Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs

Studies of the refraction and dispersion properties of two-dimensional (2D) photonic-crystal (PC) slab waveguides are reported. The photonic band structure is strongly modified in a slab PC, and only a small number of bands satisfy the guiding conditions imposed by the lack of translation symmetry in the direction perpendicular to the slab; however, it was found that a significant number of the guided modes retain the giant refraction and strong dispersion properties discovered previously in pure 2D PCs. A small change in incident angle resulted in a dramatic change in refraction angle. Furthermore, the dispersion surface exhibited a strong dependence on the frequency, resulting in a superprism effect similar to what has been predicted for pure 2D PCs. In the silicon-based slab PC studied, refraction angles as high as nearly 70 degrees were predicted for incident angles of less than 7 degrees , and frequency components differing by 3% were separated by 15 degrees . The demonstration of giant refraction and superprism phenomena in slab waveguide PCs open the possibility of developing new classes of optical devices that can, for example, be used to develop 2D optical integrated circuits for communications and computing.     

Functional MRI involving painful stimulation of the ankle and the effect of physiotherapy joint mobilization

We examined whether cerebral activation due to secondary hyperalgesia resulting from intrajoint capsaicin injection could be detected using functional magnetic resonance imaging (fMRI) in alpha-chloralose anesthetized rats. We also examined whether we could detect analgesic changes in the central nervous system response to pain as a result of physiotherapy joint manipulation. Robust activation of areas of the brain known to be associated with the processing of pain, namely the anterior cingulate (bilateral), frontal cortex (bilateral) and sensory motor cortex (contralateral), was found in all animals following injection of 25 microl of capsaicin (128 microg/ml in 7.5% DMSO) into the plantar surface of the rat hindpaw (n = 7) and 75 microL into the ankle joint (n = 13). Significantly greater activation was observed when capsaicin was injected into the plantar surface of the hindpaw compared to the ankle joint. Mechanical allodynia and secondary hyperalgesia following capsaicin injection into the ankle joint also resulted in activation of the same brain regions. Trends toward decreased areas of activation in brain regions associated with pain in animals following physiotherapy joint mobilization were observed.     

Assessing The Key Photophysical Properties of Triangulenium Dyes for DNA Binding by Alteration of the Fluorescent Core

Four-stranded G-quadruplex (G4) DNA is a non-canonical DNA topology that has been proposed to form in cells and play key roles in how the genome is read and used by the cellular machinery. Previously, a fluorescent triangulenium probe ( DAOTA-M2 ) was used to visualise G4s in cellulo, thanks to its distinct fluorescence lifetimes when bound to different DNA topologies. Herein, the library of available triangulenium probes is expanded to explore how modifications to the fluorescent core of the molecule affect its photophysical characteristics, interaction with DNA and cellular localisation. The benzo-bridged and isopropyl-bridged diazatriangulenium dyes, BDATA-M2 and CDATA-M2 respectively, featuring ethyl-morpholino substituents, were synthesised and characterised. The interactions of these molecules with different DNA topologies were studied to determine their binding affinity, fluorescence enhancement and fluorescence lifetime response. Finally, the cellular uptake and localisation of these optical probes were investigated. Whilst structural modifications to the triangulenium core only slightly alter the binding affinity to DNA, BDATA-M2 and CDATA-M2 cannot distinguish between DNA topologies through their fluorescence lifetime. It is argued theoretically and experimentally that this is due to reduced effectiveness of photoinduced electron transfer (PET) quenching. This work presents valuable new evidence into the critical role of PET quenching when using the fluorescence lifetime of triangulenium dyes to discriminate G4 DNA from duplex DNA, highlighting the importance of fine tuning redox and spectral properties when developing new triangulenium-based G4 probes.     

Synthesis of aromatic oxazolyl‐ and carboxyl‐functionalized polymers: Atom transfer radical polymerization of styrene initiated by 2‐[(4‐bromomethyl)phenyl]‐4,5‐dihydro‐4,4‐dimethyloxazole

The synthesis of a new compound, 2‐[(4‐bromomethyl)phenyl]‐4,5‐dihydro‐4,4‐dimethyloxazole ( 1 ), and its utility in the synthesis of oxazoline‐functionalized polystyrene by atom transfer radical polymerization (ATRP) methods are described. Aromatic oxazolyl‐functionalized polymers were prepared by the ATRP of styrene, initiated by ( 1 ) in the presence of copper(I) bromide/2,2′‐bipyridyl catalyst system, to afford the corresponding α‐oxazolyl‐functionalized polystyrene ( 2 ). The polymerization proceeded via a controlled free radical polymerization process to produce the corresponding α‐oxazolyl‐functionalized polymers with predictable number‐average molecular weights, narrow molecular weight distributions in high‐initiator efficiency reactions. Post‐ATRP chain end modification of α‐oxazolyl‐functionalized polystyrene ( 2 ) to form the corresponding α‐carboxyl‐functionalized polystyrene ( 3 ) was achieved by successive acid‐catalyzed hydrolysis and saponification reactions. The polymerization processes were monitored by gas chromatography analyses. The unimolecular‐functionalized initiator and functionalized polymers were characterized by thin layer chromatography, spectroscopy, size exclusion chromatography, and nonaqueous titration analysis. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Warped Convolutions,Rieffel Deformations and the Construction of Quantum Field Theories

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel’s strict deformations of C ^*–dynamical systems with automorphic actions of \mathbb Rⁿ{\mathbb R^n} , whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita–Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.     

Geometric Modular Action and Spontaneous Symmetry Breaking

We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times. We show that any internal symmetry group must commute with the representation of the Poincaré group (whose existence is assured by the CGMA) and each translation-invariant vector is also Poincaré invariant. The subspace of these vectors can be centrally decomposed into pure invariant states and the CGMA holds in the resulting sectors. As positivity of the energy is not assumed, similar results may be expected to hold for other space-times.Communicated by Klaus FredenhagenDedicated to the memory of Siegfried Schliedersubmitted 25/05/04, accepted 29/10/04     

Outer ellipsoidal approximations of the reachable set at infinity for linear systems

Outer ellipsoidal approximations to the reachable set at infinity for a linear control system with bounded scalar controls are obtained using a new method based on quadratic Lyapunov functions. These outer approximations are compared with those given by an algorithm due to Sabin and Summers, and also with certain tangential outer approximations, obtained using a fixed-point iteration scheme.This research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors gratefully acknowledge the assistance of Mr. Ryan Davies, recipient of an NSERC Undergraduate Research Award.