Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions

We demonstrate highly efficient evanescent-wave detection of fluorophore-labeled biomolecules in aqueous solutions positioned in the air holes of the microstructured part of a photonic crystal fiber. The air-suspended silica structures located between three neighboring air holes in the cladding crystal guide light with a large fraction of the optical field penetrating into the sample even at wavelengths in the visible range. An effective interaction length of several centimeters is obtained when a sample volume of less than 1 microL is used.     

Normalization of brain magnetic resonance images using histogram even-order derivative analysis

The even-ordered (2nd, 4th and 6th) derivatives of a brain MRI histogram were used to calculate a characteristic value for white matter, which was used to normalize the image intensity scale. Simulated image histograms were used to estimate the methodological error as a function of noise level, and the optimum derivative order was determined for each image type studied (T1-, T2- and density-weighted). The algorithm yielded highly reproducible results when used in conjunction with a threshold-sensitive brain segmentation algorithm. It also proved insensitive to the presence of extra-cranial tissues. This method of histogram analysis could find utility in a variety of applications that demand robust intensity normalization including image registration, brain segmentation, tissue classification and spatial inhomogeneity correction.     

Finite element prediction of wave motion in structural waveguides

A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.     

Mapping the magic numbers in binary Lennard-Jones clusters

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of Lennard-Jones parameters. In particular, we have shown that just having atoms of different sizes leads to a remarkable stabilization of polytetrahedral structures, including both polyicosahedral clusters and at larger sizes structures with disclination lines.     

Gamma rays from Kaluza-Klein dark matter

A TeV gamma-ray signal from the direction of the Galactic center (GC) has been detected by the HESS experiment. Here, we investigate whether Kaluza-Klein (KK) dark matter annihilations near the GC can be the explanation. Including the contributions from internal bremsstrahlung as well as subsequent decays of quarks and tau leptons, we find a very flat gamma-ray spectrum which drops abruptly at the dark matter particle mass. For a KK mass of about 1 TeV, this gives a good fit to the HESS data below 1 TeV. A similar model, with gauge coupling roughly 3 times as large and a particle mass of about 10 TeV, would give both the correct relic density and a photon spectrum that fits the complete range of data.     

Comparison of different methods for combining phase-contrast images obtained with multiple coils

The ability to determine coil sensitivities implies that a method optimized in terms of maximized signal-to-noise ratio (SNR) can be applied to the combination of multiple coil images. An optimization of SNR subsequently results in a minimized variance in quantitative velocity measurements using phase-contrast imaging. When coil sensitivities are unknown, the weighted mean method, utilizing the square of the signal magnitude as weights, is suitable for combination of multiple phase images. In this study, the optimized method using estimated coil sensitivities was compared to the weighted mean method both theoretically and experimentally. It is shown that absence of noise correlation between the different coil images implies no difference between the methods regarding the variance of the phase. In the practical situation, noise correlation does exist, implying an opportunity for further reduction of phase variance using the optimized method. In vitro and in vivo studies showed, however, no significant difference between the two methods studied.     

In situ reactivity and FTIR study of the wet and dry photooxidation of propane on anatase TiO2

The photocatalytic oxidation (PCO) of trace amounts of propane (500 ppm) on nanocrystalline anatase TiO2 has been investigated in situ as a function of temperature (T = 318-473 K), humidity (C(H2O) = 0-4%), and time by means of mass spectrometry and diffuse reflectance Fourier transform infrared spectroscopy (DRIFT). Propane adsorbs associatively on TiO2 at 318 K in dry air, while at 473 K small amounts of thermal dissociation products appear on the surface. In agreement with previous studies, propane is found primarily to be converted to acetone by reactions with photogenerated oxygen radicals. Various successive reaction paths exist, where the branching depends on the temperature and hydroxylation state of the surface. Under dry conditions at 318 K, acetone oxidation is initially kinetically hindered, while, above 400 K, acetone readily decomposes. The thermally assisted reaction channel leads to detrimental bonding of surface species and inhibition of the catalytic activity. It is manifested by a coloration of the sample and suggested to be coupled to surface reduction. Under humidified conditions, there is an optimum of the PCO in C(H2O) and T space, which is estimated to correspond to an equilibrium coverage of one monolayer of H2O (or bilayer). The latter reaction condition also corresponds to sustained high propane conversion and is characterized by rapid establishment of steady state rates. The optimum PCO is discussed in terms of a balance between (i) sustaining enough of a photoactive water monolayer to avoid detrimental bonding of surface species, (ii) allowing reactants to adsorb and access bulk TiO2 photoexcitations, and at the same time (iii) maximizing the thermally assisted decomposition of intermediates.     

A Local Index Formula for the Quantum Sphere

For the Dirac operator D on the standard quantum sphere we obtain an asymptotic expansion of the SU_q(2)-equivariant entire cyclic cocycle corresponding to when evaluated on the element The constant term of this expansion is a twisted cyclic cocycle which up to a scalar coincides with the volume form and computes the quantum as well as the classical Fredholm indices.Partially supported by the Norwegian Research Council.Supported by the SUP-program of the Norwegian Research Council.Acknowledgement The preparation of this paper was finished during the authors stay at Institute Mittag-Leffler in September 2003. They would like to express their gratitude to the staff at the institute and to the organizers of the year in Noncommutative Geometry.     

Approximation of the Inverse Frame Operator and Applications to Gabor Frames

A frame allows every element in a Hilbert space to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculation of the frame coefficients requires inversion of an operator S on . We show how the inverse of S can be approximated as close as we like using finite-dimensional linear algebra. In contrast with previous methods, our approximation can be used for any frame. Various consequences for approximation of the frame coefficients or approximation of the solution to a moment problem are discussed. We also apply the results to Gabor frames and frames consisting of translates of a single function.