Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity

Summary. We consider a finite-element-in-space, and quadrature-in-time-discretization of a compressible linear quasistatic viscoelasticity problem. The spatial discretization uses a discontinous Galerkin finite element method based on polynomials of degree r—termed DG(r)—and the time discretization uses a trapezoidal-rectangle rule approximation to the Volterra (history) integral. Both semi- and fully-discrete a priori error estimates are derived without recourse to Gronwall's inequality, and therefore the error bounds do not show exponential growth in time. Moreover, the convergence rates are optimal in both h and r providing that the finite element space contains a globally continuous interpolant to the exact solution (e.g. when using the standard ^k polynomial basis on simplicies, or tensor product polynomials, ^k, on quadrilaterals). When this is not the case (e.g. using ^k on quadri-laterals) the convergence rate is suboptimal in r but remains optimal in h. We also consider a reduction of the problem to standard linear elasticity where similarly optimal a priori error estimates are derived for the DG(r) approximation. Mathematics Subject Classification (2000):65N36Shaw and Whiteman would like to acknowledge the support of the US Army Research Office, Grant #DAAD19-00-1-0421, and the UK EPSRC, Grant #GR/R10844/01. Whiteman would also like to acknowledge support from TICAM in the form of Visiting Research Fellowships.     

Temperature Dependence for the Relative Raman Cross Section of the Ammonia/Water Complex

The Raman spectra of aqueous ammonia solutions have been obtained between -40 and 25 degrees C. The Raman spectrum of neat water was also obtained at 25 degrees C and is characterized by two broad peaks observed at 3200 and 3400 cm(-1). The spectrum due to water is subtracted to determine the NH(3) spectrum at all temperatures. In ammonia-water solutions, the spectrum shows three features at measured displacements of 3250, 3316, and 3400 cm(-1). The feature at 3316 cm(-1) is assigned to the Q branch of the symmetric stretch. The broad, weak features at 3250 and 3400 cm(-1), previously assigned to rotational bands, are assigned to combination bands. The NH(3) combination bands are assigned by comparing with sum frequency generation (SFG) experiments, monitoring changes with temperature, and analyzing the polarization data. The rotational structure of the Q band is also discussed. As the temperature is lowered from 25 to -40 degrees C, an increase in the Raman intensity is observed for all bands. The relative Raman scattering cross section is determined from the numerically integrated area of the NH(3) Q branch at each temperature. Copyright 2001 Academic Press.     

Focusing in microlenses close to a wavelength in diameter

Light focused from air into a spherical microlens is affected by diffraction at the lens surface as its diameter approaches the wavelength of light. Through an extension of Mie theory, we show that a converging wave that is incident upon a Si microlens with a diameter less than approximately 4lambda creates a spot as much as 25% smaller than predicted with vector diffraction theory. Si microlenses only a wavelength in diameter are shown to be virtually insensitive to variations in the maximum illumination angle, and changes in index of refraction are not found to cause the proportional changes in spot size that would be expected from vector diffraction theory.     

High pressure behavior of ZrW2O8: Gruneisen parameter and thermal properties

High pressure Raman spectroscopic studies are carried out on negative thermal expansion material ZrW2O8. The system exhibits amorphization at 2.2+/-0.3 GPa via an intermediate orthorhombic phase. In the cubic phase most modes below 50 meV are found to have negative Gruneisen parameter. Using the reported phonon density of states thermal properties are calculated and compared with the reported results. In contrast to the earlier belief, the present results show that modes of energies much higher than 10 meV also contribute substantially to the negative thermal expansion.     

