Some results in the theory of interacting electron systems

The expressions for the longitudinal dielectric function, spin and orbital susceptibilities in the static, long wavelength limit are evaluated by solving the corresponding linearized vertex functions exactly in this limit. The plasma dispersion relation to leading order in the long wave limit is similarly obtained. These are compared with the corresponding results obtained previoulsy by us by a variational solution to the same vertex equations. It is established that the variational method gives the exact results in the static, zero wave vector limit, involving the proper renormalizations. The plasma dispersion relation is found to be the same as in the exact calculation whereas the coefficient of q² in the static density correlation function has an important additional contribution to the variational result. Applications of these results are briefly discussed.     

Stability analysis of Rayleigh�CB��nard convection in a porous medium

In this paper we study the problem of Rayleigh?CBénard convection in a porous medium. Assuming that the viscosity depends on both the temperature and pressure and that it is analytic in these variables we show that the Rayleigh?CBénard equations for flow in a porous media satisfy the idea of exchange of stabilities. We also show that the static conduction solution is linearly stable if and only if the Rayleigh number is less than or equal to a critical Rayleigh number. Finally, we show that a measure of the thermal energy of the fluid decays exponentially which in turn implies that the L² norm of the perturbed temperature and velocity also decay exponentially.     

Synthesis of α-aryl nitriles through B(C6F5)3-catalyzed direct cyanation of α-aryl alcohols and thiols

Various α-aryl nitriles have been prepared in excellent yield from the corresponding α-aryl alcohols employing 3 mol % of B(C₆F₅)₃ (1) as Lewis acid catalyst and (CH₃)₃SiCN (TMSCN) as cyanide source. Cyano transfer from TMSCN to alcohol proceeds within short reaction time at rt. α-Aryl thiols also produce corresponding nitriles in good to excellent yield at reflux condition.     

Quantifying Forces Mediated by Integral Tight Junction Proteins in Cell–Cell Adhesion

Cellular adhesion and barriers formed by intercellular adhesion proteins [tight junctions (occludin and claudins) and adherens junction (E-cadherin)] are important in maintaining tissue homeostasis. However, disruption of these junction proteins is associated with diseases in the organ systems such as multiple sclerosis, diarrhea, asthma, and gastro-intestinal tract carcinomas among others. In this paper, the separation force needed to separate two cells expressing some of these proteins was measured using the dual micropipette assay. Results show that L-fibroblasts transfected with claudin-1 and claudin-2 exhibit higher separation force (~2.8 nN and 2.3 nN, respectively) as compared to control cells or cells transfected with occludin (~1 nN). Furthermore, the separation force was not affected on addition of calcium chelating agent (ethylene diamine tetra acetic acid, EDTA). The separation force was, however, significantly decreased on treating cells with the actin disrupting agent Cytochalasin-D. These results show that the dual micropipette assay is a simple and useful experimental technique for quantifying cell–cell adhesion.     

On the Oberbeck–Boussinesq approximation for fluids with pressure dependent viscosities

We derive, by using a rigorous perturbative approach, the Oberbeck–Boussinesq approximation within the framework of one of the simplest implicit constitutive theories: that of fluids with pressure dependent viscosity. To illustrate an application we use the equations derived here to study the flow of a fluid in a channel with heated walls.     

Buyer–supplier relationship and operational dynamics

This paper examines the effectiveness of business-to-business relationships in reference to the suppliers of office equipments serving the industrial accounts in Mexico. The study addresses broadly the performance-related issues as to what extent is the impact of quality of services responsible for doing business with the organizational buyers. Discussions in the paper also analyse the impact of channel function performance on relationship quality, which is moderated by the extent dependence structure of the relationship. The results of the study showed that the impact of buyer–supplier co-dependency and relationship quality significantly affects the supplier performance. It has been argued in the paper that the market orientation is positively associated with measures of channel performance such as service quality and the extent of buyer satisfaction. The study also demonstrates that in the processes of managing business relationships, cognitive dimensions like trust, commitment, and low level of conflicts provide ‘win-win’ situation for buyers and suppliers. Finally, this study attempts to make contributions to the literature on buyer–supplier relationships towards cognitive and relational perspectives leading to optimizing functional efficiency of a firm.     

An implicit three-dimensional model for describing the inelastic response of solids undergoing finite deformation

The aim of this paper is to develop a new unified class of 3D nonlinear anisotropic finite deformation inelasticity model that (1) exhibits rate-independent or dependent hysteretic response (i.e., response wherein reversal of the external stimuli does not cause reversal of the path in state space) with or without yield surfaces. The hysteresis persists with quasistatic loading. (2) Encompasses a wide range of different types of inelasticity models (such as Mullins effect in rubber, rock and soil mechanics, traditional metal plasticity, hysteretic behavior of shape memory materials) into a simple unified framework that is relatively easy to implement in computational schemes and (3) does not require any a priori particular notion of plastic strain or yield function. The core idea behind the approach is the development of an system of implicit rate equations that allow for the continuity of the response but with different rates along different directions. The theory, which is in purely mechanical setting, subsumes and generalizes many commonly used approaches for hypoelasticity and rate-independent plasticity. We illustrate its capability by modeling the Mullins effect which is the inelastic behavior of certain rubbery materials. We are able to simulate the entire cyclic response without the use of additional internal variables, i.e., the entire response is modeled by using an implicit function of stress and strain measures and their rates.     

On the development and generalizations of Cahn–Hilliard equations within a thermodynamic framework

We provide a thermodynamic basis for the development of models that are usually referred to as ??phase-field models?? for compressible, incompressible, and quasi-incompressible fluids. Using the theory of mixtures as a starting point, we develop a framework within which we can derive ??phase-field models?? both for mixtures of two constituents and for mixtures of arbitrarily many fluids. In order to obtain the constitutive equations, we appeal to the requirement that among all admissible constitutive relations that which is appropriate maximizes the rate of entropy production (see Rajagopal and Srinivasa in Proc R Soc Lond A 460:631?C651, 2004). The procedure has the advantage that the theory is based on prescribing the constitutive equations for only two scalars: the entropy and the entropy production. Unlike the assumption made in the case of the Navier?CStokes?CFourier fluids, we suppose that the entropy is not only a function of the internal energy and the density but also of gradients of the partial densities or the concentration gradients. The form for the rate of entropy production is the same as that for the Navier?CStokes?CFourier fluid. As observed earlier in Heida and Málek (Int J Eng Sci 48(11):1313?C1324, 2010), it turns out that the dependence of the rate of entropy production on the thermodynamical fluxes is crucial. The resulting equations are of the Cahn?CHilliard?CNavier?CStokes type and can be expressed both in terms of density gradients or concentration gradients. As particular cases, we will obtain the Cahn?CHilliard?CNavier?CStokes system as well as the Korteweg equation. Compared to earlier approaches, our methodology has the advantage that it directly takes into account the rate of entropy production and can take into consideration any constitutive assumption for the internal energy (or entropy).     

Platinum(II) complexes ofN-alkylphenothiazines

Summary The synthesis and physical properties of eight square-planar platinum(II) complexes, [PtLCl₂] (L =N-alkylphenothiazine) are reported. Analytical, conductometric, spectral (electronic, i.r. and¹H n.m.r.) and thermal data for the complexes are discussed.