Beyond the absorption-limited nonlinear phase shift with microring resonators

We show that the nonlinear phase shift produced by a ring resonator constructed from a given nonlinear optical material can be greater than the phase shift produced by a single pass through an infinite length of the same material when linear and nonlinear absorption are taken into consideration. The figure of merit (defined by the phase shift times the throughput) also improves for the ring resonator over that of the native nonlinear absorbing material. We finally show that these benefits of using the ring resonator as a nonlinear phase-shifting element can enhance the switching characteristics of a Mach-Zehnder interferometer.     

A sharp exponential inequality for Lorentz-Sobolev spaces on bounded domains

This paper generalizes an inequality of Moser from the case that is in the Lebesgue space to certain subspaces, namely the Lorentz spaces , where . The conclusion is that is integrable, where . This is a higher degree of integrability than in the Moser inequality when . A formula for is given and it is also shown that no larger value of works.

     

Peptide mimotopes of phomopsins: Identification, characterization and application in an immunoassay

Peptide mimotopes of plant-associated toxins offer the potential for improving analytical and diagnostic methodologies as well as providing candidates for potential protective vaccines against plant poisoning diseases. Monoclonal antibody (mAb) C₃C₁₁, which recognizes the antimicrotubule phomopsin mycotoxins, was used to isolate peptide mimics of phomopsin A from a random 15-mer phage display peptide library. A total of 46 clones were isolated that showed specific reactivity with the mAb. Amino acid sequence analysis revealed four different types of mimotope sequences, all of which contained a common motif V-A-L/V-C. Of the 46 clones isolated, 44 contained the motif V-A-L-C while 2 contained the V-A-V-C motif. All four types of phage clones inhibited the reactivity of the mAb with phomopsin A in a competition ELISA. The clone with the mimotope sequence CT VALCNMYFGAKLD demonstrated the strongest binding. It was further shown that synthetic peptides containing these mimotope amino acid sequences were able to inhibit the mAb-phomopsin A interaction, indicating that the peptide mimotopes were responsible for the specific binding, independent of the phage framework. The results also suggest that the mimotope peptides bind to mAb C₃C₁₁ at the same site as phomopsin A. The application of recombinant phage particles carrying phomopsin mimotopes in immunoassay was evaluated and the results demonstrated approximately 100-fold increase in sensitivity in comparison with a conventional immunoassay using a chemically linked phomopsin-horseradish peroxidase conjugate.     

Quantum Ergodicity of Boundary Values of Eigenfunctions

Suppose that ⁿ is a bounded, piecewise smooth domain. We prove that the boundary values (Cauchy data) of eigenfunctions of the Laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle B^*() is ergodic. Our proof is based on the classical observation that the boundary values of an interior eigenfunction , =² is an eigenfunction of an operator F_h on the boundary of with h=^–1. In the case of the Neumann boundary condition, F_h is the boundary integral operator induced by the double layer potential. We show that F_h is a semiclassical Fourier integral operator quantizing the billiard map plus a small remainder; the quantum dynamics defined by F_h can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of Zelditch-Zworski (1996). Novelties include the facts that F_h is not unitary and (consequently) the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions. Ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by S. Ozawa (1993), and was almost simultaneously proved by Gerard-Leichtnam (1993) in the case of convex C^1,1 domains (with continuous tangent planes) and with Dirichlet boundary conditions. Our methods seem to be quite different. Motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form.The first author was partially supported by an Australian Research Council Fellowship.The second author was partially supported by NSF grant #DMS-0071358 and DMS-0302518.     

Application of phased array techniques to coarse grain components inspection

Ultrasonic inspection of cast stainless steel components from primary and auxiliary cooling circuits of French Nuclear Power Plant has to face with major difficulties due to the coarse grained structure of these materials. Attenuation losses and structural noise are encountered, which limits the performances of defect detection ability, mostly in terms of degraded signal-to-noise ratio and poor sensitivity. To overcome such problems, theoretical and experimental studies have been achieved at the French Atomic Energy Commission, with support from the French Institute for Radiological Protection and Nuclear Safety. Experimental studies have been performed over stainless steel specimen of known coarse structure (equiaxial grains and/or elongated grains), containing artificial reflectors (cylindrical holes and electro-eroded surface breaking notches). Those mock-ups have been inspected using contact probes of different array designs (linear or matrix splitting), and using pulse echo or dual-element techniques. Such arrays allow to control the ultrasonic beam so as to investigate different inspection angles and focusing depths. Experiments were carried out using oblique longitudinal waves, using delay laws computed by a specific model, taking account of acoustical and geometrical properties of the probes and the inspected component. In addition, specific reconstruction techniques have been investigated to enhance the signal-to-noise ratio as well as spatial resolution. These techniques are based on beam-forming summation and multi-angle inspections. Experimental results show that such techniques allow to reduce the speckle noise and to optimise the beam resolution. Those increased performances allow to detect and to size small planar defects located at the inner wall of a thick specimen, using corner and tip diffraction echoes.     

At-sea measurements of sound penetration into sediments using a buried vertical synthetic array

Acoustic bottom penetration experiments were carried out in a medium-grain sandy bottom at a site in St. Andrews Bay, Florida. These investigations used a new buried, vertical, one-dimensional synthetic array system where a small hydrophone was water-jetted into the sediment to a depth of approximately 2 m. Once buried, this hydrophone was mounted to a vertical robotics stage that translated the hydrophone upward in 1-cm increments. A broadband (3 to 80 kHz) spherical source, positioned 50 cm above the sediment-water interface, was used to insonify the sediment. Measurements were made with insonification angles above and below the critical angle by changing the horizontal distance of the source relative to the insertion point. This new measurement system is detailed, and results are presented that include temporal, frequency, and wavenumber analysis for natural and roughened interfaces. The measured compressional sound speed and attenuation are shown to be self-consistent using the Kramers-Kronig relation. Furthermore, only a single fast compressional wave was observed. There was no observation of a second slower compressional wave as predicted by some applications of the Biot model to unconsolidated water-saturated porous media.     

Solvent-stabilized molecular capsules

Pyrrogallolarenes 2 were prepared by acid-catalyzed condensation of pyrrogallol with aldehydes. Compound 2a crystallizes from a methanol solution of quinuclidine hydrochloride to give a dimeric molecular capsule surrounding one disordered quinuclidinium cation. The molecules of 2a are connected by direct hydrogen bonds and by bridging methanol and water molecules. The chloride anion is positioned outside the capsule and is hydrogen bonded to the hydroxy groups of 2a. The shortest distance between the cation and anion was found to be 6.7 A. Crystallization of 2b from aqueous acetonitrile resulted in a dimeric capsule linked by a polar belt of 16 hydrogen bonding water molecules. Four acetonitrile molecules occupy the cavity of this dimeric capsule and assume two binding sites that differ in hydrogen bonding and electronic environment. Compounds 2 also form hydrogen-bonded dimeric molecular capsules in alcohols and aqueous acetonitrile solutions. These assemblies readily encapsulate tetramethylammonium, tetramethylphosphonium, quinuclidinium, and tropylium cations to give complexes stable on the NMR time scale at 233 K.