Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations

We study a finite element scheme for the 3D Navier-Stokes equations (NSE) that globally conserves energy and helicity and, through the use of Scott-Vogelius elements, enforces pointwise the solenoidal constraints for velocity and vorticity. A complete numerical analysis is given, including proofs for conservation laws, unconditional stability and optimal convergence. We also show the method can be efficiently computed by exploiting a connection between this method, its associated penalty method, and the method arising from using grad-div stabilized Taylor-Hood elements. Finally, we give numerical examples which verify the theory and demonstrate the effectiveness of the scheme.     

Ricci solitons on Lorentzian Walker three-manifolds

We investigate Ricci solitons on Lorentzian three-manifolds (M,g _f ) admitting a parallel degenerate line field. For several classes of these manifolds, described in terms of the defining function f, the existence of non-trivial Ricci solitons is proved.     

Negative tunneling magnetoresistance by canted magnetization in MgO/NiO tunnel barriers

The influence of the insertion of an ultrathin NiO layer between the MgO barrier and the ferromagnetic electrodes in magnetic tunnel junctions has been investigated from measurements of the tunneling magnetoresistance and via x-ray magnetic circular dichroism (XMCD). The magnetoresistance shows a high asymmetry with respect to bias voltage, giving rise to a negative value of up to -16% at 2.8 K. We attribute this effect to the formation of noncollinear spin structures at the interface of the NiO layer as inferred from XMCD measurements. The magnetic moments of the interface Ni atoms tilt from their easy axis due to exchange coupling with the neighboring ferromagnetic electrode, and the tilting angle decreases with increasing NiO thickness. The experimental observations are further supported by noncollinear spin density functional calculations.     

Active coherent beam combining of diode lasers

We have demonstrated active coherent beam combination (CBC) of up to 218 semiconductor amplifiers with 38.5?W cw output using up to eleven one-dimensional 21-element individually addressable diode amplifier arrays operating at 960?nm. The amplifier array elements are slab-coupled-optical-waveguide semiconductor amplifiers (SCOWAs) set up in a master-oscillator-power-amplifier configuration. Diffractive optical elements divide the master-oscillator beam to seed multiple arrays of SCOWAs. A SCOWA was phase actuated by adjusting the drive current to each element and controlled using a stochastic-parallel-gradient-descent (SPGD) algorithm for the active CBC. The SPGD is a hill-climbing algorithm that maximizes on-axis intensity in the far field, providing phase locking without needing a reference beam.     

Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni

Chemical state X-ray photoelectron spectroscopic analysis of first row transition metals and their oxides and hydroxides is challenging due to the complexity of their 2p spectra resulting from peak asymmetries, complex multiplet splitting, shake-up and plasmon loss structure, and uncertain, overlapping binding energies. Our previous paper [M.C. Biesinger et al., Appl. Surf. Sci. 257 (2010) 887-898.] in which we examined Sc, Ti, V, Cu and Zn species, has shown that all the values of the spectral fitting parameters for each specific species, i.e. binding energy (eV), full wide at half maximum (FWHM) value (eV) for each pass energy, spin-orbit splitting values and asymmetric peak shape fitting parameters, are not all normally provided in the literature and data bases, and are necessary for reproducible, quantitative chemical state analysis. A more consistent, practical and effective approach to curve fitting was developed based on a combination of (1) standard spectra from quality reference samples, (2) a survey of appropriate literature databases and/or a compilation of literature references and (3) specific literature references where fitting procedures are available. This paper extends this approach to the chemical states of Cr, Mn, Fe, Co and Ni metals, and various oxides and hydroxides where intense, complex multiplet splitting in many of the chemical states of these elements poses unique difficulties for chemical state analysis. The curve fitting procedures proposed use the same criteria as proposed previously but with the additional complexity of fitting of multiplet split spectra which has been done based on spectra of numerous reference materials and theoretical XPS modeling of these transition metal species. Binding energies, FWHM values, asymmetric peak shape fitting parameters, multiplet peak separation and peak area percentages are presented. The procedures developed can be utilized to remove uncertainties in the analysis of surface states in nano-particles, corrosion, catalysis and surface-engineered materials.     

Synthesis and characterization of near-infrared absorbing benzannulated aza-BODIPY dyes

A series of novel aza‐diisoindolmethine dyes 9 with six different aryl and heteroaryl groups at the indole moiety have been synthesized by the addition of aryl Grignard compounds to phthalodinitrile and subsequent reaction with formamide. A plausible reaction mechanism, through a Leuckart–Wallach‐type reduction has been confirmed by means of DFT calculations of the related transition and intermediate states. The corresponding boron difluoride complexes ( 10) of 9 were prepared in a subsequent reaction step and the spectroscopic and electrochemical properties of 9 and 10 have been investigated both experimentally and theoretically. The aza‐diisoindolmethines 9 exhibit an absorption maximum in the range from 615 to 720 nm, whereas the complexes 10 show a bathochromically shifted absorption maximum between 681 and 793 nm. Measurements of 9 and 10 by cyclic voltammetry display fully reversible redox waves for the reduction and oxidation with higher potentials for 10 . From the measured redox potentials, the HOMO and LUMO energy levels were calculated for 9 and 10 . The frontier orbital energies, the energies of the absorption bands, as well as the orbitals involved in the absorption process were calculated with DFT and compared to the measured results of 9 and 10 . The absorption maximum can be related to an intense HOMO–LUMO transition and the more‐pronounced stabilization of the LUMO upon complexation is the origin of the bathochromic shift of the absorption. Additionally, single‐crystal structures for two species, 10 d and 10 f , are reported.     

Unified syntheses of cavicularin and riccardin C: addressing the synthesis of an arene adopting a boat configuration

Concise syntheses of the natural products cavicularin (ten steps) and riccardin C (seven steps) are reported. Key features of the new synthetic route are a convergent strategy to assemble acyclic precursors and a sequence of regioselective reduction and halogenation steps to facilitate Wittig macrocyclisation and transannular ring contraction reactions.     

Automated Assessment of Cancer Drug Efficacy On Breast Tumor Spheroids in Aggrewell™400 Plates Using Image Cytometry

Journal of Fluorescence - Tumor spheroid models have proven useful in the study of cancer cell responses to chemotherapeutic compounds by more closely mimicking the 3-dimensional nature of tumors...     

Temperature Fluctuations for a System in Contact with a Heat Bath

The problem of how to define and compute temperature fluctuations for a small system in contact with a heat bath is an old one and originates from Einstein’s theory of Brownian motion. Only for a small enough system does their relative size allow a straightforward experimental verification. Here we focus on a mesoscopic system in contact with a heat bath at temperature T _° and provide a self-consistent argument showing as to why, and in what sense, the observable standard deviation of temperature from T _° equals $\sqrt{k_{\rm B}/C}T_{\circ}$ where C is the mesoscopic system’s heat capacity. Our argument is based on ergodic decomposition, a simple fact that holds for a system in thermodynamic equilibrium and away from phase-transition points. In this way we close a line of argument opened by de Haas-Lorentz a century ago.     

More about empirical evaluation of formal theory†

The purpose of this discussion is to transform the implicit equilibrium assumption endemic to network analysis into an explicit instrument for such analysis. I propose a formal model that brings together Coleman's restriction of Walras’ general equilibrium model and recent developments in describing the “social topology” of a multiple network system of actors such that a class of relational equilibria is defined. The specific equilibrium expected in a system is a function of the previously existing stratification of actors in the system. Corresponding to multiple observed networks, the model generates multiple equilibrium networks. The structural analysis of the observed networks can therefore be repeated on the equilibrium networks so as to assess the extent to which the analysis would differ if the observed relations were actually in an equilibrium state. Numerical illustration is provided by an analysis of alternative relational equilibria in the system of elite experts in methodological and mathematical sociology as such a system existed in 1975.