On the global attractor of 2D incompressible turbulence with random forcing

This study revisits bounds on the projection of the global attractor in the energy–enstrophy plane for 2D incompressible turbulence [Dascaliuc, Foias, and Jolly, 2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in particular often use a stochastic white-noise forcing to achieve a prescribed mean energy injection rate. The analytical bounds are demonstrated numerically for the case of white-noise forcing.     

Sonochemical Synthesis and Photocatalytic Properties of Metal Hydroxide and Carbonate (M:Mg, Ca, Sr or Ba) Nanoparticles

In this work Mg(OH)₂, Ca(OH)₂, CaCO₃, SrCO₃ and BaCO₃ nanoparticles were synthesized via a simple sonochemical reaction at room temperature. Nanoparticles were synthesized via a surfactant-free reaction solvent water. Nanostructures materials were characterized by scanning electron microscopy, X-ray diffraction and fourier transform infrared spectroscopy. The photocatalytic behavior of nanoparticles was evaluated using the degradation of a methyl orange aqueous solution under ultraviolet light irradiation. The results show that metal hydroxide and metal carbonate nanoparticles are promising materials with excellent performance in photocatalytic applications.     

Synthesis of Thio Analogues of Quinolone Antibacterials

A facile and rapid synthesis of thio compounds, analogues to ciprofloxacin, and norfloxacin is described.     

Polytetrafluoroethylene Sputtered PES Membranes for Membrane Distillation: Influence of RF Magnetron Sputtering Conditions

Thin films of fluorocarbon were deposited on polyethersulfone membranes via argon plasma sputtering of a poly(tetrafluoroethylene) (PTFE) target in an RF magnetron plasma reactor. The obtained deposited ultrathin coatings had nanoscale roughnesses and high degrees of fluorination. The intensity of fluorine atom in plasma environment during fluorocarbon deposition was investigated. Depending on the deposition conditions comprising working gas pressure, applied RF power, and distance between the target and the substrate, polymeric films with different chemical compositions and/or morphologies were obtained. The morphologies of the films were analyzed by means of SEM, XPS, and AFM. The results suggested that the sputtered film deposited at a higher pressure and longer target–substrate distance and moderate RF power had a surface composition and chemical structure closer to those of the PTFE film. The treated hydrophobic PES membranes with water contact angles as high as 115° were applied for the first time in an air gap membrane distillation setup for removal of benzene as a volatile organic compound from water. The results showed that the plasma-treated membranes have a comparable or superior performance to that of commercial PTFE used in membrane distillation with similar permeate flux and separation factor after 20 h long term performance.     

A differential operator and weak topology for Lipschitz maps

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak^∗ compact and convex valued maps equipped with the Scott topology, is continuous. For finite dimensional Euclidean spaces, where the L-derivative and the Clarke gradient coincide, we provide a simple characterization of the basic open subsets of the L-topology. We use this to verify that the L-topology is strictly coarser than the well-known Lipschitz norm topology. A complete metric on Lipschitz maps is constructed that is induced by the Hausdorff distance, providing a topology that is strictly finer than the L-topology but strictly coarser than the Lipschitz norm topology. We then develop a fundamental theorem of calculus of second order in finite dimensions showing that the continuous integral operator from the continuous Scott domain of non-empty convex and compact valued functions to the continuous Scott domain of ties is inverse to the continuous operator induced by the L-derivative. We finally show that in dimension one the L-derivative operator is a computable functional.     

Novel one-pot, three-component synthesis of new 2-alkyl-5-aryl-(1H)-pyrrole-4-ol in water

New 2-alkyl-5-aryl-(1H)-pyrrole-4-ol derivatives were synthesized via three-component reaction of beta-dicarbonyl compounds with arylglyoxals in the presence of ammonium acetate in water at room temperature.     

Head-to-head polymers—I. The preparation and some properties of head-to-head polypropylene

Samples of head-to-head polypropylene have been prepared by the hydrogenation of two polydienes; 1,4-poly(2,4-hexadiene) and 1,4-poly(2,3-dimethyl-1,3-butadiene). Glass transition temperatures were found to be marginally lower than for conventional polypropylene suggesting that the head-to-head placements in the chain increased the polymer flexibility.     

The Minimal Length Uncertainty and the Nonextensive Thermodynamics

In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop quantum gravity, and black-hole physics. We analytically obtain the partition function, probability function, internal energy, and the specific heat capacity of the vibrational quantum system for \(1<q<\frac {3}{2}\) and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale.     

Schrödinger–Wheeler–DeWitt Equation in Chaplygin Gas FRW Cosmological Model

We present a Chaplygin gas Friedmann–Robertson–Walker quantum cosmological model. In this work the Schutz’s variational formalism is applied with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Schrödinger–Wheeler–DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time dependent behavior of the expectation value of the scale factor, using the many-worlds interpretations of quantum mechanics.