of a hunt for it, including studies of the route of the exodus and the southern boundary of the Holy Land

by H. Clay Trumbull

The Cenomanian/Turronian Boundary Event at ODP Hole 103-641A

Drilling at ODP Site 641 (on the western margin of Galicia Bank, off northwestern Spain) revealed a thin, but pronounced, interval of black shale and gray-green claystone. Our high-resolution study combines the sedimentology, micropaleontology (palynomorphs and others), organic and inorganic geochemistry, and isotopic values of this layer to demonstrate the distinct nature of the sediment and prove that the sequence represents the local sedimentary expression of the global Cenomanian/Turonian Oceanic Anoxic Event (OAE) of Schlanger and Jenkyns (1976), Arthur and Schlanger (1979), and Jenkyns (1980), also called the Cenomanian/Turonian Boundary Event (CTBE). The most striking evidence is that the strong positive d13C excursion characterizing the CTBE sequences in shallow areas can be traced into a pronounced deep-sea expression, thus providing a good stratigraphic marker for the CTBE in various paleosettings. The isotopic excursion at Site 641 coincides with an extremely enriched trace metal content, with values that were previously unknown for the Cretaceous Atlantic. Similar to other CTBE occurrences, the organic carbon content is high (up to 11%) and the organic matter is of dominantly marine origin (kerogen type II). The bulk mineralogy of the CTBE sediments does not differ significantly from the general trend of Cretaceous North Atlantic sediments (dominance of smectite and zeolite with minor amounts of illite and scattered palygorskite, kaolinite, and chlorite); thus, no evidence for either increased volcanic activity nor a drastic climatic change in the borderlands was found. Results from Site 641 are compared with the CTBE section found at Site 398, DSDP Leg 47B (Vigo Seamount at the southern end of the Galicia Bank).

Chemobiostratigraphy of the Cretaceous/Paleocene boundary at ODP Hole 120-750A

An integrated biostratigraphic and stable isotope investigation was conducted on a high-latitude sequence across the Cretaceous/Paleogene (K/P) boundary recovered in Hole 750A in the southern Indian Ocean. The sequence consists of nannofossil chalk and is discontinuous across the boundary; missing is an estimated 0.3-m.y. late Maestrichtian and early Danian interval. Nonetheless, because calcareous nannofossil Zones NP1 and NP2 are well-developed, micropaleontological studies of the sequence have yielded a detailed record of Danian high-latitude microplankton evolution. In addition, stable carbon isotope analyses of planktonic and benthic foraminifer and bulk samples provide a record of late Maestrichtian and early Danian surface- and deep-water carbon isotope variations. Together, the carbon isotope and carbonate accumulation records serve as an index of regional marine net productivity across the boundary. Earliest Danian nannoplankton assemblages consisted mainly of persistent genera that were generally rare or absent in the Upper Cretaceous at Hole 750A. However, by 0.5-0.6 m.y. after the boundary, newly evolving Danian taxa became dominant. The turnover in nannofossil assemblages was accompanied by significant changes in rates of net productivity as gauged by carbon isotope distributions and carbonate accumulation rates. During the period dominated by persistent taxa, net productivity was extremely low, as reflected by the absence of vertical delta13C gradients and reduced carbonate accumulation rates. Later in the Danian, as new species evolved and flourished, vertical delta13C gradients reappeared and carbonate accumulation rates increased, signaling partial recovery of net productivity in this region. The absolute timing and magnitude of late Maestrichtian and early Danian biotic and geochemical changes in the southern Indian Ocean were similar to those recorded in other pelagic K/P boundary sequences from low- and mid-latitude Atlantic and Pacific sites, indicating that these events were ubiquitous.

