Exhaustive checking of sparse algebras

We checked the 107-dimensional alternative algebra constructed by E. Kleinfeld (On centers of alternative algebras, Comm. Algebra8(3) 1980, 289–297) and verified that it was alternative. To straightforwardly check the alternative law for the basis elements proved to be too time consuming for the computer. We developed a new algorithm which is much faster for sparse multiplication tables and which requires much less memory. Instead of testing the identities for all possible choices of basis elements, our algorithm is based on “factoring” the basis elements in all possible ways. The factorization algorithm took 5 minutes of C.P.U. time; it is estimated direct substitution with no consideration for sparseness would take 600 hours. Even when the substitution technique was improved to account for sparseness it is estimated it would take 12 hours of C.P.U. time. Substitution also requires 100 times as much memory space as factorization.     

Effect of distortion in electron impact excitation in Coulomb-projected Born approximation

We have calculated total and differential cross-sections for 1s →ns (n = 2, 3, 4) electron impact excitation of hydrogen and hydrogenic ions at various energies in Coulomb-projected Born approximation. Distortion due to static interactions, target polarization and exchange effects has been incorporated in the initial channel. The present calculations have been compared with other theoretical and experimental results.     

Rhodamine-Based Cu2+ -Selective Fluorosensor: Synthesis, Mechanism, and Application in Living Cells

A rhodamine B-based fluorescence probe (1) for the sensitive and selective detection of Cu²⁺ ion has been designed and synthesized using pyridine moiety. The optical properties of this compound have been investigated in acetonitrile-water binary solution (7:3 v/v). Compound 1 is found to be an excellent sensor for a biologically/physiologically very important transition metal ion (Cu²⁺) using only the two very different modes of measurements (absorption and emission); one case displayed intensity enhancement whereas in other case showed intensity depletion (quenching). A mechanistic investigation has been performed to explore the static nature of quenching process. The sensor has been found to be very effective in sensing Cu²⁺ ion inside living cells also.     

An experimental study of impact-induced failure events in homogeneous layered materials using dynamic photoelasticity and high-speed photography

The generation and the subsequent evolution of dynamic failure events in homogeneous layered materials that occur within microseconds after impact were investigated experimentally. Tested configurations include three-layer and two-layer, bonded Homalite specimens featuring different bonding strengths. High-speed photography and dynamic photoelasticity were utilized to study the nature, sequence and interaction of failure modes. A series of complex failure modes was observed. In most cases, and at the early stages of the impact event, intra-layer failure (or bulk matrix failure) appeared in the form of cracks radiating from the impact point. These cracks were opening-dominated and their speeds were less than the crack branching speed of the Homalite. Subsequent crack branching in several forms was also observed. Mixed-mode inter-layer cracking (or interfacial debonding) was initiated when the intra-layer cracks approached the interface with a large incident angle. The dynamic interaction between inter-layer crack formation and intra-layer crack growth (or the so-called “Cook–Gordon Mechanism”) was visualized for the first time. Interfacial bonding played a significant role in impact damage spreading. Cracks arrested at weak bonds and the stress wave intensity was reduced dramatically by the use of a thin but ductile adhesive layer.     

An ellipsometric investigation of Ag/SiO$\mathsf{_2}$ nanocomposite thin films

Dielectric properties of silver/SiO₂ nanocomposite thin films grown by high-pressure d.c. sputtering technique were studied by spectroscopic ellipsometry (300-800 nm). The dielectric behavior of the nanocomposite thin films largely depended on the particle size, its number density and the surrounding environments. The films showed semiconductor-like behavior up to a critical particle size and concentration, beyond which the films exhibited the typical surface plasmon resonance characteristics in their optical properties. The refractive index was also found to have a strong dependence on the particle size and its dispersion in the matrix. The results were found to be consistent with those obtained from UV-VIS optical absorbance data. Bruggeman effective medium theory was used to explain the experimental results.Received: 3 April 2002, Published online: 23 July 2003PACS:   78.67.-n Optical properties of nanoscale materials and structures - 78.67.Bf Nanocrystals and nanoparticles     

Global optimization of high harmonic generation

We investigate the relevance of the absorption limit concept in the optimization of high harmonic generation. Thanks to the first direct observation of the coherence length of the process from high-contrast Maker fringes, we unravel experimental conditions for which the harmonic dipole response is enhanced when phase matching is realized within the absorption limit, leading to record conversion efficiencies in argon. Moreover, we show that harmonic generation in guided or freely propagating geometries are equivalent in the loose focusing regime. This analysis is generalized to other advanced phase-matching schemes, thereby predicting the possibility to boost the conversion efficiencies using light noble gases.     

Solid state polymorphism of liquid crystals in confined geometries

Solid polymorphism of 4-alkyl-4'-cyanobiphenyl (nCB) was studied so far as a function of thermal history. In this paper we show that metastable solid phases of 4-octyl-4'-cyanobiphenyl (8CB) are also formed when the mesogens are confined in porous silica matrices and we study their structure by neutron diffraction and by Raman spectroscopy. Three metastable solid states are identified: one crystalline phase K', two frozen-in smectic-like phases K(s) and K'(s). We discuss the relation between the structure of the metastable solid phases and that of the mesomorph phases.