Combined natural convection heat and mass transfer in an enclosure having finite thickness walls

Unsteady three-dimensional conjugate heat and mass transfer in an enclosure having finite thickness heat-conducting walls has been analyzed numerically. The governing unsteady, three-dimensional flow, energy and contaminant transport equations for the gas cavity and unsteady heat conduction equation for solid walls, written in dimensionless terms of the vector potential functions, the vorticity vector, the temperature and the concentration, have been solved using an iterative implicit finite-difference method. Main attention was paid to the effects of the Rayleigh number, buoyancy ratio and the dimensionless time on the flow structure and heat and mass transfer regimes. It should be noted that the dominant cause of the oscillations in the dimensionless time dependences of the average Nusselt number on the heat source surface and the average Sherwood number on the contaminant source surface at Ra>5?10⁵ is the mutual influence of the analyzed object geometry and the thermo-diffusivity impact on the flow. The change in the buoyancy ratio can lead to the essential modifications of the flow, temperature and concentration fields owing to the significant influence of the concentration gradient.     

The Role of Noise in Finite Ensembles of Nanomagnetic Particles

The dynamics of finitely many nanomagnetic particles are described by the stochastic Landau–Lifshitz–Gilbert equation. We show that the system relaxes exponentially quickly to the unique invariant measure which is described by a Boltzmann distribution. We present two approaches to verify this result. The first uses the general theory of (Meyn and Tweedy, Adv Appl Prob 24:542–574, 1992; Meyn and Tweedy, Adv Appl Prob 25:487–517 1993; Meyn and Tweedy, Adv Appl Prob 25:518–548, 1993) for Markov chains, which involves the concepts of a Lyapunov structure, and irreducibility of transition probabilities; we show exponential convergence in a supremum topology, but lack explicit rates. The second approach shows exponential ergodicity in a weaker L ² topology, with an explicit rate of convergence of the Arrhenius type law. Then, we discuss two implicit discretizations to approximate transition functions at both finite and infinite times: the first scheme is shown to inherit the geometric ‘unit-length’ property of single spins, as well as the Lyapunov structure, and is shown to be geometrically ergodic; moreover, iterates converge strongly with a rate for finite times. The second scheme is computationally more efficient since it is linear; it is shown to converge weakly at an optimal rate for all finite times. We use a general result of Shardlow and Stuart (Siam J Numer Anal 37(4):1120–1137 2000) to conclude convergence to the invariant measure of the limiting problem for both discretizations.     

Application of a high-speed laser-induced fluorescence technique for studying the three-dimensional structure of annular gas–liquid flow

The wavy structure of liquid film in annular gas?Cliquid flow was studied using a high-speed modification of the laser-induced fluorescence (LIF) technique, which was adapted for three-dimensional measurements. The three-dimensional structure of different types of waves in regimes with and without liquid entrainment was investigated. A comparison of the circumferential size of different types of waves was performed. Disturbance waves at high liquid Reynolds numbers were shown to be circumferentially non-uniform, and it was shown that this non-uniformity affects the generation of ripples.     

Synthesis of the new adducts of imines and enamines with PH acids and their derivatives

Nucleophilic or radical addition of esters of trivalent organophosphorus acids with PH fragments to various imines and enamines is proposed as convenient methods for the synthesis of new substituted aminomethyl organophosphorus compounds with three‐, four‐, and five‐coordinated phosphorus. Also the new functionalized derivatives of these compounds with acyl and methanesulfonyl moieties are synthesized, and some properties of the obtained compounds are presented. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:70–80, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20513     

4-Arylation of 3-alkoxypyrazoles

Following the study of the alkoxypyrazoles nitrogen's reactivity toward arylation or alkylation reactions, we report here our results on the introduction of various aryl groups on carbon 4 position of 3-alkoxypyrazoles. This was achieved from the corresponding 4-halogeno derivatives via a Suzuki-Miyaura aryl-aryl coupling reaction. The unexpected difficulties (lack of reactivity or unwanted halogen reduction) encountered in the C-4 arylation of NH-free 4-halogenopyrazoles led us to design solutions to this recurrent problem. The cleavage of the 3-alkoxy group was also investigated using hydrogen bromide in acetic acid or boron tribromide in dichloromethane. This led, in one case, to the observation of a remarkable neighboring group-assisted electrophilic aryl boronylation. This second part of our work paves the way to the synthesis of many original chemical libraries featuring 3-alkoxy 1,4-diaryl pyrazoles as well as the corresponding 1,4-diaryl pyrazol-3-ones.     

Palladium-catalyzed sequential indole synthesis using sterically hindered amines

A palladium catalyst derived from a bulky N-heterocyclic carbene ligand enabled a modular synthesis of indoles bearing sterically hindered N-alkyl or N-aryl substituents through a reaction sequence comprising an intermolecular N-arylation and an intramolecular hydroamination.     

Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval

In this note, we consider the scheduling problem of minimizing the sum of the weighted completion times on a single machine with one non-availability interval on the machine under the non-resumable scenario. Together with a recent 2-approximation algorithm designed by Kacem [I. Kacem, Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers & Industrial Engineering 54 (2008) 401–410], this paper is the first successful attempt to develop a constant ratio approximation algorithm for this problem. We present two approaches to designing such an algorithm. Our best algorithm guarantees a worst-case performance ratio of 2+ε$2+\epsilon$.     

Local flux mimetic finite difference methods

We develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral meshes. To approximate the velocity (vector variable), the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per n-gonal mesh face in three dimensions. To approximate the pressure (scalar variable), the method uses one degree of freedom per element. A specially chosen quadrature rule for the L ²-product of vector-functions allows for a local flux elimination and reduction of the method to a cell-centered finite difference scheme for the pressure unknowns. Under certain assumptions, first-order convergence is proved for both variables and second-order convergence is proved for the pressure. The assumptions are verified on simplicial meshes for a particular quadrature rule that leads to a symmetric method. For general polyhedral meshes, non-symmetric methods are constructed based on quadrature rules that are shown to satisfy some of the assumptions. Numerical results confirm the theory.