Traces for star products on the dual of a Lie algebra

In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is unimodular. In a next step we show that the traces of the BCH star-product are given by the \ad-invariant functionals. Particular examples are the integration over coadjoint orbits. We show that for a compact Lie group and a regular orbit one can even achieve that this integration becomes a positive trace functional. In this case we explicitly describe the corresponding GNS representation. Finally we discuss how invariant deformations on a group can be used to induce deformations of spaces where the group acts on.Comment: 18 pages, LaTeX2e. Updated reference

Infinitesimal deformations of a formal symplectic groupoid

Given a formal symplectic groupoid $G$ over a Poisson manifold $(M, \pi_0)$, we define a new object, an infinitesimal deformation of $G$, which can be thought of as a formal symplectic groupoid over the manifold $M$ equipped with an infinitesimal deformation $\pi_0 + \epsilon \pi_1$ of the Poisson bivector field $\pi_0$. The source and target mappings of a deformation of $G$ are deformations of the source and target mappings of $G$. To any pair of natural star products $(\ast, \tilde\ast)$ having the same formal symplectic groupoid $G$ we relate an infinitesimal deformation of $G$. We call it the deformation groupoid of the pair $(\ast, \tilde\ast)$. We give explicit formulas for the source and target mappings of the deformation groupoid of a pair of star products with separation of variables on a Kaehler- Poisson manifold. Finally, we give an algorithm for calculating the principal symbols of the components of the logarithm of a formal Berezin transform of a star product with separation of variables. This algorithm is based upon some deformation groupoid.Comment: 22 pages, the paper is reworked, new proofs are adde

The Stability of Bredigite and Other Ca-Mg Silicates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65844/1/j.1151-2916.1980.tb10213.x.pd

Nanometer-scale characterization of laser-driven compression, shocks, and phase transitions, by x-ray scattering using free electron lasers

We study the feasibility of using small angle X-ray scattering (SAXS) as a new experimental diagnostic for intense laser-solid interactions. By using X-ray pulses from a hard X-ray free electron laser, we can simultaneously achieve nanometer and femtosecond resolution of laser-driven samples. This is an important new capability for the Helmholtz international beamline for extreme fields at the high energy density endstation currently built at the European X-ray free electron laser. We review the relevant SAXS theory and its application to transient processes in solid density plasmas and report on first experimental results that confirm the feasibility of the method. We present results of two test experiments where the first experiment employs ultra-short laser pulses for studying relativistic laser plasma interactions, and the second one focuses on shock compression studies with a nanosecond laser system

Nanoscale transient magnetization gratings excited and probed by femtosecond extreme ultraviolet pulses

We utilize coherent femtosecond extreme ultraviolet (EUV) pulses derived from a free electron laser (FEL) to generate transient periodic magnetization patterns with periods as short as 44 nm. Combining spatially periodic excitation with resonant probing at the dichroic M-edge of cobalt allows us to create and probe transient gratings of electronic and magnetic excitations in a CoGd alloy. In a demagnetized sample, we observe an electronic excitation with 50 fs rise time close to the FEL pulse duration and ~0.5 ps decay time within the range for the electron-phonon relaxation in metals. When the experiment is performed on a sample magnetized to saturation in an external field, we observe a magnetization grating, which appears on a sub-picosecond time scale as the sample is demagnetized at the maxima of the EUV intensity and then decays on the time scale of tens of picoseconds via thermal diffusion. The described approach opens prospects for studying dynamics of ultrafast magnetic phenomena on nanometer length scales

Global Drivers on Southern Ocean Ecosystems: Changing Physical Environments and Anthropogenic Pressures in an Earth System

Copyright © 2020 Morley, Abele, Barnes, Cárdenas, Cotté, Gutt, Henley, Höfer, Hughes, Martin, Moffat, Raphael, Stammerjohn, Suckling, Tulloch, Waller and Constable. The manuscript assesses the current and expected future global drivers of Southern Ocean (SO) ecosystems. Atmospheric ozone depletion over the Antarctic since the 1970s, has been a key driver, resulting in springtime cooling of the stratosphere and intensification of the polar vortex, increasing the frequency of positive phases of the Southern Annular Mode (SAM). This increases warm air-flow over the East Pacific sector (Western Antarctic Peninsula) and cold air flow over the West Pacific sector. SAM as well as El Niño Southern Oscillation events also affect the Amundsen Sea Low leading to either positive or negative sea ice anomalies in the west and east Pacific sectors, respectively. The strengthening of westerly winds is also linked to shoaling of deep warmer water onto the continental shelves, particularly in the East Pacific and Atlantic sectors. Air and ocean warming has led to changes in the cryosphere, with glacial and ice sheet melting in both sectors, opening up new ice free areas to biological productivity, but increasing seafloor disturbance by icebergs. The increased melting is correlated with a salinity decrease particularly in the surface 100 m. Such processes could increase the availability of iron, which is currently limiting primary production over much of the SO. Increasing CO2 is one of the most important SO anthropogenic drivers and is likely to affect marine ecosystems in the coming decades. While levels of many pollutants are lower than elsewhere, persistent organic pollutants (POPs) and plastics have been detected in the SO, with concentrations likely enhanced by migratory species. With increased marine traffic and weakening of ocean barriers the risk of the establishment of non-indigenous species is increased. The continued recovery of the ozone hole creates uncertainty over the reversal in sea ice trends, especially in the light of the abrupt transition from record high to record low Antarctic sea ice extent since spring 2016. The current rate of change in physical and anthropogenic drivers is certain to impact the Marine Ecosystem Assessment of the Southern Ocean (MEASO) region in the near future and will have a wide range of impacts across the marine ecosystem

Haplotype Structure of the ENPP1 Gene and Nominal Association of the K121Q Missense Single Nucleotide Polymorphism With Glycemic Traits in the Framingham Heart Study

OBJECTIVE—A recent meta-analysis demonstrated a nominal association of the ectonucleotide pyrophosphatase phosphodiesterase 1 (ENPP1) K→Q missense single nucleotide polymorphism (SNP) at position 121 with type 2 diabetes. We set out to confirm the association of ENPP1 K121Q with hyperglycemia, expand this association to insulin resistance traits, and determine whether the association stems from K121Q or another variant in linkage disequilibrium with it

Configuration of the Northern Antarctic Peninsula Ice Sheet at LGM based on a new synthesis of seabed imagery

We present a new seafloor map for the northern Antarctic Peninsula (AP), including swath multibeam data sets from five national programs. Our map allows for the examination and interpretation of Last Glacial Maximum (LGM) paleo-ice-flow paths developed on the seafloor from the preservation of mega-scale glacial lineations, drumlinized features, and selective linear erosion. We combine this with terrestrial observations of flow direction to place constraints on ice divides and ice domes on the AP continental shelf during the LGM time interval. The results show a flow bifurcation as ice exits the Larsen B embayment. Flow emanating off the Seal Nunataks (including Robertson Island) is directed toward the southeast, then eastward as the flow transits toward the Robertson Trough. A second, stronger “streaming flow” is directed toward the southeast, then southward as ice overflowed the tip of the Jason Peninsula to reach the southern perimeter of the embayment. Our reconstruction also refines the extent of at least five other distinct paleo-icestream systems that, in turn, serve to delineate seven broad regions where contemporaneous ice domes must have been centered on the continental shelf at LGM. Our reconstruction is more detailed than other recent compilations because we followed specific ice-flow indicators and have kept tributary flow paths parallel

Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm

BACKGROUND: Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available. METHODS: A formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data. RESULTS: The degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5–5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation. CONCLUSION: Dimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms