Quantum double and multiparameter quantum groups

After Drinfe'd and Jimbo construction [3,7] of quantized universal envelop¬ing algebra associated to each complex simple Lie algebra, larger classes of quasitriangular Hopf algebras as been founded [1,12] and studied [8]. We prove that the multiparameter quantum group defined by Reshetikhin and De Concini-Kac-Procesi are indeed equivalent. Besides we write this algebra as the quantum double of a Borel-type sub-Hopf-algebra     

Use of Gemini surfactants to stabilize TiO2 P25 colloidal dispersions

Photocatalytically active TiO₂ P25 nanoparticles, widely used for practical applications, were investigated. The nominal size of TiO₂ P25 nanoparticles is 21 nm, but they easily agglomerate in aqueous media, depending on pH and ionic strength. TiO₂ P25 aqueous dispersions were stabilized by alkanediyl-α,ω-bis-N-dodecyl-N, N′-dimethyl-ammonium bromide, cationic Gemini surfactant. The optimal conditions required to obtain stable dispersions, without formation of large agglomerates, were experienced. The stabilization of TiO₂ P25 nanoparticles by cationic Gemini surfactant was investigated in some details. Different amounts of Gemini surfactant were used, at concentrations between 1.0 and 250 × 10⁻⁶ mol L⁻¹, well below the critical micelle concentration. Dynamic light scattering and zeta potential analyses estimated the particle size and the dispersions stability. When the proper amount of Gemini surfactant was used, the resulting nanoparticles were still poly-disperse, but large agglomerates disappeared and were remarkably redispersible.     

The coupling of Chern–Simons theory to topological gravity

We couple Chern–Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin–Vilkovisky action. Standard BRST transformations of the gauge field are modified by terms involving both its anti-field and the super-ghost of topological gravity. Beyond the obvious couplings to the metric and the gravitino, the BV action includes hitherto neglected couplings to the super-ghost. We use this result to determine the topological anomalies of certain higher ghost deformations of SU(N)$\mathit{SU}(N)$ Chern–Simons theory, introduced years ago by Witten. In the context of topological strings these anomalies, which generalize the familiar framing anomaly, are expected to be cancelled by couplings of the closed string sector. We show that such couplings are obtained by dressing the closed string field with topological gravity observables.     

New class of aggregates in aqueous solution: an NMR, thermodynamic, and dynamic light scattering study

We investigated the aggregation properties of two classes of aromatic and hydrophobic compounds, namely chloroacetamides and ethyl 3-phenyl-2-nitropropionates, in moderately concentrated aqueous solution (millimolar range). The identification of all species present in solution under specific experimental conditions was performed by 1D and 2D NMR, pulsed gradient spin-echo NMR, and dynamic light scattering techniques. Some physical-chemical properties (viscosity, surface tension, and colligative properties) of the aqueous solutions were also determined. Both classes of compounds behave quite similarly: in solution, three distinct species, namely a monomeric species, small and mobile aggregates, and large and stiff aggregates, are observed. The results give insight into a new class of aggregates, held together by pi-pi interactions, which show an unusual associative behavior in water.     

Transport of a heated granular gas in a washboard potential

We study numerically the motion of a one dimensional array of Brownian particles in a washboard potential, driven by an external stochastic force and interacting via short range repulsive forces. In particular, we investigate the role of instantaneous elastic and inelastic collisions on the system dynamics and transport. The system displays a locked regime, where particles may move only via activated processes and a running regime where particles drift along the direction of the applied field. By tuning the value of the friction parameter controlling the Brownian motion we explore both the overdamped dynamics and the underdamped dynamics. In the two regimes we considered the mobility and the diffusivity of the system as functions of the tilt and other relevant control parameters such as coefficient of restitution, particle size, and total number of particles. We find that while in the overdamped regime the results for the interacting systems present similarities with the known noninteracting case, in the underdamped regime the inelastic collisions determine a rich variety of behaviors among which is an unexpected enhancement of the inelastic diffusion.     

Hydrolytic disproportionation of coordinated white phosphorus in [CpRu(dppe)(η-P4)]PF6 [dppe = 1,2-bis(diphenylphosphino)ethane]

The reaction of [CpRu(dppe)Cl] (1), dppe = 1,2-bis(diphenylphosphino)ethane, with one equivalent of P₄ in the presence of TlPF₆ affords the stable complex [CpRu(dppe)(η¹-P₄)]PF₆ (2) which contains the tetrahedral P₄ molecule η¹-bound to the metal. The tetraphosphorus ligand readily reacts with water upon mixing acetone or THF solutions of the complex with excess water. The complexes [CpRu(dppe)(PH₃)]PF₆ (5) and [CpRu(dppe){P(OH)₃}]PF₆ (6), identified among the hydrolysis products, contain the PH₃ molecule and, respectively, the unstable P(OH)₃ tautomer of the phosphorous acid bound to the CpRu(dppe) fragment. In CH₂Cl₂ the coordinated P(OH)₃ molecule in 6 easily yields the compound [CpRu(dppe){PF(OH)₂}]PF₂O₂ (8), via hydrolysis of the hexafluorophosphate anion and F/OH substitution in the coordinated P(OH)₃ molecule. All the compounds have been characterized by elemental analyses and NMR measurements. The crystal structures of 2 and 8 have been determined by X-ray diffraction methods.