Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. Th...

We propose and analyze a Multilevel Richardson-Romberg (ML2R) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pag07] and the variance control resulting from the stratification introduced in the Multilevel Monte Carlo (MLMC) method (see [Gil08, Hei01]). Thus, in standard frameworks like discretization schemes of diffusion proc...

Knutson, Tao, and Woodward [KTW04] formulated a Littlewood–Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil [Vak06] and Wheeler–Zinn-Justin [WZ16] have found additional triangular puzzle pieces that allow one to express structure constants for K-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlew...

We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson...

For mixture models with unknown number of components, Bayesian approaches, as considered by Escobar and West (1995) and Richardson and Green (1997), are reconciled here through a simple Gibbs sampling approach. Specifically, we consider exactly the same direct set up as used by Richardson and Green (1997), but put Dirichlet process prior on the mixture components; the latter has also been used ...

Monoclinic crystals of native bovine superoxide dismutase and its monocyano derivative were studied by means of electron paramagnetic resonance spectroscopy. Through computer simulation of the spectra, the directions of the principal axes of the magnetic tensors (g and A) have been found with respect to the crystal principal axes and with respect to the positions of atoms bear the Cu(II) as pre...

The taxonomy of Antarctic fishes has been predominantly based on morphological characteristics rather than on genetic criteria. A typical example is the Notothenia group, which includes N. coriiceps Richardson, 1844, N. neglecta Nybelin, 1951 and N. rossii Richardson, 1844. The Polymerase Chain Reaction and Restriction Fragment Length Polymorphism (PCR-RFLP) technique was used to determine whet...

Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient V ′ can only destabilize a stably stratified medium with squared Brunt–Väisälä frequency N 2 if V ′2/4 > N2. We find this is no longer true when the medium is a magn...

Experimental data from four field campaigns are used to explore the variability of the bulk Richardson number of the entire planetary boundary layer (PBL), Ribc, which is a key parameter for calculating the PBL height (PBLH) in numerical weather and climate models with the bulk Richardson number method. First, the PBLHs of three different thermally stratified boundary layers (i.e., strongly sta...

We show that the Littlewood-Richardson coeecients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for aane symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in 21] in terms of ribbon tableaux.