Faithful actions of locally compact quantum groups on classical spaces

We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141–160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.     

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     

Controlling a bunch of multiple filaments by means of a beam diameter

We demonstrate a three orders of magnitude increase and stability in the backscattered fluorescence signal from nitrogen molecules by terawatt femtosecond laser pulse induced air filaments using a new method. The method is based on squeezing the initial beam diameter using a telescope. The effect of laser shot-to-shot fluctuations was included in numerical simulations by a random distribution of the initial intensity in both squeezed and non-squeezed beams. Statistical processing of the simulation results shows that the average diameter of plasma channels as well as the total amount of free electrons generated in a bunch of multiple filaments in air is larger in the squeezed beam. Shot-to-shot stability of the simulated plasma density increases in the squeezed beam. The change of this plasma density with propagation distance is in good qualitative agreement with the change of the range-corrected nitrogen fluorescence signal with distance. PACS 42.65.Jx; 42.60.Jf; 42.68.Ay; 42.68.Wt     

ENSTAR detector forη- mesic studies

We have initiated a search for a new type of nuclear matter, theη-mesic nucleus, using beams from the multi-GeV hadron facility, COSY at Juelich, Germany. A large acceptance scintillator detector, ENSTAR has been designed and built at BARC, Mumbai and fully assembled and tested at COSY. A test run for calibration and evaluation has been completed. In this contribution we present the design and technical details of the ENSTAR detector and how it will be used to detect protons and pions (the decay products ofη-mesic bound state). The detector is made of plastic scintillators arranged in three concentric cylindrical layers. The readout of the detectors is by means of optical fibres. The layers are used to generate ΔE –E spectra for particle identification and total energy information of stopped particles. The granularity of the detector allows for position (θ and ?ø determination making the event reconstruction kinematically complete