Analysis of Polymer Dynamics by NMR Modulated Gradient Spin Echo

NMR modulated gradient spin echo method, which allows the quantification of polymer segmental displacement via the measurement of the velocity autocorrelation, requires the formulation of theoretical predictions in the frequency domain in order to test their validity. We worked out the velocity autocorrelation spectrum of the segmental motion according to the Rouse and the tube/reptation model to compare it to the experimental results obtained by the new NMR technique. The analysis of polybutadiene shows the segmental velocity autocorrelation spectrum typical for the reptation-like motion of polymer in a “tube”. The measurement of bulk water indicates a kind of Rouse motion in a network of hydrogen bonds.     

Marcinkiewicz's theorem on operator multipliers of Fourier series

We give some sufficient conditions on the operators which for each imply the inequality

     

Linear and nonlinear propagation of light beams in two-dimensional photorefractive photonic lattices formed in lithium niobate

Special features of linear and nonlinear propagation of coherent light beams in two-dimensional photorefractive photonic lattices optically induced in the lithium niobate crystal doped with iron are experimentally investigated. The two-dimensional gratings are formed by consecutive recording of two one-dimensional photorefractive gratings in the crystal. Experiments were performed using He-Ne laser irradiation with a wavelength of 633 nm. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 58–62, September, 2006.     

Nano-antenna-assisted harmonic generation

We report on low-order harmonic generation utilising the plasmonic field enhancement in arrays of rod-type gold optical antennae. Furthermore, we examine their suitability to support high-order harmonic generation (HHG). The low-order harmonics are used as a tool to investigate the nonlinear properties of the antennae. Particular attention is paid to the thermal properties, which become significant at the peak intensities necessary for HHG. A theoretical model explains the experimental findings and enables future improvements. In experiments we observe up to the fifth harmonic order and measure a field enhancement sufficient to support high-order harmonic generation. Moreover, we find a damage threshold for the antennae.     

Tamm oscillations in semi-infinite nonlinear waveguide arrays

We demonstrate the existence of nonlinear Tamm oscillations at the interface between a substrate and a one-dimensional waveguide array with either cubic or saturable, self-focusing or self-defocusing nonlinearity. Light is trapped in the vicinity of the array boundary due to the interplay between the repulsive edge potential and Bragg reflection inside the array. In the special case when this potential is linear these oscillations reduce themselves to surface Bloch oscillations.     

Starlikeness and Certain Class of Rational Functions

A new criterion for starlikeness in the unit disc and an application to a certain class of rational functions are given.     

Nano- sensing and catalysis technologies for managing food-water-energy (FEW) resources in farming

As the world population grows and new environmental, sustainability, and security challenges emerge, it becomes critical to consider and propose solutions for problems at the nexus of Food, Water, and Energy (FEW). These three are key resources critical for the human health and welfare. Managing effectively the FEW resources in the context of farming, while focusing on lactation cattle, is the theme of this work. The solutions presented here are based on nano-sensing and catalysis. Novel gas sensing technologies are described that can monitor the health of the livestock, monitor the feed conversion efficiency in their feed, and help reduce the water footprint related to the production of animal products (such as milk). Water quality control and water clean-up technologies along with energy harvesting tools based on nanofibrous mats are also presented; these help reduce the carbon footprint of the farming processes. Implementing these integrated systems in any agricultural facility will promote the sustainable production of meat and meat products.