Lax pair tensors in arbitrary dimensions

A recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and coupling-constant metamorphosis to obtain a geometric Lax formulation. We also exploit the results to construct integrable spacetimes, satisfying the weak energy condition.Comment: 8 pages, uses IOP style files. Minor correction. Submitted to J. Phys

Exact relativistic stellar models with liquid surface. I. Generalizing Buchdahl's n=1n=1 polytrope

A family of exact relativistic stellar models is described. The family generalizes Buchdahl's n=1 polytropic solution. The matter content is a perfect fluid and, excluding Buchdahl's original model, it behaves as a liquid at low pressures in the sense that the energy density is non-zero in the zero pressure limit. The equation of state has two free parameters, a scaling and a stiffness parameter. Depending on the value of the stiffness parameter the fluid behaviour can be divided in four different types. Physical quantities such as masses, radii and surface redshifts as well as density and pressure profiles are calculated and displayed graphically. Leaving the details to a later publication, it is noted that one of the equation of state types can quite accurately approximate the equation of state of real cold matter in the outer regions of neutron stars. Finally, it is observed that the given equation of state does not admit models with a conical singularity at the center.Comment: 19 pages, 12 figures (16 eps files), LaTeX2e with the standard packages amssymb, amsmath, graphicx, subfigure, psfra

Lax pair tensors and integrable spacetimes

The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation -- the three-particle open Toda lattice -- is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.Comment: 10 pages, LaTe

On the Use of Blanketed Atmospheres as Boundary Conditions for Stellar Evolutionary Models

Stellar models have been computed for stars having [Fe/H] = 0.0 and -2.0 to determine the effects of using boundary conditions derived from the latest MARCS model atmospheres. The latter were fitted to the interior models at both the photosphere and at tau = 100, and at least for the 0.8-1.0 solar mass stars considered here, the resultant evolutionary tracks were found to be nearly independent of the chosen fitting point. Particular care was taken to treat the entire star as consistently as possible; i.e., both the interior and atmosphere codes assumed the same abundances and the same treatment of convection. Tracks were also computed using either the classical gray T(tau,T_eff) relation or that derived by Krishna Swamy (1966) to derive the boundary pressure. The latter predict warmer giant branches (by ~150 K) at solar abundances than those based on gray or MARCS atmospheres, which happens to be in good agreement with the inferred temperatures of giants in the open cluster M67 from the latest (V-K)-T_eff relations. Most of the calculations assumed Z=0.0125 (Asplund et al.), though a few models were computed for Z=0.0165 (Grevesse & Sauval) to determine the dependence of the tracks on Z_\odot. Grids of "scaled solar, differentially corrected" (SDC) atmospheres were also computed to try to improve upon theoretical MARCS models. When they were used as boundary conditions, the resultant tracks agreed very well with those based on a standard scaled-solar (e.g., Krishna Swamy) T(tau,T_eff) relation, independently of the assumed metal abundance. Fits of isochrones to the C-M diagram of the [Fe/H] = -2 globular cluster M68 were examined, as was the possibility that the mixing-length parameter varies with stellar parameters.Comment: 54 pages, including 20 figures and 3 tables; accepted (July 2007) for publication in the Astrophysical Journa

Combining population genomics and ecological niche modeling to assess taxon limits between Carex jemtlandica and C. lepidocarpa

Carex section Ceratocystis (Cyperaceae) is a group of recently evolved plant species, in which hybridization is frequent, introgression is documented, taxonomy is complex, and morphological boundaries are vague. Within this section, a unified taxonomic treatment of the Carex jemtlandica-Carex lepidocarpa species complex does not exist, and Norway may currently be the sole country accepting species rank for both. Carex jemtlandica is mainly confined to Fennoscandia and is thus a Fennoscandian conservation responsibility. This motivated us to test the principal hypothesis that both C. jemtlandica and C. lepidocarpa represent evolutionary significant units, and that both deserve their current recognition at species level. We investigated their evolutionary distinctiveness in Norway, using restriction site-associated DNA sequencing and ecological niche modeling. Our genomic results reveal two genetic clusters, largely corresponding to C. jemtlandica and C. lepidocarpa that also remain distinct in sympatry, despite clear indications of ongoing hybridization and introgression. The ecological niche modeling suggests that they occupy different environmental niches. Jointly, our results clearly show that C. jemtlandica and C. lepidocarpa represent separately evolving entities that should qualify recognition as evolutionary significant units. Given the high level of introgression compared to other hybridizing species pairs in Carex we recommend treating C. jemtlandica as a subspecies of C. lepidocarpa.Peer reviewe

