Effect of phase shift in shape changing collision of solitons in coupled nonlinear Schrödinger equations

Soliton interactions in systems modelled by coupled nonlinear Schr?dinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features: shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature. Received 1st October 2001 / Received in final form 4 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: lakshman@bdu.ernet.in     

Synchrotron Radiation Provides a Plausible Explanation for the Generation of a Free Radical Adduct of Thioxolone in Mutant Carbonic Anhydrase II

Thioxolone acts as a prodrug in the presence of carbonic anhydrase II (CA II), whereby the molecule is cleaved by thioester hydrolysis to the carbonic anhydrase inhibitor, 4-mercaptobenzene-1,3-diol (TH0). Thioxolone was soaked into the proton transfer mutant H64A of CA II in an effort to capture a reaction intermediate via X-ray crystallography. Structure determination of the 1.2 ? resolution data revealed the TH0 had been modified to a 4,4'-disulfanediyldibenzene-1,3-diol, a product of crystallization conditions, and a zinc ligated 2,4-dihydroxybenzenesulfenic acid, most likely induced by radiation damage. Neither ligand was likely a result of an enzymatic mechanism.     

Localized coherent structures of (2+1) dimensional generalizations of soliton systems

We briefly review the recent progress in obtaining (2+1) dimensional integrable generalizations of soliton equations in (1+1) dimensions. Then, we develop an algorithmic procedure to obtain interesting classes of solutions to these systems. In particular using a Painlevé singularity structure analysis approach, we investigate their integrability properties and obtain their appropriate Hirota bilinearized forms. We identify line solitons and from which we introduce the concept of ghost solitons, which are patently boundary effects characteristic of these (2+1) dimensional integrable systems. Generalizing these solutions, we obtain exponentially localized solutions, namely the dromions which are driven by the boundaries. We also point out the interesting possibility that while the physical field itself may not be localized, either the potential or composite fields may get localized. Finally, the possibility of generating an even wider class of localized solutions is hinted by using curved solitons.     

Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.     

Gas bubbles in simulation and experiment

An experimental setup for the examination of single bubbles, rising in a liquid, is presented. Its main part is a rotating chamber, in which the bubble is spatially stabilized by a balance of buoyancy, drag, and lift forces. This allows for long observation periods in time. Experimental results are presented for air bubbles in silicone oil. The experimental results are validated by a comparison with numerical simulations. A modified, mass-conserving level-set method is used for the representation of the free interface, while an immersed-boundary formulation is engaged for the conservation equations. The agreement between experiment and simulation, and to available correlations from literature, is found to be perfect. It is shown that the influence of the liquid shear due to the rotation is negligible. Also, for the presented liquid system, no influence by Marangoni stresses could be found, which makes the system of air and silicone oil a good choice for validation purposes.     

New approximate analytical expressions for transient concentration profiles and current pertaining to a homogeneous chemical reaction at hemispherical microelectrodes

A mathematical model corresponding to homogeneous chemical reactions under transient chronoamperometry conditions at hemispherical microelectrodes has been developed. The analytical solutions for the concentration of species and current were obtained using Duhamel's theorem. This closed-form theoretical expression pertains to the transient concentration profiles and fluxes of chemical species involved in chemical and electrochemical reactions at hemispherical microelectrodes. As t → ∞, the analytical expressions corresponding to the concentration and current approach steady-state values. The solutions obtained are explicit only under limiting current conditions. The approximate expressions for concentrations and current as functions of time corresponding to the EC' and CE mechanisms at hemispherical microelectrodes are also reported.     

Chemoenzymatic synthesis of the polyketide macrolactone 10-deoxymethynolide

The polyketide synthase-derived pikromycin thioesterase (Pik TE) is unique in its ability to catalyze the cyclization of 12- and 14-membered macrolactones. In this investigation, the total synthesis of the natural hexaketide chain elongation intermediate as its N-acetyl cysteamine (NAC) thioester has been achieved, and its reaction with Pik TE demonstrated the ability of Pik TE to catalyze its macrolactonization to the natural product 10-deoxymethynolide. A steady-state kinetic analysis of the hexaketide chain intermediate with Pik TE was done. A preliminary substrate specificity study with unnatural hexaketide analogues was accomplished, demonstrating the importance of total synthesis in obtaining access to advanced polyketide intermediates. The results show the sensitivity of Pik TE to minor substrate modifications, and illustrate the potential use of thioesterases as versatile macrolactonization catalysts.     

Structural characterization and oxidative dehydrogenation activity of V2O5/Ce(x)Zr(1-x)O2/SiO2 catalysts

The thermal stability of a nanosized Ce(x)Zr(1-x)O2 solid solution on a silica surface and the dispersion behavior of V2O5 over Ce(x)Zr(1-x)O2/SiO2 have been investigated using XRD, Raman spectroscopy, XPS, HREM, and BET surface area techniques. Oxidative dehydrogenation of ethylbenzene to styrene was performed as a test reaction to assess the usefulness of the VOx/Ce(x)Zr(1-x)O2/SiO2 catalyst. Ce(x)Zr(1-x)O2/SiO2 (1:1:2 mol ratio based on oxides) was synthesized through a soft-chemical route from ultrahigh dilute solutions by adopting a deposition coprecipitation technique. A theoretical monolayer equivalent to 10 wt % V2O5 was impregnated over the calcined Ce(x)Zr(1-x)O2/SiO2 sample (773 K) by an aqueous wet impregnation technique. The prepared V2O5/Ce(x)Zr(1-x)O2/SiO2 sample was subjected to thermal treatments from 773 to 1073 K. The XRD measurements indicate the presence of cubic Ce0.75Zr0.25O2 in the case of Ce(x)Zr(1-x)O2/SiO2, while cubic Ce0.5Zr0.5O2 and tetragonal Ce0.16Zr0.84O2 in the case of V2O5/Ce(x)Zr(1-x)O2/SiO2 when calcined at various temperatures. Dispersed vanadium oxide induces more incorporation of zirconium into the ceria lattice, thereby decreasing its lattice size and also accelerating the crystallization of Ce-Zr-O solid solutions at higher calcination temperatures. Further, it interacts selectively with the ceria portion of the composite oxide to form CeVO4. The RS measurements provide good evidence about the dispersed form of vanadium oxide and the CeVO4 compound. The HREM studies show the presence of small Ce-Zr-oxide particles of approximately 5 nm size over the surface of amorphous silica and corroborate with the results obtained from other techniques. The catalytic activity studies reveal the ability of vanadium oxide supported on Ce(x)Zr(1-x)O2/SiO2 to efficiently catalyze the ODH of ethylbenzene at normal atmospheric pressure. The remarkable ability of Ce(x)Zr(1-x)O2 to prevent the deactivation of supported vanadium oxide leading to stable activity in the time-on-stream experiments and high selectivity to styrene are other important observations.