Large eddy simulation of turbulence in engineering applications

Flows of engineering interest which have been investigated with the large eddy simulation (LES) technique are discussed. Using this technique the filtered Navier-Stokes equations are solved to simulate the three-dimensional unsteady motion. Not only the statistically-averaged fields, but in addition, the spatial and temporal variations in the flow fields can be examined. Grids are equidistant in the three coordinate directions and typically consist of 150,000 to 200,000 mesh cells. Examples of flows include the turbulent boundary layer with a sudden change in the freestream pressure gradient and the separating and reattaching flow behind a rearward-facing step. Results which illustrate the large-scale structure of these two high Reynolds number turbulent flows are discussed in the present paper.     

Hom-Lie quadratic and Pinczon Algebras

Presenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.     

Algèbre Pré-Gerstenhaber à homotopie près

This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations . and $[,]$. An important example of such a structure is the Gerstenhaber algebra (i.e. commutatitve structure with degree 0 and Lie structure with degree ?1). The notion of Gerstenhaber algebra up to homotopy ($G_{\infty }$ algebra) is known: it is a codifferential bicogebra.Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing a similar construction for a $\text{pre}{G}_{\infty }$ algebra.Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts.     

A third order partial differential equation for isotropic boundary based triangular Bézier surface generation

We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bézier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bézier surfaces.     

Yolk-shell gold nanoparticles as model materials for support-effect studies in heterogeneous catalysis: Au, @C and Au, @ZrO2 for CO oxidation as an example

The use of nanostructured yolk-shell materials offers a way to discriminate support and particle-size effects for mechanistic studies in heterogeneous catalysis. Herein, gold yolk-shell materials have been synthesized and used as model catalysts for the investigation of support effects in CO oxidation. Carbon has been selected as catalytically inert support to study the intrinsic activity of the gold nanoparticles, and for comparison, zirconia has been used as oxidic support. Au, @C materials have been synthesized through nanocasting using two different nonporous-core@mesoporous-shell exotemplates: Au@SiO(2)@ZrO(2) and Au@SiO(2)@m-SiO(2). The catalytic activity of Au, @C with a gold core of about 14 nm has been evaluated and compared with Au, @ZrO(2) of the same gold core size. The strong positive effect of metal oxide as support material on the activity of gold has been proved. Additionally, size effects were investigated using carbon as support to determine only the contribution of the nanoparticle size on the catalytic activity of gold. Therefore, Au, @C with a gold core of about 7 nm was studied showing a less pronounced positive effect on the activity than the metal oxide support effect.     

Lie groups whose coadjoint orbits are of dimension smaller or equal to two

We give a complete classification of the class of connected, simply connected Lie groups whose coadjoint orbits are of dimension smaller or equal to two.     

Analytic vectors and irreducible representations of nilpotent Lie groups and algebras

Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, U the universal enveloping algebra of G, M a simple module on U with kernel Ker dU, then there exists an automorphism of U keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U.