Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

Sedimentological and provenance response to Cambrian closure of the Clymene ocean: The upper Alto Paraguai Group, Paraguay belt, Brazil

Final Gondwana amalgamation was marked by the closure of the Neoproterozoic Clymene ocean between the Amazonia craton and central Gondwana. The events which occurred in the last stage of this closure were recorded in the upper Alto Paraguai Group in the foreland of the Paraguay orogen. Outcrop-based fades analysis of the siliciclastic rocks of upper Alto Paraguai Group, composed of the Sepotuba and Diamantino Formations, was carried out in the Diamantino region, within the eastern part of the Barra dos Bugres basin, Mato Grosso state, central-western Brazil. The Sepotuba Formation is composed of sandy shales with planar to wave lamination interbedded with fine-grained sandstone with climbing ripple cross-lamination, planar lamination, swaley cross-stratification and tangential to sigmoidal cross-bedding with mud drapes, related to marine offshore deposits. The lower Diamantino Formation is composed of a monotonous, laterally continuous for hundreds of metres, interbedded siltstone and fine-grained sandstone succession with regular parallel lamination, climbing ripple cross-lamination and ripple-bedding interpreted as distal turbidites. The upper part of this formation consists of fine to medium-grained sandstones with sigmoidal cross-bedding, planar lamination, climbing ripple cross-lamination, symmetrical to asymmetrical and linguoid ripple marks arranged in lobate sand bodies. These fades are interbedded with thick siltstone in coarsening upward large-scale cycles related to a delta system. The Sepotuba Formation characterises the last transgressive deposits of the Paraguay basin representing the final stage of a marine incursion of the Clymene ocean. The progression of orogenesis in the hinterland resulted in the confinement of the Sepotuba sea as a foredeep sub-basin against the edge of the Amazon craton. Turbidites were generated during the deepening of the basin. The successive filling of the basin was associated with progradation of deltaic lobes from the southeast, in a wide lake or a restricted sea that formed after 541 +/- 7 Ma. Southeastern to east dominant Neoproterozoic source regions were confirmed by zircon grains that yielded ages around 600 to 540 Ma, that are interpreted to be from granites in the Paraguay orogen. This overall regressive succession recorded in the Alto Paraguai Group represents the filling up of a foredeep basin after the final amalgamation of westem Gondwana in the earliest Phanerozoic. (C) 2011 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Annealing effects on nanostructured gold-polymethylmethacrylate composites: Small-angle x-ray scattering analysis

Composites formed of a polymer-embedded layer of sub-10 nm gold nanoclusters were fabricated by very low energy (49 eV) gold ion implantation into polymethylmethacrylate. We used small angle x-ray scattering to investigate the structural properties of these metal-polymer composite layers that were fabricated at three different ion doses, both in their original form (as-implanted) and after annealing for 6 h well above the polymer glass transition temperature (150 degrees C). We show that annealing provides a simple means for modification of the structure of the composite by coarsening mechanisms, and thereby changes its properties. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720464]

