Compact efficient broadband grating coupler for silicon-on-insulator waveguides

We have designed a high-efficiency broadband grating coupler for coupling between silicon-on-insulator (SOI) waveguides and optical fibers. The grating is only 13 microm long and 12 microm wide, and the size of the grooves is optimized numerically. For TE polarization the coupling loss to single-mode fiber is below 1 dB over a 35-nm wavelength range when using SOI with a two-pair bottom reflector. The tolerances to fabrication errors are also calculated.     

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.     

Impurities and quantum interference in the chains of YBa2Cu3O6+x

Motivated by recent experiments, we study the electronic structure near impurities in the chains of YBa2Cu3O6+x. Using a model of proximity induced chain superconductivity, we show that a resonance state in the chain density of states is induced only by a magnetic impurity. The spatial form of the resonance reflects the particle-hole nature of chain superconductivity and therefore distinguishes it from other broken symmetry phases. Because of quantum interference effects between impurities, the chains can undergo a quantum phase transition into a polarized state.     

Light absorption of (oxy-)hemoglobin assessed by spectroscopic optical coherence tomography

The combination of optical coherence tomography and spectroscopy may allow for highly localized, quantitative measurements of tissue spectral properties. We present, for the first time to our knowledge, quantitative measurements of the absorption coefficients of phantoms and of hemoglobin and oxygenated hemoglobin with spectroscopic optical coherence tomography (SOCT). Our results suggest that SOCT will be able to provide localized, quantitative oxygenation measurements.     

Retrospective intra-scan motion correction

This paper analyzes the effects of intra-scan motion and demonstrates the possibility of correcting them directly in k-space with a new automatic retrospective method. The method is presented for series of 2D acquisitions with Cartesian sampling. Using a reference k-space acquisition (corrected for translations) within the series, intra-scan motion parameters are accurately estimated for each trajectory in k-space of each data set in the series resulting in pseudo-random sample positions. The images are reconstructed with a Bayesian estimator that can handle sparse arbitrary sampling in k-space and reduces intra-scan rotation artefacts to the noise level. The method has been assessed by means of a Monte Carlo study on axial brain images for different signal-to-noise ratios. The accuracy of motion estimates is better than 0.1 degrees for rotation, and 0.1 and 0.05 pixel, respectively, for translation along the read and phase directions for signal-to-noise ratios higher than 6 of the signals on each trajectory. An example of reconstruction from experimental data corrupted by head motion is also given.     

New a posteriori error estimates for singular boundary value problems

In this paper, we discuss the asymptotic properties and efficiency of several a posteriori estimates for the global error of collocation methods. Proofs of the asymptotic correctness are given for regular problems and for problems with a singularity of the first kind. We were also strongly interested in finding out which of our error estimates can be applied for the efficient solution of boundary value problems in ordinary differential equations with an essential singularity. Particularly, we compare estimates based on the defect correction principle with a strategy based on mesh halving. AMS subject classification 65L05Supported in part by the Austrian Research Fund (FWF) grant P-15072-MAT and SFB Aurora.     

Coloring-flow duality of embedded graphs

Let be a directed graph embedded in a surface. A map is a tension if for every circuit , the sum of on the forward edges of is equal to the sum of on the backward edges of . If this condition is satisfied for every circuit of which is a contractible curve in the surface, then is a local tension. If holds for every , we say that is a (local) -tension. We define the circular chromatic number and the local circular chromatic number of by and , respectively. The invariant is a refinement of the usual chromatic number, whereas is closely related to Tutte's flow index and Bouchet's biflow index of the surface dual .

From the definitions we have . The main result of this paper is a far-reaching generalization of Tutte's coloring-flow duality in planar graphs. It is proved that for every surface and every 0$">, there exists an integer so that holds for every graph embedded in with edge-width at least , where the edge-width is the length of a shortest noncontractible circuit in .

In 1996, Youngs discovered that every quadrangulation of the projective plane has chromatic number 2 or 4, but never 3. As an application of the main result we show that such `bimodal' behavior can be observed in , and thus in for two generic classes of embedded graphs: those that are triangulations and those whose face boundaries all have even length. In particular, if is embedded in some surface with large edge-width and all its faces have even length , then . Similarly, if is a triangulation with large edge-width, then . It is also shown that there exist Eulerian triangulations of arbitrarily large edge-width on nonorientable surfaces whose circular chromatic number is equal to 5.

     

Physics of size selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against the extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.     

Experimental observation of universality in depolarized light scattering

Experimental results on light depolarization due to multimode scattering are reported. By means of polarization tomography, we characterize the depolarizing power and the polarization entropy of a broad class of optically scattering media and confirm the recently predicted universal behavior of these two quantities [Phys. Rev. Lett. 94, 090406 (2005)].     

Ring-closing alkyne metathesis approach toward the synthesis of alkyne mimics of thioether A-, B-, C-, and DE-ring systems of the lantibiotic nisin Z

[reaction: see text] Ring-closing alkyne metathesis toward the synthesis of the alkyne-brigded A-, B-, C-, and (D)E-ring mimics of the peptide antibiotic nisin Z is described. We have successfully synthesized alkyne-bridged cyclic peptides containing 4-7 amino acid residues in yields ranging from 18 to 82%.