Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Positive commutators at the bottom of the spectrum

Bony and Häfner have recently obtained positive commutator estimates on the Laplacian in the low-energy limit on asymptotically Euclidean spaces; these estimates can be used to prove local energy decay estimates if the metric is non-trapping. We simplify the proof of the estimates of Bony-Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), by applying a sharp Poincaré inequality. Our main result is the positive commutator estimate

     

Surprising Inability of Singlet Oxygen-generated 6-Hydroperoxycholesterol to Induce Damaging Free Radical Lipid Peroxidation in Cell Membranes†

Singlet oxygen attack on cholesterol (Ch), a prominent monounsaturated lipid of mammalian cell plasma membranes, gives rise to three hydroperoxide (ChOOH) isomers, 5α-OOH, 6α-OOH and 6β-OOH, the latter two in lower yield than 5α-OOH, and 6α-OOH in lowest yield. A third possible positional isomer, 7α-OOH and 7β-OOH, is produced by free radical attack. In the presence of iron and ascorbate (Fe/AH), 5α-OOH or 6β-OOH in phosphatidylcholine/Ch/ChOOH (20:15:1 by mol) liposomes was reduced to its corresponding alcohol, the rate constant being approximately the same for both ChOOHs. Using [¹⁴C]Ch as an in situ probe, we found that liposomal 5α-OOH readily set off free radical-mediated (chain) peroxidation reactions when exposed to Fe/AH, whereas 6β-OOH under the same conditions did not. Moreover, liposomal 5α-OOH triggered robust chain peroxidation in [¹⁴C]Ch-labeled L1210 cells, leading to cell death, whereas 6β-OOH was essentially inert in this regard. Thus, 5α-OOH and 6β-OOH undergo iron-catalyzed reductive turnover, but only the former can provoke toxic membrane damage. These novel findings have important implications for UVA-induced photodamage in Ch-rich tissues like skin and eye, where ¹O₂ often plays a major role.     

Hydrogen Generation Through Indirect Biophotolysis in Batch Cultures of the Nonheterocystous Nitrogen-Fixing Cyanobacterium <Emphasis Type="Italic">Plectonema boryanum</Emphasis>

The nitrogen-fixing nonheterocystous cyanobacterium Plectonema boryanum was used as a model organism to study hydrogen generation by indirect biophotolysis in nitrogen-limited batch cultures that were continuously illuminated and sparged with argon/CO₂ to maintain anaerobiosis. The highest hydrogen-production rate (i.e., 0.18 mL/mg day or 7.3 μmol/mg day) was observed in cultures with an initial medium nitrate concentration of 1 mM at a light intensity of 100 μmol/m² s. The addition of photosystem II (PSII) inhibitor 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) did not reduce hydrogen-production rates relative to unchallenged controls for 50 to 150 h, and intracellular glycogen concentrations decreased significantly during the hydrogen generation period. The insensitivity of the hydrogen-production process to DCMU is indicative of the fact that hydrogen was not derived from water splitting at PSII (i.e., direct biophotolysis) but rather from electrons provided by intracellular glycogen reserves (i.e., indirect biophotolysis). It was shown that hydrogen generation could be sustained for long time periods by subjecting the cultures to alternating cycles of aerobic, nitrogen-limited growth and anaerobic hydrogen production.     

Probing the local structure of liquid water by X-ray absorption spectroscopy

It was recently suggested that liquid water primarily comprises hydrogen-bonded rings and chains, as opposed to the traditionally accepted locally tetrahedral structure (Wernet et al. Science 2004, 304, 995). This controversial conclusion was primarily based on comparison between experimental and calculated X-ray absorption spectra (XAS) using computer-generated ice-like 11-molecule clusters. Here we present calculations which conclusively show that when hydrogen-bonding configurations are chosen randomly, the calculated XAS does not reproduce the experimental XAS regardless of the bonding model employed (i.e., rings and chains vs tetrahedral). Furthermore, we also present an analysis of a recently introduced asymmetric water potential (Soper, A. K. J. Phys.: Condens. Matter 2005, 17, S3273), which is representative of the rings and chains structure, and make comparisons with the standard SPC/E potential, which represents the locally tetrahedral structure. We find that the calculated XAS from both potentials is inconsistent with the experimental XAS. However, we also show the calculated electric field distribution from the rings and chains structure is strongly bimodal and highly inconsistent with the experimental Raman spectrum, thus casting serious doubt on the validity of the rings and chains model for liquid water.     