Materiali Ceramici per Edilizia con Funzionalità Fotocatalitica

This thesis wad aimed at the study and application of titanium dioxide photocatalytic activity on ceramic materials. As a matter of fact, photocatalysis is a very promising method to face most of the problems connected with the increasing environmental pollution. Furthermore, titanium dioxide, in its anatase crystallographic phase, is one of the most investigated photocatalytic material and results to be perfectly compatible with silicate body mixes. That goal was pursued by two different strategies: 1. the addition to a body mix used for heavy clay products of several titania powders, with different mean crystallite size, surface area, morphology and anatase/rutile ratio and a titania nanosuspension as well. The titania addition followed two procedures: bulk and spray addition over the ceramic samples surface. Titania was added in two different percentages: 2.5 and 7.5 wt.% in both of the methods. The ceramic samples were then fired at three maximum temperatures: 900, 950 and 1000 °C. Afterwards, the photocatalytic activity of the prepared ceramic samples was evaluated by following the degradation of an organic compound in aqueous medium, under UV radiation. The influence of titania morphological characteristics on the photoactivity of the fired materials was studied by means of XRD and SEM observations. The ceramic samples, sprayed with a slip containing 7.5 wt.% of titania powder and fired at 900 °C, have the best photoactivity, with a complete photo-decomposition of the organic compound. At 1000 °C no sample acted as a photocatalyst due to the anatase-to-rutile phase transformation and to the reaction between titania and calcium and iron oxides in the raw materials. 2. The second one foresaw the synthesis of TiO2-SiO2 solid solutions, using the following stoichiometry: Ti1-xSixO2 where x = 0, 0.1, 0.3 and 0.5 atoms per formula unit (apfu). The mixtures were then fired following two thermal cycles, each with three maximum temperatures. The effect of SiO2 addition into the TiO2 crystal structure and, consequently, on its photocatalytic activity when fired at high temperature, was thoroughly investigated by means of XRD, XPS, FE-SEM, TEM and BET analysis. The photoactivity of the prepared powders was assessed both in gas and liquid phase. Subsequently, the TiO2-SiO2 solid solutions, previously fired at 900 °C, were sprayed over the ceramic samples surface in the percentage of 7.5 wt.%. The prepared ceramic samples were fired at 900 and 1000 °C. The photocatalytic activity of the ceramic samples was evaluated in liquid phase. Unfortunately, that samples did not show any appreciable photoactivity. In fact, samples fired at 900 °C showed a pretty low photoactivity, while the one fired at 1000 °C showed no photoactivity at all. This was explained by the excessive coarsening of titania particles. To summarise, titania particle size, more than its crystalline phase, seems to have a relevant role in the photocatalytic activity of the ceramic samples.

Sintesi e caratterizzazione di nanopolveri composite allumina-zirconia

Il presente lavoro di tesi riguarda la sintesi di nanopolveri allumina-zirconia, seguendo tre differenti metodologie (sintesi per coprecipitazione, sintesi con il metodo dei citrati, sintesi idrotermale assistita da microonde) e il trattamento termico (calcinazione) delle polveri ottenute, mediante tecniche di riscaldamento convenzionali ed alternative (microonde). Lo scopo del lavoro è consistito nell’individuare, tra le tecniche esaminate, quella più idonea e conveniente, per la preparazione di nanopolveri cristalline 95 mol% Al2O3 – 5 mol% ZrO2 e nell’esaminare gli effetti che la calcinazione condotta con le microonde, ha sulle caratteristiche finali delle polveri, rispetto ai trattamenti termici convenzionali. I risultati ottenuti al termine del lavoro hanno evidenziato che, tra le tecniche di sintesi esaminate, la sintesi idrotermale assistita da microonde, risulta il metodo più indicato e che, il trattamento termico eseguito con le microonde, risulta di gran lunga vantaggioso rispetto a quello convenzionale. La sintesi idrotermale assistita da microonde consente di ottenere polveri nano cristalline poco agglomerate, che possono essere facilmente disaggregate e con caratteristiche microstrutturali del tutto peculiari. L’utilizzo di tale tecnica permette, già dopo la sintesi a 200°C/2ore, di avere ossido di zirconio, mentre per ottenere gli ossidi di alluminio, è sufficiente un ulteriore trattamento termico a basse temperature e di breve durata (400°C/ 5 min). Si è osservato, inoltre, che il trattamento termico condotto con le microonde comporta la formazione delle fasi cristalline desiderate (ossidi di alluminio e zirconio), impiegando (come per la sintesi) tempi e temperature significativamente ridotti. L’esposizione delle polveri per tempi ridotti e a temperature più basse consente di evitare la formazione di aggregati duri nelle nanopolveri finali e di contrastare il manifestarsi di fenomeni di accrescimento di grani, preservando così la “nanostruttura” delle polveri e le sue caratteristiche proprietà.

