Error analysis of discontinuous Galerkin discretizations of a class of linear wave-type problems

In this paper we consider central fluxes discontinuous Galerkin space discretizations of a general class of wave-type equations of Friedrichs’ type. This class includes important examples such as Maxwell’s equations and wave equations. We prove an optimal error bound which holds under suitable regularity assumptions on the solution. Our analysis is performed in a framework of evolution equations on a Hilbert space and thus allows for the combination with various time integration schemes

Korn's second inequality and geometric rigidity with mixed growth conditions

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $L^p+L^q$ and in $L^{p,q}$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces

Introduction to special section on The U.S. IOOS Coastal and Ocean Modeling Testbed

Strong and strategic collaborations among experts from academia, federal operational centers, and industry have been forged to create a U.S. IOOS Coastal and Ocean Modeling Testbed (COMT). The COMT mission is to accelerate the transition of scientific and technical advances from the coastal and ocean modeling research community to improved operational ocean products and services. This is achieved via the evaluation of existing technology or the development of new technology depending on the status of technology within the research community. The initial phase of the COMT has addressed three coastal and ocean prediction challenges of great societal importance: estuarine hypoxia, shelf hypoxia, and coastal inundation. A fourth effort concentrated on providing and refining the cyberinfrastructure and cyber tools to support the modeling work and to advance interoperability and community access to the COMT archive. This paper presents an overview of the initiation of the COMT, the findings of each team and a discussion of the role of the COMT in research to operations and its interface with the coastal and ocean modeling community in general. Detailed technical results are presented in the accompanying series of 16 technical papers in this special issue

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

The EROS2 search for microlensing events towards the spiral arms: the complete seven season results

The EROS-2 project has been designed to search for microlensing events towards any dense stellar field. The densest parts of the Galactic spiral arms have been monitored to maximize the microlensing signal expected from the stars of the Galactic disk and bulge. 12.9 million stars have been monitored during 7 seasons towards 4 directions in the Galactic plane, away from the Galactic center. A total of 27 microlensing event candidates have been found. Estimates of the optical depths from the 22 best events are provided. A first order interpretation shows that simple Galactic models with a standard disk and an elongated bulge are in agreement with our observations. We find that the average microlensing optical depth towards the complete EROS-cataloged stars of the spiral arms is $\bar{\tau} =0.51\pm .13\times 10^{-6}$, a number that is stable when the selection criteria are moderately varied. As the EROS catalog is almost complete up to $I_C=18.5$, the optical depth estimated for the sub-sample of bright target stars with $I_C<18.5$ ($\bar{\tau}=0.39\pm >.11\times 10^{-6}$) is easier to interpret. The set of microlensing events that we have observed is consistent with a simple Galactic model. A more precise interpretation would require either a better knowledge of the distance distribution of the target stars, or a simulation based on a Galactic model. For this purpose, we define and discuss the concept of optical depth for a given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic

The Promigratory Activity of the Matricellular Protein Galectin-3 Depends on the Activation of PI-3 Kinase

Expression of galectin-3 is associated with sarcoma progression, invasion and metastasis. Here we determined the role of extracellular galectin-3 on migration of sarcoma cells on laminin-111. Cell lines from methylcholanthrene-induced sarcomas from both wild type and galectin-3−/− mice were established. Despite the presence of similar levels of laminin-binding integrins on the cell surface, galectin-3−/− sarcoma cells were more adherent and less migratory than galectin-3+/+ sarcoma cells on laminin-111. When galectin-3 was transiently expressed in galectin-3−/− sarcoma cells, it inhibited cell adhesion and stimulated the migratory response to laminin in a carbohydrate-dependent manner. Extracellular galectin-3 led to the recruitment of SHP-2 phosphatase to focal adhesion plaques, followed by a decrease in the amount of phosphorylated FAK and phospho-paxillin in the lamellipodia of migrating cells. The promigratory activity of extracellular galectin-3 was inhibitable by wortmannin, implicating the activation of a PI-3 kinase dependent pathway in the galectin-3 triggered disruption of adhesion plaques, leading to sarcoma cell migration on laminin-111

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm–Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results)