Progress in direct-drive inertial confinement fusion research at the laboratory for laser energetics

Direct-drive inertial confinement fusion (ICF) is expected to demonstrate high gain on the National Ignition Facility (NIF) in the next decade and is a leading candidate for inertial fusion energy production. The demonstration of high areal densities in hydrodynamically scaled cryogenic DT or D₂ implosions with neutron yields that are a significant fraction of the “clean” 1-D predictions will validate the ignition-equivalent direct-drive target performance on the OMEGA laser at the Laboratory for Laser Energetics (LLE). This paper highlights the recent experimental and theoretical progress leading toward achieving this validation in the next few years. The NIF will initially be configured for X-ray drive and with no beams placed at the target equator to provide a symmetric irradiation of a direct-drive capsule. LLE is developing the “polar-direct-drive” (PDD) approach that repoints beams toward the target equator. Initial 2-D simulations have shown ignition. A unique “Saturn-like” plastic ring around the equator refracts the laser light incident near the equator toward the target, improving the drive uniformity. LLE is currently constructing the multibeam, 2.6-kJ/beam, petawatt laser system OMEGA EP. Integrated fast-ignition experiments, combining the OMEGA EP and OMEGA Laser Systems, will begin in FY08.     

Phenotype and in vitro function of mature MDDC generated from cryopreserved PBMC of cancer patients are equivalent to those from healthy donors

Background  

Monocyte-derived-dendritic-cells (MDDC) are the major DC type used in vaccine-based clinical studies for a variety of cancers. In order to assess whether in vitro differentiated MDDC from cryopreserved PBMC of cancer patients are functionally distinct from those of healthy donors, we compared these cells for their expression of co-stimulatory and functional markers. In addition, the effect of cryopreservation of PBMC precursors on the quality of MDDC was also evaluated using samples from healthy donors.     

Separation of single‐walled carbon nanotubes with aromatic group functionalized polymethacrylates and building blocks contribution to the enrichment

We previously showed that in N,N‐dimethylformamide (DMF), poly(9‐anthracenylmethyl methacrylate) (PAMMA) and poly(2‐naphthylmethacrylate) selectively disperse semiconducting and metallic single‐walled carbon nanotubes (SWNTs), respectively. We have also proposed a new noncovalent polymer interaction based on photon induced dipole–dipole interaction to account for the metallicity‐based selectivity. In this article, we investigate two other polymethacrylates, that is, poly(benzyl methacrylate) (PBMA) and poly(methylmethacrylate)‐co‐(9‐anthracenylmethyl acrylate) (PMMA‐c‐PAMA) in the light of our previously proposed photon‐induced dipole–dipole interaction. We find that PBMA and PMM‐c‐PAMMA in DMF show no metallicity selectivity. The different selective behavior of the four polymers in DMF manifests the decisive influence of the side aromatic group in determining their metallicity selectivity. The nonpreferential energy transfer from PMMA‐c‐PAMA to SWNTs and the nonoverlap of PBMA fluorescence (in the ultraviolet range) with nanotube absorption account for their nonselectivity of specific nanotube species. Further, the parallel relationship between the diameters of extracted tube species and the affinity between polymers and solvents suggests the leading role of the polymeric conformation on the diameter selectivity. A sufficient (i.e., 2 weeks) standing time of the SWNTs solution after sonication, during which the polymers presumably optimize their conformation to the SWNTs, was found to be essential to the enrichment. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Crystallization and stereocomplexation behavior of poly(D‐ and L‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) block copolymers

The thermal properties, crystallization, and morphology of amphiphilic poly(D ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PDLA‐b‐PDMAEMA) and poly (L ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PLLA‐b‐PDMAEMA) copolymers were studied and compared to those of the corresponding poly(lactide) homopolymers. Additionally, stereocomplexation of these copolymers was studied. The crystallization kinetics of the PLA blocks was retarded by the presence of the PDMAEMA block. The studied copolymers were found to be miscible in the melt and the glassy state. The Avrami theory was able to predict the entire crystallization range of the PLA isothermal overall crystallization. The melting points of PLDA/PLLA and PLA/PLA‐b‐PDMAEMA stereocomplexes were higher than those formed by copolymer mixtures. This indicates that the PDMAEMA block is influencing the stability of the stereocomplex structures. For the low molecular weight samples, the stereocomplexes particles exhibited a conventional disk‐shape structure and, for high molecular weight samples, the particles displayed unusual star‐like shape morphology. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1397–1409, 2011     

An overview of the diversity represented in commercially-available databases

Molecular Diversity -