The grain-scale distribution and behaviour of melt and fluid in crystalline analogue systems

The production, segregation and migration of melt and aqueous fluids (henceforth called liquid) plays an important role for the transport of mass and energy within the mantle and the crust of the Earth. Many properties of large-scale liquid migration processes such as the permeability of a rock matrix or the initial segregation of newly formed liquid from the host-rock depends on the grain-scale distribution and behaviour of liquid. Although the general mechanisms of liquid distribution at the grain-scale are well understood, the influence of possibly important modifying processes such as static recrystallization, deformation, and chemical disequilibrium on the liquid distribution is not well constrained. For this thesis analogue experiments were used that allowed to investigate the interplay of these different mechanisms in-situ. In high-temperature environments where melts are produced, the grain-scale distribution in “equilibrium” is fully determined by the liquid fraction and the ratio between the solid-solid and the solid-liquid surface energy. The latter is commonly expressed as the dihedral or wetting angle between two grains and the liquid phase (Chapter 2). The interplay of this “equilibrium” liquid distribution with ongoing surface energy driven recrystallization is investigated in Chapter 4 and 5 with experiments using norcamphor plus ethanol liquid. Ethanol in contact with norcamphor forms a wetting angle of about 25°, which is similar to reported angles of rock-forming minerals in contact with silicate melt. The experiments in Chapter 4 show that previously reported disequilibrium features such as trapped liquid lenses, fully-wetted grain boundaries, and large liquid pockets can be explained by the interplay of the liquid with ongoing recrystallization. Closer inspection of dihedral angles in Chapter 5 reveals that the wetting angles are themselves modified by grain coarsening. Ongoing recrystallization constantly moves liquid-filled triple junctions, thereby altering the wetting angles dynamically as a function of the triple junction velocity. A polycrystalline aggregate will therefore always display a range of equilibrium and dynamic wetting angles at raised temperature, rather than a single wetting angle as previously thought. For the deformation experiments partially molten KNO3–LiNO3 experiments were used in addition to norcamphor–ethanol experiments (Chapter 6). Three deformation regimes were observed. At a high bulk liquid fraction >10 vol.% the aggregate deformed by compaction and granular flow. At a “moderate” liquid fraction, the aggregate deformed mainly by grain boundary sliding (GBS) that was localized into conjugate shear zones. At a low liquid fraction, the grains of the aggregate formed a supporting framework that deformed internally by crystal plastic deformation or diffusion creep. Liquid segregation was most efficient during framework deformation, while GBS lead to slow liquid segregation or even liquid dispersion in the deforming areas.

Catastrophic Flooding In North-Central Pennsylvania: Geomorphic Findings From The September 2011 Event And Their Significance To

Tropical Storm Lee produced 25-36 cm of rainfall in north-central Pennsylvania on September 4th through 8th of 2011. Loyalsock Creek, Muncy Creek, and Fishing Creek experienced catastrophic flooding resulting in new channel formation, bank erosion, scour of chutes, deposition/reworking of point bars and chute bars, and reactivation of the floodplain. This study was created to investigate aspects of both geomorphology and sedimentology by studying the well-exposed gravel deposits left by the flood, before these features are removed by humans or covered by vegetation. By recording the composition of gravel bars in the study area and creating lithofacies models, it is possible to understand the 2011 flooding. Surficial clasts on gravel bars are imbricated, but the lack of imbrication and high matrix content of sediments at depth suggests that surface imbrication of the largest clasts took place during hyperconcentrated flow (40-70% sediment concentration). The imbricated clasts on the surface are the largest observed within the bars. The lithofacies recorded are atypical for mixed-load stream lithofacies and more similar to glacial outburst flood lithofacies. This paper suggests that the accepted lithofacies model for mixed-load streams with gravel bedload may not always be useful for interpreting depositional systems. A flume study, which attempted to duplicate the stratigraphy recorded in the field, was run in order to better understand hyperconcentrated flows in the study area. Results from the study in the Bucknell Geology Flume Laboratory indicate that surficial imbrication is possible in hyperconcentrated conditions. After flooding the flume to entrain large amounts of sand and gravel, deposition of surficially imbricated gravel with massive or upward coarsening sedimentology occurred. Imbrication was not observed at depth. These experimental flume deposits support our interpretation of the lithofacies discovered in the field. The sizes of surficial gravel bar clasts show clear differences between chute and point bars. On point bars, gravels fine with increasing distance from the channel. Fining also occurs at the downstream end of point bars. In chute deposits, dramatic fining occurs down the axis of the chute, and lateral grain sizes are nearly uniform. Measuring the largest grain size of sandstone clasts at 8-11 kilometer intervals on each river reveals anomalies in the downstream fining trends. Gravel inputs from bedrock outcrops, tributaries, and erosion of Pleistocene outwash terraces may explain observed variations in grain size along streams either incised into the Appalachian Plateau or located near the Wisconsinan glacial boundary. Atomic Mass Spectrometry (AMS) radiocarbon dating of sediment from recently scoured features on Muncy Creek and Loyalsock Creek returned respective ages of 500 BP and 2490 BP. These dates suggest that the recurrence interval of the 2011 flooding may be several hundred to several thousand years. This geomorphic interval of recurrence is much longer then the 120 year interval calculated by the USGS using historical stream gauge records.

