An analytical homogenization method for heterogeneous porous materials

The objective of this work is to develop an analytical homogenization method to estimate the effective mechanical properties of fluid-filled porous media with periodic microstructure. The method is based on the equivalent inclusion concept of homogenization applied earlier for solid–solid mixture. It is assumed that porous media are described by the poroelastic constitutive law developed by Biot where porosity is a material parameter. By solving the governing equations of poroelasticity in Fourier transformed domain, the relation between periodic strain and eigenstrain in porous media is established. This relation is subsequently used in an average consistency condition involving both solid and fluid phase stresses and strains. The geometry of the porous microstructure is captured in the g-integral. This homogenization method can also be applied to estimate the equivalent properties of solid–fluid mixture where a pure solid and fluid can be modeled by assuming very low and high porosity, respectively. Several examples are considered to establish this new method by comparing with other existing analytical and numerical methods of homogenization. As an application, poroelastic properties of cortical bone fibril are estimated and compared with previously computed values.     

Leading-Order Dynamics of Gravity-Driven Flows in?Free-Standing Soap Films

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier?CStokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.     

A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.

     

On the Cardinality of a Reduced Unique-Range Set

Ukrainian Mathematical Journal - Two meromorphic functions are said to share a set S ? ?∪{∞} ignoring multiplicities (IM) if S has the same preimages under both functions....     

Exact solution to the curve crossing problems of two linear diabatic potentials by transfer matrix method

In the present work we have reported a simple exact analytical solution to the curve crossing problem of two linear diabatic potentials by transfer matrix method. Our problem assumes the crossing of two linear diabatic potentials which are coupled to each other by an arbitrary coupling (in contrast to linear potentials in the vicinity of crossing points) and for numerical calculation purposes this arbitrary coupling is taken as Gaussian coupling which is further expressed as a collection of Dirac delta functions. Further we calculated the transition probability from one diabatic potential to another by the use of this method.     

Formation of nanoscale aggregates of a coumarin derivative in Langmuir–Blodgett film

In the present communication, we report the formation of organized nanoscale aggregates of a coumarin derivative 7 Hydroxy-N-Octadecyl Coumarin-3-Carboxamide (7HNO3C) at the air–water interface and in Langmuir–Blodgett (LB) films in the presence and absence of stearic acid (SA). A pressure-area isotherm reveals that the 7HNO3C form stable monolayer at the air–water interface. However, the stability can be improved by mixing it with a fatty acid stearic acid (SA). The miscibility study shows that the nature of interaction is strongly dependent on the mixing ratio and surface pressure. At a mole fraction of 0.4 of 7HNO3C in SA, the attractive and repulsive interaction between these two molecules balance each other forming a stable film with nanoscale aggregates. UV-Vis absorption spectroscopic studies reveal the nature of the aggregates in LB films. Scanning electron microscopy gives compelling visual evidence of formation of nanoscale aggregates in the mixed LB films.     

Solutions of Yang's EuclideanR-gauge equations and self-duality

Under some assumptions and transformations of variables, Yang's equations forR-gauge fields on Euclidean space lead to conformally invariant equations permitting one to obtain infinitely many other solutions from any solution of these conformally invariant equations. These conformally invariant equations closely resemble the mathematically interesting generalized Lund-Regge equations. Some exact solutions of these conformally in variant equations are obtained. Except for some singular situations, these solutions are self-dual.     

Solvent relaxation of a room-temperature ionic liquid [bmim][PF6] confined in a ternary microemulsion

In this paper we have reported the solvent and rotational relaxation of 1-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim][PF₆]) confined in tween 20/([bmim][PF₆]/water microemulsion using coumarin 153 (C-153) as probe. The most interesting feature of our experiment was that we observed an increase in solvent relaxation time with increase in R (R = tween 20-to-[bmim][PF₆] molar ratio). This is due to the fact that with increase in [bmim][PF₆] content of the microemulsions, the microviscosity of the pool of the microemulsions increases, and motion of ions of [bmim][PF₆] is hindered in the pool of microemulsions. Since motion of ions is responsible for solvation in room-temperature ionic liquids (RTILs), solvent-relaxation time increases with increase in R.