Determination of sulfite and manganese in sediments from the K/T boundary

The solid-state-physics technique of electron spin resonance (ESR) has been employed in an exploratory study of marine limestones and impact-related deposits from Cretaceous-Tertiary (KT) boundary sites including Spain (Sopelana and Caravaca), New Jersey (Bass River), the U.S. Atlantic continental margin (Blake Nose, ODP Leg 171B/1049/A), and several locations in Belize and southern Mexico within -600 km of the Chicxulub crater. The ESR spectra of SO3(1-) (a radiation-induced point defect involving a sulfite ion substitutional for CO3(2-) which has trapped a positive charge) and Mn(2+) in calcite were singled out for analysis because they are unambiguously interpretable and relatively easy to record. ESR signal strengths of calcite-related SO3(1-) and Mn(2+) have been studied as functions of stratigraphic position in whole-rock samples across the KT boundary at Sopelana, Caravaca, and Blake Nose. At all three of these sites, anomalies in SO3(1-) and/or Mn(2+) intensities are noted at the KT boundary relative to the corresponding background levels in the rocks above and below. At Caravaca, the SO3(1-) background itself is found to be lower by a factor of 2.7 in the first 30,000 years of the Tertiary relative to its steady-state value in the last 15,000 years of the Cretaceous, indicating either an abrupt and quasi-permanent change in ocean chemistry (or temperature) or extinction of the marine biota primarily responsible for fixing sulfite in the late Cretaceous limestones. An exponential decrease in the Mn(2+) concentration per unit mass calcite, [Mn(2+)], as the KT boundary at Caravaca is approached from below (1/e characteristic length =1.4 cm) is interpreted as a result of post-impact leaching of the seafloor. Absolute ESR quantitative analyses of proximal impact deposits from Belize and southern Mexico group naturally into three distinct fields in a twodimensional [SO3(1-)]-versus-[Mn(2+)] scatter plot. These fields contain (I) limestone ejecta clasts, (II) accretionary lapilli, and (III) a variety of SO3(1-) -depleted/Mn(2+) enriched impact deposits. Data for the investigated non-impact-related Cretaceous and Tertiary marine limestones (Spain and Blake Nose) fall outside of these three fields. With reference to thes enon-impact deposits, fields I, II, and III can be respectively characterized as Mn(2+) -depleted, SO3(1-) -enhanced, and SO3(1-) -depleted. It is proposed that (1) field I represents calcites from the Yucatin Platform, and that the Mn(2+) -depleted signature can be used as an indicator of primary Chicxulub ejecta in deep marine environments and (2) field II represents calcites that include a component formed in the vapor plume, either from condensation in the presence of CO2/SO3(1-) -rich vapors, or reactions between CaO and CO2/SO3 rich vapors, and that this SO3(1-) -enhanced signature can be used as an indicator of impact vapor plume deposits. Given these two propositions, the ESR data for the Blake Nose deposits are ascribed to the presence of basal coarse calcitic Chicxulub ejecta clasts, while the finer components that are increasingly represented toward the top are interpreted to contain high- SO3(1-) calcite from the vapor plume. The apparently-undisturbed Bass River deposit may contain even higher concentrations of vapor-plume calcite. None of the three components included in field III appear to be represented at distal, deep marine KT-boundary sites; this field may include several types of impact-related deposits of diverse origins and diagenetic histories.

Analyses of shocked quartz from the K-P boundary

The precise cause and timing of the Cretaceous-Paleocene (K-P) mass extinction 65 Ma ago remains a matter of debate. Many advocate that the extinction was caused by a meteorite impact at Chicxulub, Mexico, and a number of potential kill-mechanisms have been proposed for this. Although we now have good constraints on the size of this impact and chemistry of the target rocks, estimates of its environmental consequences are hindered by a lack of knowledge about the obliquity of this impact. An oblique impact is likely to have been far more catastrophic than a sub-vertical one, because greater volumes of volatiles would have been released into the atmosphere. The principal purpose of this study was to characterize shocked quartz within distal K-P ejecta, to investigate whether the quartz distribution carried a signature of the direction and angle of impact. Our analyses show that the total number, maximum and average size of shocked quartz grains all decrease gradually with paleodistance from Chicxulub. We do not find particularly high abundances in Pacific sites relative to Atlantic and European sites, as has been previously reported, and the size-distribution around Chicxulub is relatively symmetric. Ejecta samples at any one site display features that are indicative of a wide range of shock pressures, but the mean degree of shock increases with paleodistance. These shock- and size-distributions are both consistent with the K-P layer having been formed by a single impact at Chicxulub. One site in the South Atlantic contains quartz indicating an anomalously high average shock degree, that may be indicative of an oblique impact with an uprange direction to the southeast +/- 45°. The apparent continuous coverage of proximal ejecta in this quadrant of the crater, however, suggests a relatively high impact angle of >45°. We conclude that some of the more extreme predictions of the environmental consequences of a low-angle impact at Chicxulub are probably not applicable.

Glassy objects from DSDP Hole 5-32 in the northeastern Pacific Ocean

Small glassy spheres, ellipsoids, teardrops, cylinders and dumbbells occur in large numbers in Tertiary deep sea clays cored in the northeastern Pacific by the Deep Sea Drilling Project. These objects morphologically resemble microtektites, but have the composition of an oceanic tholeiite. On the basis of their composition and stratigraphic relationship it is considered that they are of volcanic origin and most likely have been formed in deep water by submarine volcanic processes.