Estimation with Interval Censored Data in Longitudinal Studies

In biostatistical applications interest often focuses on the estimation of the distribution of a time-until-event variable T. If one observes whether or not T exceeds an observed monitoring time at a random number of monitoring times, then the data structure is called interval censored data. We extend this data structure by allowing the presence of a possibly time-dependent covariate process that is observed until end of follow up. If one only assumes that the censoring mechanism satisfies coarsening at random, then, by the curve of dimensionality, typically no regular estimators will exist. To fight the curse of dimensionality we follow the approach of Robins and Rotnitzky (1992) by modeling parameters of the censoring mechanism. We model the right-censoring mechanism by modeling the hazard of the follow up time, conditional on T and the covariate process. For the monitoring mechanism we avoid modeling the joint distribution of the monitoring times by only modeling a univariate hazard of the pooled monitoring times, conditional on the follow up time, T, and the covariates process, which can be estimated by treating the pooled sample of monitoring times as i.i.d. In particular, it is assumed that the monitoring times and the right-censoring times only depend on T through the observed covariate process. We introduce inverse probability of censoring weighted (IPCW) estimator of the distribution of T and of smooth functionals thereof which are guaranteed to be consistent and asymptotically normal if we have available correctly specified semiparametric models for the two hazards of the censoring process. Furthermore, given such correctly specified models for these hazards of the censoring process, we propose a one-step estimator which will improve on the IPCW estimator if we correctly specify a lower-dimensional working model for the conditional distribution of T, given the covariate process, that remains consistent and asymptotically normal if this latter working model is misspecified. It is shown that the one-step estimator is efficient if each subject is at most monitored once and the working model contains the truth. In general, it is shown that the one-step estimator optimally uses the surrogate information if the working model contains the truth. It is not optimal in using the interval information provided by the current status indicators at the monitoring times, but simulations in Peterson, van der Laan (1997) show that the efficiency loss is small.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.

LARGE SCALE LANDSLIDE ON THE ONTONAGON RIVER, MICHIGAN

In 2003, a large landslide occurred along the Ontonagon River, located in the Upper Peninsula of Michigan, and adjacent to US-45 in Ontonagon County. The failure took place during the springtime, when the river reached a peak discharge that was the second highest on record. The volume of the slide has been estimated to be approximately 1,400,000 cubic yards. The colluvium blocked the river, forcing a new channel to be carved around the debris. The landslide consisted of a silt layer at its base, overlain by a coarsening upward sand sequence, and finally a varved glacio-lacustrine clay with sparse dropstone inclusions making up the upper section of hillside.

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.

