Showing papers in "Journal of the Indian Institute of Science in 2003"

Elastic-plastic analysis of R/C coupled shear walls: Theequivalent stiffness ratio of the tie elements

Abstract: Bar frame modelling is a popular method in coupled shear wall systems in structural design. In this process, determining the stiffness of the tie beams is important. In this study, results obtained by finite-element analysis of R/C coupled shear wall systems having several geometries in elastic-plastic space are considered. Using SPSS (Ver.5.0) statistical package program, an equivalent tie beam stiffness modification parameter is provided. The formula which defines the ratio between the plastic and elastic equivalent stiffness modification parameters is also given.

The congruence subgroup problem

Abstract: Colloquium talk in IISc on October 28, 2005 This article is an exposition on the ‘congruence subgroup problem’. This subject is at a common ground shared by group theory and number theory. It deals with certain groups defined arithmetically and their subgroup structure. This is a relatively modern subject having taken off in the mid 1960’s after Klein’s early investigations on the modular group. Apart from interest in its own right, the subject gains importance also because of connections with the theory of automorphic forms which is central to number theory. This exposition is meant to introduce the subject to professional mathematicians working in other areas. At the end, some recent work by the author is mentioned.

Identity, energy, environment, and dynamics of interfacial water molecules in a micellar solution*

Abstract: The structure and energetics of interfacial water molecules in the aqueous micelle of cesium perfluorooctanoate have been investigated using-large scale atomistic molecular dynamics simulations, with the primary objective of classifying them. The simulations show that the water molecules at the interface fall into two broad classes, bound (IBW) and free (IFW), present in a ratio of 9:1. The bound water molecules can be further categorized based on the number of hydrogen bonds (one or two) that they form with the surfactant headgroups. The hydrogen bonds of the doubly hydrogen bonded species (IBW2) are found to be, on the average, slightly weaker than that in the singly bonded species (IBW1). The environment around interfacial water molecules is more ordered than that in the bulk. The surface water molecules have substantially lower potential energy due to interaction with the micelle. In particular, both forms of IBW have energies lower by about 2.5 to 4.0 kcal/mole. Entropy is found to play an important role in determining the relative concentration of the species. The lifetime and the intermolecular vibrational frequencies of the hydrogen bonds that the water molecules form with the hydrophilic, polar headgroups (PHG) of the surfactants, are calculated. Our classification (S. Balasubramanian, S. Pal and B. Bagchi, Evidence for bound and free water species in the hydration shell of an aqueous micelle, Curr. Sci., 84, 428-430 (2003); S. Pal, S. Balasubramanian and B. Bagchi, Identity, energy, and environment of interfacial water molecules in a micellar solution, J. Phys. Chem. B, 107, 5194-5202 (2003)) of the interfacial water molecules, based on structural and energetic considerations, into IBW and IFW is further validated by their dynamics (S. Pal, S. Balasubramanian, and B. Bagchi, Dynamics of bound and free water in an aqueous micellar solution: Analysis of the lifetime and vibrational frequencies of hydrogen bonds at a complex interface, Phys. Rev. E, 67, 061502-1-061502-10 (2003)). Lifetime correlation functions of the water-surfactant hydrogen bonds show the long lived nature of the bound water species. Surprisingly, the water molecules that are singly hydrogen bonded to the surfactants have longer lifetime than those that form two such hydrogen bonds. The free water molecules that do not form any such hydrogen bonds behave similar to bulk one in their reorientational dynamics. A few water molecules that form two such hydrogen bonds are orientationally locked in for durations of the order of a few hundreds of picoseconds, that is, much longer than their average lifetime.

Comparison of inherent properties of glass fibre filters

Abstract: In Indian urban atmosphere, toxic elements are found in micro and sub-micro levels. Glass microfibre filters are used for collection of air samples for determination of trace quantities of these toxic metals in the air and it is preferable to choose filter containing low blank concentration. The concentration of Pb, Cr, Ni and Cd in the fil-ters manufactured by three manufacturers, viz. Gelman, Whatman and Nupore is studied in this paper. Though comparable, the least concentrations were observed in the filter manufactured by M/s Nupore Filtration Systems, India. The concentration of Fe and Zn however is very high in the range of 70251 and 18166604 mg/g, respectively, in all the filters.