Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.     

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.     

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.     

Spectroscopic and computational characterization of CuII-OOR (R = H or cumyl) complexes bearing a Me6-tren ligand

A copper(II)-hydroperoxo complex, [Cu(Me(6)-tren)(OOH)](+) (2), and a copper(ii)-cumylperoxo complex, [Cu(Me(6)-tren)(OOC(CH(3))(2)Ph)](+) (3), were synthesized by reacting [Cu(Me(6)-tren)(CH(3)CN)](2+) (1) with H(2)O(2) and cumyl-OOH, respectively, in the presence of triethylamine. These intermediates, 2 and 3, were successfully characterized by various physicochemical methods such as UV-vis, ESI-MS, resonance Raman and EPR spectroscopies, leading us to propose structures of the Cu(II)-OOR species with a trigonal-bipyramidal geometry. Density functional theory (DFT) calculations provided geometric and electronic configurations of 2 and 3, showing trigonal bipyramidal copper(II)-OOR geometries. These copper(II)-hydroperoxo and -cumylperoxo complexes were inactive in electrophilic and nucleophilic oxidation reactions.     

Cupric superoxo-mediated intermolecular C-H activation chemistry

The new cupric superoxo complex [LCu(II)(O(2)(?-))](+), which possesses particularly strong O-O and Cu-O bonding, is capable of intermolecular C-H activation of the NADH analogue 1-benzyl-1,4-dihydronicotinamide (BNAH). Kinetic studies indicated a first-order dependence on both the Cu complex and BNAH with a deuterium kinetic isotope effect (KIE) of 12.1, similar to that observed for certain copper monooxygenases.     

Electronic structure of a low-spin heme/Cu peroxide complex: spin-state and spin-topology contributions to reactivity

This study details the electronic structure of the heme–peroxo–copper adduct {[(F8)Fe(DCHIm)]-O2-[Cu(AN)]}+ (LS(AN)) in which O2(2–) bridges the metals in a μ-1,2 or “end-on” configuration. LS(AN) is generated by addition of coordinating base to the parent complex {[(F8)Fe]-O2-[Cu(AN)]}+ (HS(AN)) in which the O2(2–) bridges the metals in an μ-η2:η2 or “side-on” mode. In addition to the structural change of the O2(2–) bridging geometry, coordination of the base changes the spin state of the heme fragment (from S = 5/2 in HS(AN) to S = 1/2 in LS(AN)) that results in an antiferromagnetically coupled diamagnetic ground state in LS(AN). The strong ligand field of the porphyrin modulates the high-spin to low-spin effect on Fe–peroxo bonding relative to nonheme complexes, which is important in the O–O bond cleavage process. On the basis of DFT calculations, the ground state of LS(AN) is dependent on the Fe–O–O–Cu dihedral angle, wherein acute angles (<~150°) yield an antiferromagnetically coupled electronic structure while more obtuse angles yield a ferromagnetic ground state. LS(AN) is diamagnetic and thus has an antiferromagnetically coupled ground state with a calculated Fe–O–O–Cu dihedral angle of 137°. The nature of the bonding in LS(AN) and the frontier molecular orbitals which lead to this magneto-structural correlation provide insight into possible spin topology contributions to O–O bond cleavage by cytochrome c oxidase.     

Some monotonicity properties of Schur powers of matrices and related inequalities

A series of inequalities are developed relating the spectral radius ?(A ° B) of the Schur product A ° B of two nonnegative matrices A and B with those of ?(A ° A) and ?(B ° B) yielding $\text{?(A ° B) ? [?(A ° A)?(B ° B)]}\text{1}\text{2}$. As a corollary it is proved that the spectral radius of the Schur powers ?_r = ?(A^[r]), A^[r] = A ° A °?°A (r factors) satisfies $\text{(}\text{1}\text{r}\text{)}\text{log}\text{?}{}_{\mathrm{r}}$ is decreasing while $\text{(}\text{1}\text{r?1}\text{)}\text{log}\text{?}{}_{\mathrm{r}}$ is increasing, the latter provided A is a stochastic matrix. The entropy of a finite stationary Markov chain is identified with $\text{d?}{}_{\mathrm{r}}\text{dr|}{}_{\mathrm{r=1}}$. A number of majorization comparisons for the spectral radius of Schur powers is given.     

Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

A function f(x) defined on $\text{X}$ = $\text{X}$₁ × $\text{X}$₂ × … × $\text{X}$_n where each $\text{X}$_i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on $\text{X}$, is said to be multivariate totally positive of order 2 (MTP₂). A random vector Z = (Z₁, Z₂,…, Z_n) of n-real components is MTP₂ if its density is MTP₂. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ^?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP₂ properties. The MTP₂ property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP₂ kernels are presented and amplified by a wide variety of applications.