Mineralogical and geochemical data from five lake sediment cores of Lake Donggi Cona

Sediments of Lake Donggi Cona on the northeastern Tibetan Plateau were studied to infer changes in the lacustrine depositional environment, related to climatic and non-climatic changes during the last 19 kyr. The lake today fills a 30 X 8 km big and 95 m deep tectonic basin, associated with the Kunlun Fault. The study was conducted on a sediment-core transect through the lake basin, in order to gain a complete picture of spatiotemporal environmental change. The recovered sediments are partly finely laminated and are composed of calcareous muds with variable amounts of carbonate micrite, organic matter, detrital silt and clay. On the basis of sedimentological, geochemical, and mineralogical data up to five lithological units (LU) can be distinguished that document distinct stages in the development of the lake system. The onset of the lowermost LU with lacustrine muds above basal sands indicates that lake level was at least 39 m below the present level and started to rise after 19 ka, possibly in response to regional deglaciation. At this time, the lacustrine environment was characterized by detrital sediment influx and the deposition of siliciclastic sediment. In two sediment cores, upward grain-size coarsening documents a lake-level fall after 13 cal ka BP, possibly associated with the late-glacial Younger Dryas stadial. From 11.5 to 4.3 cal ka BP, grainsize fining in sediment cores from the profundal coring sites and the onset of lacustrine deposition at a litoral core site (2m water depth) in a recent marginal bay of Donggi Cona document lake-level rise during the early tomid-Holocene to at least modern level. In addition, high biological productivity and pronounced precipitation of carbonate micrites are consistent with warm and moist climate conditions related to an enhanced influence of summer monsoon. At 4.3 cal ka BP the lake system shifted from an aragonite- to a calcite-dominated system, indicating a change towards a fully open hydrological lake system. The younger clay-rich sediments are moreover non-laminated and lack any diagenetic sulphides, pointing to fully ventilated conditions, and the prevailing absence of lake stratification. This turning point in lake history could imply either a threshold response to insolation-forced climate cooling or a response to a non-climatic trigger, such as an erosional event or a tectonic pulse that induced a strong earthquake, which is difficult to decide from our data base.

(Table 3) Sedimentation rates of stage 1 and last glacial maximum from different Holes during cruises of RRS Discovery in 1984-1985 and 1987-1988, and RRS James Clark Ross in 1992-1993

Within the Scotia Sea, the axis of the Antarctic Circumpolar Current (ACC) is geographically confined, and sediments therefore contain a record of palaeo-flow speed uncomplicated by ACC axis migration. We outline Holocene and Last Glacial Maximum (LGM) current-controlled sedimentation using data from 3.5-kHz profiles, cores and current meter moorings. Geophysical surveys show areas of erosion and deposition controlled by Neogene basement topography. Deposition occurs in mounded sediment drifts or flatter areas, where 500-1000 m of sediment overlies acoustic basement. 3.5-kHz profiles show parallel, continuous sub-bottom reflectors with highest sedimentation rates in the centre of the drifts, and reflectors converging towards marginal zones of non-deposition. Locally, on the flanks of continental blocks (e.g. South Georgia), downslope processes are dominant. The absence of mudwaves on the sediment drifts may result from the unsteadiness of ACC flow. A core transect from the ACC axis south to the boundary with the Weddell Gyre shows a southward decrease in biogenic content, controlled by the Polar Front and the spring sea-ice edge. Both these features lay farther north at LGM. The cores have been dated by relative abundance of the radiolarian Cycladophora davisiana, and by changes in the biogenic Ba content, a palaeoproductivity indicator. Sedimentation rates range from 3 to 17 cm/ka. The grain size of Holocene sediments shows a coarsening trend from south to north, consistent with strongest bottom-current flow near the ACC axis, though interpretation is complicated by the presence of biogenic grains. Year-long current meter records indicate mean speeds from 7 cm/s in the south to 12 cm/s in the north, with benthic storm frequency increasing northwards. LGM sediments are predominantly terrigenous and show a clearer northward-coarsening trend, with well-sorted silts in the northern Scotia Sea. Assuming a constant terrigenous source, this implies stronger ACC flow at the LGM, contrasting with weaker Weddell Gyre flow deduced from earlier work.