Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Application of scaled particle theory to alkyl-aryl surfactants: a two zone model of micellar core

Scaled Particle Theory (SPT) has been applied to predict the total free energies of micellization of ionic as well as nonionic micellar systems containing an aryl ring. A modification of the previously developed model has been made, proposing a two-zone model of micellar core which corroborates with the structural information available for such systems. The results are in good agreement with experimental data and also confirm the dictating role of cavity forming free energies for such systems

Potential-distance relationships of clay-water systems considering the Stern theory

This paper deals with the use of Stem theory as applied to a clay-water electrolyte system, which is more realistic to understand the force system at micro level man the Gouy-Chapman theory. The influence of the Stern layer on potential-distance relationship has been presented quantitatively for certain specified clay-water systems and the results are compared with the Gouy-Chapman model. A detailed parametric study concerning the number of adsorption spots on the clay platelet, the thickness of the Stern layer, specific adsorption potential and the value of dielectric constant of the pore fluid in the Stern layer, was carried out. This study investigates that the potential obtained at any distance using the Stern theory is higher than that obtained by the Gouy-Chapman theory. The hydrated size of the ion is found to have a significant influence on the potential-distance relationship for a given clay, pore fluid characteristics and valence of the exchangeable ion.

The structural theory and physical organic chemistry

Woolley's revolutionary proposal that quantum mechanics does not sanction the concept of ''molecular structure'' - which is but only a ''metaphor'' - has fundamental implications for physical organic chemistry. On the one hand, the Uncertainty Principle limits the precision with which transition state structures may be defined; on the other, extension of the structure concept to the transition state may be unviable. Attempts to define transition states have indeed caused controversy. Consequences for molecular recognition, and a mechanistic classification, are also discussed.

The approximate parametrization of the curve of intersection of implicit surfaces

A clear definition of an approximate parametrization of the curve of intersection of (n-1) implicit surfaces in Rn is given. It is justified that marching methods yield such an approximation.

Theory of electron transfer processes via chemisorbed intermediates: Part II. Current-potential characteristics

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Solvation dynamics in monohydroxy alcohols: Agreement between theory and different experiments

Recently three different experimental studies on ultrafast solvation dynamics in monohydroxy straight-chain alcohols (C-1-C-4) have been carried out, with an aim to quantify the time constant (and the amplitude) of the ultrafast component. The results reported are, however, rather different from different experiments. In order to understand the reason for these differences, we have carried out a detailed theoretical study to investigate the time dependent progress of solvation of both an ionic and a dipolar solute probe in these alcohols. For methanol, the agreement between the theoretical predictions and the experimental results [Bingemann and Ernsting J. Chem. Phys. 1995, 102, 2691 and Horng et al. J: Phys, Chern, 1995, 99, 17311] is excellent. For ethanol, propanol, and butanol, we find no ultrafast component of the time constant of 70 fs or so. For these three liquids, the theoretical results are in almost complete agreement with the experimental results of Horng et al. For ethanol and propanol, the theoretical prediction for ionic solvation is not significantly different from that of dipolar solvation. Thus, the theory suggests that the experiments of Bingemann and Ernsting and those of Horng et al. studied essentially the polar solvation dynamics. The theoretical studies also suggest that the experimental investigations of Joo et al. which report a much faster and larger ultrafast component in the same series of solvents (J. Chem. Phys. 1996, 104, 6089) might have been more sensitive to the nonpolar part of solvation dynamics than the polar part. In addition, a discussion on the validity of the present theoretical approach is presented. In this theory the ultrafast component arises from almost frictionless inertial motion of the individual solvent molecules in the force field of its neighbors.

Some recent advances in the theory of homogeneous isotropic turbulence

We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.

Strong shock approximation in the new theory of shock dynamics

This paper investigates the propagation of a strong shock into an inhomogeneous medium using the new theory of shock dynamics. The equations are simple to solve and involve no trial-and-error method commonly used in this case. The results compare favourably with earlier results obtained in the case of self-similar flows, which arise as a special case of this theory.

The log delta log t method for the determination of the coefficient of consolidation

The behaviour of saturated soils undergoing consolidation is very complex, It may not follow Terzaghi's theory over the entire consolidation process, Different soils may behave in such a way as to fit into Terzaghi's theory over some specific stages of the consolidation process (percentage of consolidation), This may be one of the reasons for the difficulties faced by the existing curve-fitting procedures in obtaining the coefficient of consolidation, c(v). It has been shown that the slope of the initial linear portion of the theoretical log U-log T curve is constant over a wider range of degree of consolidation, U, when compared with the other methods in use, This initial well-defined straight line in the log U-log T plot intersects the U = 100% line at T = pi/4, which corresponds to U = 88.3%, The proposed log delta-log t method is based on this observation, which gives the value of c(v) through simple graphical construction, In the proposed method, which is more versatile, identification of the characteristic straight lines is very clear; the intersection of these lines is more precise and the method does not depend upon the initial compression for the determination of c(v).

Mapping adaptive resonance theory onto ring and mesh architectures

In recent years, parallel computers have been attracting attention for simulating artificial neural networks (ANN). This is due to the inherent parallelism in ANN. This work is aimed at studying ways of parallelizing adaptive resonance theory (ART), a popular neural network algorithm. The core computations of ART are separated and different strategies of parallelizing ART are discussed. We present mapping strategies for ART 2-A neural network onto ring and mesh architectures. The required parallel architecture is simulated using a parallel architectural simulator, PROTEUS and parallel programs are written using a superset of C for the algorithms presented. A simulation-based scalability study of the algorithm-architecture match is carried out. The various overheads are identified in order to suggest ways of improving the performance. Our main objective is to find out the performance of the ART2-A network on different parallel architectures. (C) 1999 Elsevier Science B.V. All rights reserved.

Mean-field theory of charge ordering and phase transitions in the colossal-magnetoresistive manganites

We study phase transitions in the colossal-magnetoresistive manganites by using a mean-field theory both at zero and non-zero temperatures. Our Hamiltonian includes double-exchange, superexchange, and Hubbard terms with on-site and nearest-neighbour Coulomb interaction, with the parameters estimated from earlier density-functional calculations. The phase diagrams show magnetic and charge-ordered (or charge-disordered) phases as a result of the competition between the double-exchange, superexchange, and Hubbard terms, the relative effects of which are sensitively dependent on parameters such as doping, bandwidth, and temperature. In accord with the experimental observations, several important features are reproduced from our model, namely, (i) a phase transition from an insulating, charge-ordered antiferromagnetic to a metallic, charge-disordered ferromagnetic state near dopant concentration x = 1/2, (ii) the reduction of the transition temperature TAF-->F by the application of a magnetic field, (iii) melting of the charge order by a magnetic field, and (iv) phase coexistence for certain values of temperature and doping. An important feature, not reproduced in our model, is the antiferromagnetism in the electron-doped systems, e.g., La1-xCaxMnO3 over the entire range of 0.5 less than or equal to x less than or equal to 1, and we suggest that a multi-band model which includes the unoccupied t(2g) orbitals might be an important ingredient for describing this feature.