A comparison result for a class of quasilinear elliptic partial differential equations

A comparison theorem and a uniqueness corollary for positive solutions to the equation

on the closure of a bounded open set are found. The important hypotheses on the nonlinear coefficients are that each p_i is positive and monotone increasing in u while q is monotone decreasing in u. An application is made to equations arising in the theory of chemical reactors.     

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated.     

The formation of biaxial nematic phases in binary mixtures of thermotropic liquid-crystals composed of uniaxial molecules

ABSTRACT

Monte Carlo simulations in the isothermal-isobaric ensemble are used to investigate the formation of an ordered, biaxial nematic phase in a binary mixture of thermotropic liquid crystals. The orientational dependence of the interaction between molecules of each pure component is the same as in the well-known Maier-Saupe model; each pure component of the mixture is therefore capable of forming a uniaxial nematic phase. For the interaction between molecules of different components, we use the same Maier-Saupe model but change the sign of the coupling constant. As a consequence a T-shaped arrangement of these molecules is energetically favoured. The formation of the biaxial phase occurs in two steps. At higher temperatures T, one of the components forms a uniaxial nematic phase whereas the other is in a quasi two-dimensional restricted isotropic liquid state. We develop a simple theoretical model to understand the high degree of (ostensible) nematic order in the latter. At lower T, the second component becomes nematic and then the entire mixture of the two compounds has biaxial symmetry. The biaxial nematic phase does not demix into domains rich in molecules of one or the other species.     

Syntheses of 3-Chloro-7-[(Chlorocarbonyl)Methoxy]-4-Methylcoumarin

Two efficient syntheses of 3-chloro-7-[(chlorocarbonyl)methoxy]-4-methylcoumarin are described, one utilizing traditional chemistry starting from 3-chloro-7-hydroxy-4-methylcoumarin, while the other uses a novel reagent, sulfuryl chloride/thionyl chloride, in a one-pot reaction starting from 7-(carboxymethoxy)-4-methylcoumarin.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Molecular Design Principles for Near‐Infrared Absorbing and Emitting Indolizine Dyes

Desirable components for dye‐sensitzed solar cell (DSC) sensitizers and fluorescent imaging dyes include strong donating building blocks coupled with well‐balanced acceptor functionalities for absorption beyond the visible range. We have evaluated the effects of increasing acceptor strengths and incorporation of dye morphology controlling groups on molar absorptivity and absorption breadth with indolizine donor‐based dyes. Indolizine‐based D –A and D –π–A sensitizers incorporating bis‐rhodanine, tricyanofuran (TCF), and cyanoacrylic acid functionalities were analyzed for performance in DSC devices. The TCF derivatives were also evaluated as near‐infrared (NIR)‐emissive materials with the AH25 emissions extending past 1000 nm.