Lie groupoids and the Frölicher-Nijenhuis bracket

The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frölicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different characterizations of multiplicative vector-valued forms.     

A retrodictive stochastic simulation algorithm

In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.     

All-optical generation of 40 Gb/s single sideband signals using a fiber Bragg grating

In this work, we demonstrate a reliable all-optical technique for performing optical double sideband (ODSB) to single sideband (OSSB) format conversion of a 40 Gb/s non-return-to-zero signal. It is based on the optimization of a detuned optical filter, which was implemented on a fiber Bragg grating (FBG) with a complex apodization profile. An OSSB signal with negligible distortion was obtained, as the FBG presented a nearly ideal frequency response. Higher tolerance to chromatic dispersion enabled by the OSSB signal in comparison to the ODSB signal was demonstrated on both simulation and experimental results.     

Positional isomers of linear sodium dodecyl benzene sulfonate: solubility, self-assembly, and air/water interfacial activity

Commercial linear alkyl benzene sulfonates (ABS) are a very important class of anionic surfactants that are employed in a wide variety of applications, especially those involving wetting and detergency. Linear ABS surfactants generally consist of a complex mixture of different chain lengths and positional isomers. This diversity and level of complexity makes it difficult to develop fundamental structure-property correlations for the commercial surfactants. In this work, six monodisperse headgroup positional isomers of sodium para-dodecyl benzene sulfonate (Na-x-DBS, x = 1-6) have been studied. The influence of headgroup position and added electrolyte (NaCl) on the solubility and self-assembly (micellar and vesicular aggregation and lyotropic liquid crystalline phase behavior) in the temperature range from 10 to 90 degrees C have been investigated. Additionally, the air-aqueous solution interfacial adsorption at 25 (no added NaCl) and 50 degrees C (from 0 to 1.0 M added NaCl) has been examined. The observed physicochemical behavior is interpreted in terms of local molecular packing constraints, and in the case of the lyotropic liquid crystalline behavior global aggregate packing constraints as well.     

Accuracy of the multipole expansion applied to a sphere in a creeping flow parallel to a wall

An example system is studied to discuss precision of the multipoleexpansion, applied to determine forces exerted on particlesby a viscous low-Reynolds-number fluid flow. A single spherein an ambient flow (pure shear, quadratic, and modulated shear)parallel to a close plane wall is considered. Forces and torquesexerted by the ambient flow on a motionless sphere are evaluated.Their precision is determined and related to a multipole orderof the truncation. Similar analysis is performed for a movingsphere with no ambient flow and for a freely moving sphere.Relative motion of the sphere with respect to the wall givesrise to strong lubrication interactions. It is analysed howthese interactions affect accuracy of the pure multipole expansion,and what are the smallest distances where it becomes insufficient.An alternative precise method is applied, in which lubricationexpressions are subtracted from the hydrodynamic forces andtorques, and the residue is evaluated as a fast-convergent seriesof inverse powers of the distance between the sphere centreand the wall. The accuracy of this procedure is carefully analysed.     

Nonionic urea surfactants: formation of inverse hexagonal lyotropic liquid crystalline phases by introducing hydrocarbon chain unsaturation

The homo-interaction between urea moieties residing in close proximity to each other generally results in very strong intermolecular hydrogen bonding. The bifurcated hydrogen bonding exhibited by n-alkyl substituted ureas means that for those urea surfactants possessing medium and long hydrocarbon chain substituents the crystal to isotropic liquid melting point is high and the solubility in water is very low, compared to other similar chain length nonionic surfactants. In addition, saturated n-alkyl urea surfactants do not form lyotropic liquid crystalline phases in water. In this work the strong intermolecular hydrogen bonding of the urea headgroup has been ameliorated through the introduction of unsaturated hydrocarbon chains, viz., oleyl (cis-octadec-9-enyl), linoleyl (cis, cis-octadec-9,12-dienyl), and linolenyl (cis, cis, cis-octadec-9,12,15-trienyl) with one, two, and three carbon double bonds, respectively. Unsaturation in the C18 urea surfactants lowers the melting point and promotes an inverse hexagonal phase, in oleyl urea-water and linoleyl urea-water systems, which is thermodynamically stable in excess water. As the degree of unsaturation is increased to three in linolenyl urea, there is a tendency for autoxidation/polymerization. The occurrence of an inverse hexagonal phase in the nonionic urea surfactant-water systems has been rationalized in terms of both local molecular and global self-assembled aggregate packing constraints.     

Nanostructure and amphiphile self-assembly in polar molecular solvents: amides and the "solvophobic effect"

The ability of low molecular weight amides to support amphiphile self-assembly is shown to be a general feature for this class of solvents. This report extends the number of known polar solvents which can support amphiphile self-assembly by five new amides; more than doubling the number of known amides able to serve as amphiphile self-assembly media. The formation of lyotropic liquid crystalline phases by cationic and non-ionic surfactants in these liquid amides is reported. The ability of a solvent to promote amphiphile self-assembly is governed by the "solvophobic effect" and is linked to the solvent cohesiveness. The Gordon parameter which is a measure of the solvent cohesiveness was found to provide a guide to an amides capacity to support lyotropic liquid crystalline phase diversity and thermal stability ranges of those phases. The "solvophobic effect" and steric hindrance factors were compared between amide's and protic ionic liquids possessing analogous chemical structures and also being able to promote amphiphile self-assembly.     

Electron emission from diamondoids: a diffusion quantum Monte Carlo study

We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.     

Einstein-Podolsky-Rosen entanglement strategies in two-well Bose-Einstein condensates

Criteria suitable for measuring entanglement between two different potential wells in a Bose-Einstein condensation are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or a dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen paradox.