The History of Flow Chemistry at Eli Lilly and Company

Flow chemistry was initially used for speed to early phase material delivery in the development laboratories, scaling up chemical transformations that we would not or could not scale up batch for safety reasons. Some early examples included a Newman Kwart Rearrangement, Claisen rearrangement, hydroformylation, and thermal imidazole cyclization. Next, flow chemistry was used to enable safe scale up of hazardous chemistries to manufacturing plants. Examples included high pressure hydrogenation, aerobic oxidation, and Grignard formation reactions. More recently, flow chemistry was used in Small Volume Continuous (SVC) processes, where highly potent oncolytic molecules were produced by fully continuous processes at about 10 kg/day including reaction, extraction, distillation, and crystallization, using disposable equipment contained in fume hoods

Diving And Amphibious Behaviour In Free-Living Crocodylus porosus

Twelve estuarine crocodiles (6-51 kg) were fitted with recording back packs in order to study the longevity, frequency and daily/tidal rhythm of natural dives by crocodiles free-living in their familiar habitat. Despite disinterest shown by captive crocodiles in removing their jackets in tank trials, all but one of the seven crocodiles recaptured 5-16 days after release had shed their jackets and recorders. Results from the 9.75 kg animal showed that it had a prolonged emergence during each daylight low tide (basking?), that it dived mainly in daylight hours (feeding?), predominantly in the upper half of the tide and that most dives were of very short duration (1-5 minutes). Even the longest dive, 30 minutes, was well within the aerobic capabilities of a crocodile this size. Although these results are from a single animal, and may turn out to be quite atypical, if attachment problems are solved, the method has clear potential for revealing much about the daily activity patterns of free-ranging crocodiles and other animals

A stock-flow cohort model of the national car fleet

Purpose Various regulatory and fiscal policy instruments are in force to reduce the amount of greenhouse gases and local pollutants emitted by private cars. The incentives operate primarily—or exclusively—on the newest generation of cars. But how fast will technological developments affecting new vehicle models penetrate into the car fleet? The speed at which the adverse effects of private car use will be mitigated through the normal vehicle renewal process, or through an accelerated one, carries considerable interest. Suitable modelling tools are needed. This paper aims to demonstrate the usefulness and flexibility of a bottom-up stock-flow modelling approach to private car fleet forecasting and policy analysis. Methods In the BIG model of the Norwegian automobile fleet, the annual stocks and flows characterising the car fleet are specified as matrices of 682 mutually exclusive and exhaustive cells, formed by cross-tabulations between 22 vehicle segments and 31 age classes. New car registrations follow from a disaggregate generic discrete choice model based on two decades of complete sales data for individual passenger car models. Results Example projections are presented onto the 2050 horizon under a low carbon fiscal policy scenario as well as a business-as-usual scenario. The fiscal policy is seen to make a large difference in terms of long term fuel consumption and CO2 emissions. Conclusions Stock-flow cohort modelling of the automobile fleet is a powerful and handy tool for policy analysis. Even quite simple and straightforward accounting relations may provide important insights into the dynamics of fleet development. It is possible to incorporate, into the stock-flow modelling framework, interesting and useful behavioural relations, explaining aggregate automobile ownership and travel demand, scrapping and survival rates, or consumer choice in the market for new cars

Association of Genetic Markers with CSF Oligoclonal Bands in Multiple Sclerosis Patients

Objective:to explore the association between genetic markers and Oligoclonal Bands (OCB) in the Cerebro Spinal Fluid (CSF) of Italian Multiple Sclerosis patients.Methods:We genotyped 1115 Italian patients for HLA-DRB1*15 and HLA-A*02. In a subset of 925 patients we tested association with 52 non-HLA SNPs associated with MS susceptibility and we calculated a weighted Genetic Risk Score. Finally, we performed a Genome Wide Association Study (GWAS) with OCB status on a subset of 562 patients. The best associated SNPs of the Italian GWAS were replicated in silico in Scandinavian and Belgian populations, and meta-analyzed.Results:HLA-DRB1*15 is associated with OCB+: p = 0.03, Odds Ratio (OR) = 1.6, 95% Confidence Limits (CL) = 1.1-2.4. None of the 52 non-HLA MS susceptibility loci was associated with OCB, except one SNP (rs2546890) near IL12B gene (OR: 1.45; 1.09-1.92). The weighted Genetic Risk Score mean was significantly (p = 0.0008) higher in OCB+ (7.668) than in OCB- (7.412) patients. After meta-analysis on the three datasets (Italian, Scandinavian and Belgian) for the best associated signals resulted from the Italian GWAS, the strongest signal was a SNP (rs9320598) on chromosome 6q (p = 9.4×10-7) outside the HLA region (65 Mb).Discussion:genetic factors predispose to the development of OCB