Central limit theorems for a class of irreducible multicolor urn models

We take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.     

Exciton dynamics in alternating polyfluorene/fullerene blends

Exciton dynamics in alternating copolymer/fullerene solar cell blends have been investigated using femtosecond transient absorption spectroscopy. The acceptor concentrations have been varied over a wide range. Experimental data, kinetic modeling and simulations, all indicate that the efficiency of exciton conversion to charges is 100% even at acceptor concentrations as low as 20 wt%. The reported dependence of solar cell efficiency on fullerene concentration may thus arise from other factors. However, there exists an acceptor concentration threshold (5 wt%) below which a substantial fraction of the excitations remain unquenched. The results, we believe are very relevant to optimization of performance efficiency by clever manipulation of morphology. We have also observed exciton–exciton energy transfer in these blends at low acceptor concentrations.     

Controlling J aggregation in fluorescein by bile salt hydrogels

Aggregation of the well-known xanthene dye, fluorescein has been studied in the restricted environment of a bile salt hydrogel and in the bile salt micelles. It has been observed that the hydrogel can be used to some extent “control” the type of aggregation in fluorescein, since J-aggregate formation is favored at the expense of H-aggregates in the gel. In contrast to the hydrogel, the effect of normal bile salt micelles is less dramatic, i.e., bile salt micelles do not lead to significant change in the type of dye aggregation.     

Double Coil Resonance Experiment and Partial Reduction of Wave Packet in Quantum Mechanics

Interference and measurement aspects for the double coil resonance experiment are reanalyzed. The resulting situation is analogous to partial reduction of wave packet in quantum mechanics. Using convergence results of relative frequencies, magnitudes of the intensity are calculated when prior probabilities are assigned to the coefficients associated with the states.     

A binary solvent of water and propanol for use in high-average power dye lasers

Water is an inherently safe solvent for laser dyes and posses far better photo thermal characteristics in comparison to the commonly used organic solvents in dye lasers. However, water solution of dye needs a suitable deaggregating additive to suppress non-radiative dimers and to achieve similar laser efficiency. We have carried out systematic studies on comparative performances of dye lasers, pumped by low-repetition-rate Nd-YAG, as well as high-repetition-rate copper vapour lasers using Rhodamine 6G dye solutions in ethanol and various binary solvents of water. Among different additives in water, for the first time, the results of our studies on the application of water solvent in dye lasers could clearly establish that binary solvent comprising of normal or heavy water and about 18% to 25% n-propanol has produced similar efficiency, better photochemical stability and superior thermo-optic properties than ethanol solvent in high-repetition rate oscillator-amplifier operation. PACS 42.55.Mv; 32.50.+d; 42.70.jk     

Eigenmodes for electromagnetic waves propagating in a toroidalcavity

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived     

Density functional theory study of the geometry, energetics, and reconstruction process of Si111 surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3x3 to 9x9 dimer-adatom-stacking fault (DAS) structures. These calculations used the Perdew-Burke-Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7x7 structure, with a surface energy of 1.044 eV/1x1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1x1 structure. We obtain an energy barrier at the 2x2 cell size and confirm that the 7x7 regular stage of the SSC model (corresponding to the DAS 7x7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si111 1x1 surface.     

Environmental effects on the aggregation of some xanthene dyes used in lasers

The effect of solvents, halo substituents and surfactants on the aggregation of xanthene dyes (fluorescein and eosin Y) has been investigated. It has been found that polar protic solvents promote the aggregation of both the dyes while polar aprotic solvents hinder the aggregation process. Apolar solvents can disintegrate the aggregates previously formed in aqueous medium. The nature of the driving forces for aggregation in the two dyes is different. Surfactants bearing charge opposite to the dye molecules facilitate aggregation. These observations bear direct relevance to the possible use of fluorescein and eosin Y as quantum yield standards, photosensitizers, laser dyes and biological labels.     

Spatiotemporal rheochaos in nematic hydrodynamics

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order-parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.     

Two-step melting of the vortex solid in layered superconductors with random columnar pins

We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.