Fractal Weyl laws for chaotic open systems

We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of n disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.     

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.     

Non-linear resonances in the forced responses of plates,part II: Asymmetric responses of circular plates

The dynamic analogue of the von Karman equations is used to study the forced response, including asymmetric vibrations and traveling waves, of a clamped circular plate subjected to harmonic excitations when the frequency of excitation is near one of the natural frequencies. The method of multiple scales, a perturbation technique, is used to solve the non-linear governing equations. The approach presented provides a great deal of insight into the nature of the non-linear forced resonant response. It is shown that in the absence of internal resonance (i.e., a combination of commensurable natural frequencies) or when the frequency of excitation is near one of the lower frequencies involved in the internal resonance, the steady state response can only have the form of a standing wave. However, when the frequency of excitation is near the highest frequency involved in the internal resonance it is possible for a traveling wave component of the highest mode to appear in the steady state response.     

Vibrations of nearly annular and circular plates

A general procedure is presented to determine the natural frequencies and mode shapes of nearly annular and circular plates. A straightforward perturbation procedure is used with a transfer of the boundary conditions to obtain solutions given by simple expressions. As well as yielding good accuracy quantitatively, the method accurately predicts qualitative behavior. Numerical results are presented for clamped elliptical and square plates.     

Studies toward the total synthesis of angelmicin B (hibarimicin B): synthesis of a model CD-D' arylnaphthoquinone

[structure: see text] A synthesis of arylnaphthoquinone 22 corresponding to the CD-D' unit of angelmicin B via the Suzuki coupling of the D' arylboronic acid 15 with the CD bromonaphthoquinone 21 is described. The mild conditions for the Suzuki cross-coupling leading to 22 may prove to be useful for the eventual late-stage coupling of the two highly functionalized halves of angelmicin B.     

LP-Based Heuristic Algorithms for Interconnecting Token Rings via Source Routing Bridges

We develop a method to determine the topology of a network that interconnects a number of token rings using source routing bridges. The purpose is to compute a topology that provides low response delays for network users at a minimal cost of bridge installations. We formulate this network design problem as a mixed binary integer linear program. We develop effective heuristic algorithms. The algorithms exploit the topology and routing solutions of the linear programming relaxation in a sophisticated manner which we believe is new in the literature. The model incorporates performance issues, such as network stability, bridge overflow, back pressure effect and broadcast storm, that are specific to the underlying communication technology. By formally incorporating these performance issues, we tighten the model formulation and improve the quality of the LP bound considerably. Computational results are reported for problems with up to 20 token rings and 190 potential bridge locations.     

B and collider physics: Working group report

This report summarises the work done during WHEPP-6 (Institute of Mathematical Sciences, Chennai, India, Jan 3–15, 2000) in Working group on ‘B and collider physics’.     

Bis-spirochromanones as potent inhibitors of Mycobacterium tuberculosis: synthesis and biological evaluation

Molecular Diversity - On the basis of reported antimycobacterial property of chroman-4-one pharmacophore, a series of chemically modified bis-spirochromanones were synthesized starting from...     

Synthesis of amphiphilic triblock copolymers as multidentate ligands for biocompatible coating of quantum dots

One barrier to apply current tri-octylphosphine oxide (TOPO) based quantum dots (QDs) to biomedical imaging is that the TOPO on TOPO-QDs can be replaced by the proteins in living system, which may cause the degradation of QDs and/or deactivation of protein. In order to develop biocompatible optical imaging agents, a novel triblock copolymer, designed as a multidentate ligand, was synthesized to coat quantum dot nanocrystals (QDs). The copolymer consists of a polycarboxylic acid block at one end and a polythiol block at the other end with an intervening cross-linked poly(styrene-co-divinylbenzene) block bridging the ends. The multiple mercapto groups from the polythiol block act as multidentate ligands to stabilize QDs, while the polycarboxylic acid block improves the water solubility of QDs and offers reaction sites for surface modification or conjugation with bimolecules. The cross-linked poly(styrene-co-divinylbenzene) block provides a densely compacted hydrophobic shell. This shell will act as a barrier to inhibit the degradation of QDs by preventing the diffusion of ions and small molecules into the core of QDs. This new multidentate polymer coating facilitates the transfer of QDs from organic solvent into aqueous phase. The QDs directly bound to multidentate mercapto groups instead of TOPO are less likely to be affected by the mercapto or disulfide groups within proteins or other biomolecules. Therefore, this research will provide an alternative coating material instead of TOPO to produce QDs which could be more suitable for in vivo use under complex physiological conditions.