Approximate Controllability of Neutral Stochastic Functional Differential Systems with Infinite Delay

In this article, we consider a class of control systems governed by the neutral stochastic functional differential equations with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.     

Studies on polymer concretes based on optimized aggregate mix proportion

Polymer concretes are composite materials made of polymeric binders with filler materials. The filler materials form the major component of the polymer concrete and the distribution of their particle size influences the properties of polymer concrete. Hence using an optimized aggregate mix proportion having least void content, a series of polymer concretes of different compositions were designed on the basis of mixture design concept of design of experiments. For each composition, compressive strength was checked at different intervals of time. The effects of variables such as binder content and curing time on the properties were discussed. Further, the compressive strength obtained were optimized and compared with the experimental data. The coefficient of correlation between the experimental values and predicted values was found to be high proving the fitness of the selected model.     

Structure and dynamics of charged macromolecules: Minimal representation of biological systems

Structures and functions of various biological macromolecules at cellular levels are controlled by electrostatic, excluded-volume, macromolecular topological connectivity, and hydrodynamic forces. Some aspects of these challenging issues will be addressed. Specifically we will focus our discussions on (a) pattern recognition by macromolecules and complexation, (b) coupling between conformational transitions and phase transitions, (c) chromosomal condensation, (d) collective behavior of charged macromolecules in crowded environments, (e) coupled dynamics of macromolecular assemblies in charged solutions, and (f) polymer transport through pores. Even the simpler synthetic systems exhibit many puzzles which will be resolved using our theoretical formulation. In addition to exploring an understanding of biological processes, the context of fabrication of new synthetic materials will be remarked.     

Scattering properties of a single semiflexible polyelectrolyte

The structure factor of a single semiflexible polyelectrolyte has been calculated as a function of chain length, intrinsic backbone stiffness, and salt concentration. Because of the insignificant coupling of the intrinsic stiffness and electrostatic persistence length, we carry out our calculations in the flexible limit. Within the variational scheme adopted here, we obtain fractal dimensions consistent with our earlier calculations of the configurational properties. As the chain length is increased, the electrostatic interaction is progressively screened, leading to the crossover regions. In the first crossover, the effective fractal dimension, D_eff, is as low as 1, and in the second crossover D_eff is 5/3, although the radius of gyration exponent is 2/5. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2644–2652, 2001     

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.     

Effect of micropillar surface texturing on friction under elastic dry reciprocating contact

Surface texturing is considered to be a promising method to improve the tribological properties. Depending upon the experimental conditions, the effect of texturing varies from favourable to unnoticeable to detrimental. In this work, surfaces with micropillars are studied under elastic dry reciprocating contact. An array of micropillars with different pillar heights are generated on stainless steel using wire-cut electrical discharge machining. The effect of stiffness of the micropillars on friction is investigated, keeping the number of micropillars in contact with a flat aluminium alloy (Al6061) slider and contact geometry constant. Reciprocating experiments are carried out against a flat surface such that about 81 micropillars are in contact. From the experimental results, it is found that the coefficient of friction is independent of the stiffness of the texture elements. However, work done per cycle significantly varied with the stiffness of texture element and applied normal load. A lumped system model with Coulomb friction shows that the work done per cycle varies quadratically with the normal load. The experimental results agree with this simplified model except in the incipient sliding regime. These results show how the work done per cycle varies, for different contact stiffness under elastic contact even though the coefficient of friction remains constant. The implication of this study for a macroscopic measured coefficient of friction as a function of microscopic asperity level friction is discussed.     

Triple points in solutions of polydisperse semiflexible polymers

When a mother solution of semiflexible polymers with differing molecular weights is forced to undergo phase transition, cloud and shadow curves emerge instead of a coexistence curve. For the first time, we calculate the cloud and shadow curves for an isotropic-nematic transition coupled to polydispersity and predict novel triple points. Because of the emergence of new triple points, polydispersity allows the occurrence of anisotropic phases at much lower polymer concentrations than for the monodisperse solutions.     

Nature of spin excitations in two-dimensional mott insulators: undoped cuprates and other materials

We investigate the excitation spectrum of a two-dimensional resonating valence bond (RVB) state. Treating the pi-flux phase with antiferromagnetic correlations as a variational ground state, we recover the long wavelength magnon as an "RVB exciton." However, this excitation does not exhaust the entire spectral weight and the high-energy spectrum is dominated by fermionic excitations. The latter can be observed directly by inelastic neutron scattering, and we predict their characteristic energy scales along different high symmetry directions in the magnetic Brillouin zone. We also interpret experimental results on two magnon Raman scattering and midinfrared absorption within this scenario.