Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model

We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a forbidden gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of exchange of stability between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.Received: 31 October 2003, Published online: 17 February 2004PACS: 63.20.Pw Localized modes - 63.20.Ry Anharmonic lattice modes - 42.65.Wi Nonlinear waveguides     

Microfluidic biosensing systems. Part II. Monitoring the dynamic production of glucose and ethanol from microchip-immobilised yeast cells using enzymatic chemiluminescent micro-biosensors

A microfluidic flow injection (microFIA) system was employed for handling and monitoring of cell-released products from living cells immobilised on silicon microchips. The dynamic release of glucose and ethanol produced from sucrose by immobilised Saccharomyces cerevisiae cells was determined using microchip biosensors (micro-biosensors) with either co-immobilised glucose oxidase-horseradish peroxidase (GOX-HRP), or alcohol oxidase-horseradish peroxidase (AOX-HRP), catalysing a series of reactions ending up with chemiluminescence (CL) generated from HRP-catalysed oxidation of luminol in presence of p-iodophenol (PIP). The yeast cells were attached by first treating them with polyethylenimine (PEI) followed by adsorption to the microchip surface. The cell loss during assaying was evaluated qualitatively using scanning electron microscopy (SEM), showing that no cells were lost after 35 min liquid handling of the cell chip at 10 microl min(-1). The enzymes were immobilised on microchips via PEI-treatment followed by glutaraldehyde (GA) activation. The GOX-HRP micro-biosensors could be used during five days without any noticeable decrease in response, while the AOX-HRP micro-biosensors showed continuously decreasing activity, but could still be used employing calibration correction. The glucose and ethanol released from the immobilised yeast chips were quantitatively monitored, by varying the incubation time with sucrose, showing the possibilities and advantages of using a microfluidic system set-up for cell-based assays.     

Optimal topological test for degeneracies of real Hamiltonians

We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.     

Application of isomorphous replacement in the structure determination of a cubic liquid crystal phase and location of counterions

A second generation monodendron with dodecyl end-groups based on the AB(3) monomer 3,4,5-trihydroxy benzoate has previously been shown to form a thermotropic cubic phase with Pmthremacr;n symmetry (Balagurusamy et al., J. Am. Chem. Soc. 1997, 119, 1539). A structure consisting of spherical "micelles" was proposed originally, but an alternative choice of structure factor phases, giving a structure of interlocked squashed columns, could not be ruled out by diffraction data on the original material alone. We have therefore synthesized two selectively fluorinated equivalent compounds, the carboxylic acid and its Rb salt, to be able to apply a variant of the isomorphous replacement crystallographic technique. On the basis of the electron density maps of the new labeled compounds, reconstructed using small-angle X-ray diffraction intensities, the interlocking columns model is unequivocally rejected and the spheres model is upheld. Furthermore, the location of the metal cation in the center of the "micelles" is directly confirmed. Micellar diameter was shown to decrease on fluorination of the dodecyl chain ends, and increase significantly on introduction of Rb. This is interpreted in terms of changes in the number of wedge-shaped dendrons fitting into a spherical micelle due to their changing taper angle. It was found that the Rb-rich regions at the centers of six out of eight "micelles" in the unit cell are elongated in the direction of their closest packing. This adds support to the suggestion of a partial "column-like" character of stacked rows of such micelles, consistent with the position of the Pmthremacr;n phase next to the columnar phase in the phase sequence of most taper-shape compounds. The results illustrate the potential of isomorphous replacement, used a great deal in protein crystallography, in structure investigation of liquid crystals and supramolecular soft matter.     

Applications of high-order harmonics

We review applications of high-order harmonic generation in different fields of physics, from spectroscopic studies of atoms and molecules, to interferometry and plasma diagnostics and nonlinear optics.Received: 11 December 2002, Published online: 24 April 2003PACS: 32.80.Fb Photoionization of atoms and ions - 42.65.Ky Frequency conversion; harmonic generation, including higher-order harmonic generationD. Descamps: Present address: CEA/DRECAM/SPAM, CEN Saclay, 91105 Gif-sur-Yvette, France.     

Bounds for the Distance Between Nearby Jordan and Kronecker Structures in a Closure Hierarchy

Computing the fine-canonical-structure elements of matrices and matrix pencils are ill-posed problems. Therefore, besides knowing the canonical structure of a matrix or a matrix pencil, it is equally important to know what are the nearby canonical structures that explain the behavior under small perturbations. Qualitative strata information is provided by our StratiGraph tool. Here, we present lower and upper bounds for the distance between Jordan and Kronecker structures in a closure hierarchy of an orbit or bundle stratification. This quantitative information is of importance in applications, e.g., distance to more degenerate systems (uncontrollability). Our upper bounds are based on staircase regularizing perturbations. The lower bounds are of EckartYoung type and are derived from a matrix representation of the tangent space of the orbit of a matrix or a matrix pencil. Computational results illustrate the use of the bounds. Bibliography: 42 titles.     

Oscillatory instabilities of standing waves in one-dimensional nonlinear lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal 0,pi. Incommensurate analytic SWs with |Q|>pi/2 may however appear as "quasistable," as their instability growth rate is of higher order.     

Theoretical investigation of high pressure phases of carbon dioxide

The recent discovery of a new solid phase of carbon dioxide ( CO2-V) has made it apparent that the properties of this vital chemical species are drastically altered under high pressure conditions. The reported transition at around 40 GPa from the Cmca phase ( CO2-III), which is a molecular solid, into the novel phase, which was observed to be quartzlike, clearly suggests a dramatic change of the chemical, electronic, and structural properties. We here present a theoretical analysis of the implications of this metamorphosis. At even higher pressures, we predict the existence of a very hard phase of the stishovite type.     

Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C

We study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms. This generalises work of Coleman, and is a first step in an ongoing project to extend the cohomological approach to classicality to higher-dimensional Shimura varieties.