Canonical and Noncanonical Recursion Operators in Multidimensions

The hierarchies of evolution equations associated with the spectral operators ?_x?_y ? R?_y ? Q and ?_x?_y ? Q in the plane are considered. In both cases a recursion operator Ф₁₂, which is nonlocal and generates the hierarchy, is obtained. It is shown that only in the first case does the recursion operator satisfy the canonical geometrical scheme in 2 + 1 dimensions proposed by Fokas and Santini. The general procedure proposed allows one to derive, at the same time, the evolution equations associated with a given linear spectral problem and their Backlund transformations (if they exist), with no need to verify by long and tedious computations the algebraic properties of Ф₁₂. Two equations in the first hierarchy can be considered as two different integrable generalizations in the plane of the dispersive long wave equation. All equations in this hierarchy are shown to be both a dimensional reduction of bi-Hamiltonian n × n matrix evolution equations in multidimensions and a generalization in the plane of bi-Hamiltonian n × n matrix evolution equations on the line.     

Temperature dependence of C-axis electrical resistivity and thermopower of graphite intercalation compounds

Results on the temperature variation from 2 ? T ? 300 K of the c-axis electrical resistivity and thermopower of a donor stage-5 potassium and an acceptor stage-2 FeCl₃ graphite intercalation compounds are reported. Comparing the data with those of the literature reveals for both compounds a different qualitative behavior for low and high stages.     

Experimental study of vortex emission behind bluff obstacles in a gas liquid vertical two-phase flow

Vortex emission behind cylinders with trapezoidal cross section was experimentally studied in air-water vertical two-phase flows (liquid velocities vary from 45 cm/s to 2 m/s inside a 15 cm ID pipe); the void fraction ranged from 0 to 25%. The measurements were performed at room pressure and temperature. Two flow regimes were observed. For void fraction smaller than 10% vortex emission remained stable and its frequency sharply defined. However, the rms amplitude of the associated pressure fluctuations strongly decreased. These results were explained by bubble trapping inside the vortex cores. This effect was verified experimentally and analyzed using optical fiber probe measurements. Above a 10% void fraction, vortex emission became erratic. Its spectrum became broader but could be identified up to 25% void fraction.     

Low temperature thermal conductivity of graphite-FeCl3 intercalation compounds

The low-temperature variation of the in-plane thermal conductivity of graphite- FeCl₃ intercalation compounds is reported. Around room temperature, though holes are participating, there is an important lattice contribution, but much smaller than in pristine graphite. The electronic contribution dominates in the liquid helium range. These preliminary results suggest lattice thermal conductivity measurements as a new tool to investigate defects introduced by intercalation.     

Directed evolution of hybrid enzymes: Evolving enantioselectivity of an achiral Rh-complex anchored to a protein

The concept of utilizing the methods of directed evolution for tuning the enantioselectivity of synthetic achiral metal-ligand centers anchored to proteins has been implemented experimentally for the first time.     

Interplay of Peltier and Seebeck effects in nanoscale nonlocal spin valves

We have experimentally studied the role of thermoelectric effects in nanoscale nonlocal spin valve devices. A finite element thermoelectric model is developed to calculate the generated Seebeck voltages due to Peltier and Joule heating in the devices. By measuring the first, second, and third harmonic voltage response nonlocally, the model is experimentally examined. The results indicate that the combination of Peltier and Seebeck effects contributes significantly to the nonlocal baseline resistance. Moreover, we found that the second and third harmonic response signals can be attributed to Joule heating and temperature dependencies of both the Seebeck coefficient and resistivity.     

Influence of turbulence on the dynamo threshold

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale, and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold and increases it for any noise at large scale. For small-scale noise, the result depends on its correlation time and on the magnetic Prandtl number.     

Linear programming solutions and distance functions under α-returns to scale

This note generalizes analytical relationships among activity variables of Dataenvelopment analysis models previously derived in a previous article by theauthors of this note. We relax the assumption of constant returns to scale byshowing that the key results hold under a weaker assumption of homogeneity. Weuse the notion of α-returns to scale to extend the analysis tostrictly increasing and decreasing returns, covering now the whole range ofreturns to scale for multi-output homogenous technologies.     

Raman Scattering from Liquid Crystals

Abstract

The use of Raman scattering technique as a tool for studying local order in complex liquid crystal systems is illustrated by three examples, namely the locally anisotropic liquid L-phase, lipid membranes, and PDLC's.