Smagorinsky constant in LES modeling of anisotropic MHD turbulence

Turbulent fluctuations in magnetohydrodynamic (MHD) flows can become strongly anisotropic or even quasi-2D under the action of an applied magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds numbers. It has been found in earlier DNS and LES of homogeneous turbulence that the degree of anisotropy is predominantly determined by the value of the magnetic interaction parameter and only slightly depends on the Reynolds number, type of large-scale dynamics, and the length scale. Furthermore, it has been demonstrated that the dynamic Smagorinsky model is capable of self-adjustment to the effects of anisotropy. In this paper, we capitalize on these results and propose a simple and effective generalization of the traditional non-dynamic Smagorinsky model to the case of anisotropic MHD turbulence.      

Random Motion with Uniformly Distributed Directions and Random Velocity

In this paper we deal with uniformly distributed direction of motion or isotropic motion at random speed or velocity where the direction alternations occur according to the renewal epochs of a general distribution. We derive the renewal equation for the characteristic function of the transition density of the multidimensional motion. Then, by using the renewal equation, we study the behavior of the transition density near the sphere of its singularity for one-, two-, three-, and four-dimensional cases. To illustrate our solution methodology we present detailed calculations of many solvable examples.     

Synthesis,Crystal Structure and Lithium Motion of Li8SeN2 and Li8TeN2

The compounds Li₈EN₂ with E = Se, Te were obtained in form of orange microcrystalline powders from reactions of Li₂E with Li₃N. Single crystal growth of Li₈SeN₂ additionally succeeded from excess lithium. The crystal structures were refined using single‐crystal X‐ray diffraction as well as X‐ray and neutron powder diffraction data (I4₁md, No. 109, Z = 4, Se: a = 7.048(1) Å, c = 9.995(1) Å, Te: a = 7.217(1) Å, c = 10.284(1) Å). Both compounds crystallize as isotypes with an anionic substructure motif known from cubic Laves phases and lithium distributed over four crystallographic sites in the void space of the anionic framework. Neutron powder diffraction pattern recorded in the temperature range from 3 K to 300 K and X‐ray diffraction patterns using synchrotron radiation taken from 300 K to 1000 K reveal the structural stability of both compounds in the studied temperature range until decomposition. Motional processes of lithium atoms in the title compounds were revealed by temperature dependent NMR spectroscopic investigations. Those are indicated by significant changes of the ⁷Li NMR signals. Lithium motion starts for Li₈SeN₂ above 150 K whereas it is already present in Li₈TeN₂ at this temperature. Quantum mechanical calculations of NMR spectroscopic parameters reveal clearly different environments of the lithium atoms determined by the electric field gradient, which are sensitive to the anisotropy of charge distribution at the nuclear sites. With respect to an increasing coordination number according to 2 + 1, 3, 3 + 1, and 4 for Li(3), Li(4), Li(2), and Li(1), respectively, the values of the electric field gradients decrease. Different environments of lithium predicted by quantum mechanical calculations are confirmed by ⁷Li NMR frequency sweep experiments at low temperatures.     

Synthesis of Haloglyoximes

A one-stage synthesis of haloglyoximes from substituted acetamidoximes has been described.     

Matrix‐covariant representation of high‐order configuration interaction and coupled cluster theories

We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix‐covariant expressions independent of the basis set used. The corresponding variational CI equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix‐covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high‐order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin‐flip approximation closely related to high‐order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three‐electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many‐body problem. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The Geometric Markov Renewal Processes with Application to Finance

We introduce the geometric Markov renewal processes as a model for a security market and study this processes in a series scheme. We consider its approximations in the form of averaged, merged and double averaged geometric Markov renewal processes. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes are presented. Martingale properties, infinitesimal operators of geometric Markov renewal processes are presented and a Markov renewal equation for expectation is derived. As an application, we consider the case of two ergodic classes. Moreover, we consider a generalized binomial model for a security market induced by a position dependent random map as a special case of a geometric Markov renewal process.     

Synthesis of poly(ethyl acrylate) by single electron transfer‐degenerative chain transfer living radical polymerization in water catalyzed by Na2S2O4

Living radical polymerization of ethyl acrylate was achieved by single‐electron‐transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionite. The plots of number‐average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This method leads to the preparation of α,ω‐di(iodo)poly(ethyl acrylate) (α,ω‐di(iodo)PEtA) macroinitiator that can be further functionalized. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering, a differential viscometer and refractive index. The method studied in this work represents a possible route to prepare well‐tailored macromolecules made of ethyl acrylate in environmental friendly reaction medium. To the best of our knowledge there is no previous report dealing with the synthesis of PEtA by any LRP approach in aqueous medium. Furthermore, the method described in this article was successfully applied in pilot scale reactions under industrial production conditions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 421–432, 2008     

ChemInform Abstract: Neutron Diffraction Study of Li4Ti5O12 at Low Temperatures.

The crystal structure of the title electrode material is determined by neutron powder diffraction in the temperature range 3.4—300 K.