Asymptotics of Karhunen-Loeve Eigenvalues and Tight Constants for Probability Distributions of Passive Scalar Transport

In this paper we study the asymptotics of the probability distribution function for a certain model of freely decaying passive scalar transport. In particular we prove rigorous large n, or semiclassical, asymptotics for the eigenvalues of the covariance of a fractional Brownian motion. Using these asymptotics, along with some standard large deviations results, we are able to derive tight asymptotics for the rate of decay of the tails of the probability density for a generalization of the Majda model of scalar intermittency originally due to Vanden Eijnden. We are also able to derive asymptotically tight estimates for the closely related problem of small L₂ ball probabilities for a fractional Brownian motion.     

Synthesis and partial biological evaluation of a small library of differentially-linked beta-C-disaccharides

The synthesis of a small library of differentially-linked beta-C-disaccharides has been carried out through the use of a radical allylation-RCM strategy. Acids 6 were prepared by Keck allylation of a suitable carbohydrate-based radical precursor, followed by oxidative cleavage of the formed alkene. Dehydrative coupling of these acids with the known olefin alcohol 5 then gave the precursor esters 7 in excellent yield. Methylenation of the esters 7 was followed by RCM and in situ hydroboration-oxidation of the formed glycals to furnish the protected beta-C-disaccharides 10 in good overall yield. Five examples were then deprotected and screened for their efficacy as enzyme inhibitors of beta-glycosidase and against several solid-tumor cell lines for in vitro differential cytotoxicity.     

Functional and tuneable amino acid polymers prepared by RAFT polymerization

We report the application of reversible addition‐fragmentation chain transfer polymerization using a novel chain transfer agent toward the synthesis of a variety of copolymers containing proline‐derived monomeric units. This methodology enables ready access to a number of polymeric species with narrow molecular weight distributions, reliable functional unit incorporations, and high conversions. The methodology is also a facile approach to novel copolymeric species incorporating amino acids, which possess unique material properties and the potential for further organocatalytic application. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Finite field elements of high order arising from modular curves

In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit modular towers. In particular, we give two explicit constructions based on two examples of his formulas and demonstrate that the resulting elements have high order. Between the two constructions, we are able to generate high order elements in every characteristic. Despite the use of the modular recursions of Elkies, our methods are quite elementary and require no knowledge of modular curves. We compare our results to a recent result of Voloch. In order to do this, we state and prove a slightly more refined version of a special case of his result.      

Binary aspects and particle multiplicities of the fragments from natAg+340 MeV 40Ar deep inelastic collisions

Deep inelastic fragments from the reaction ^natAg+340 MeV ⁴⁰Ar have been studied in coincidence. Charged particles (10 ≦ Z ≦ 32) were detected and identified in Z by means of a ΔE?E telescope, while the complementary fragments were detected in a one-dimensional, solid-state position-sensitive detector. Both in-plane and out-of-plane correlations were measured. The results confirm the binary nature of the deep inelastic process for this reaction. From the measured energies and angles of the fragments and the atomic number of one of the fragments, it was possible to determine the total mass loss due to the de-excitation of the fragments as well as the total evaporated charge at symmetry. An iterative procedure is discussed which enables one to determine the masses and kinetic energies of the fragments before evaporation, as well as the total number of particles evaporated by each fragment. The widths of the in-plane and out-of-plane correlations agree with the results of the iterative calculations, as do evaporation calculations which are based on the charge equilibrium model. The experimental results support the charge equilibrium model and indicate that thermal equilibrium is achieved between the fragments at fixed mass asymmetry.