A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Physics and chemistry of silicene nano-ribbons

We review our recent discovery of silicene in the form of silicon nano-ribbons epitaxially grown on silver (1 1 0) or (1 0 0) surfaces, which paves the way for the growth of graphene-like sheets. We further draw some perspectives for this unique novel material upon mild hydrogenation.     

Novel Copolymers of Styrene and Alkyl and Alkoxy Ring‐Trisubstituted Methyl 2‐Cyano‐3‐phenyl‐2‐propenoates

Electrophilic trisubstituted ethylene monomers, akyl and alkoxy ring‐trisubstituted methyl 2‐cyano‐3‐phenyl‐2‐propenoates, RC₆H₂CH[dbnd]C(CN)CO₂CH_3, (where R is 2,3‐dimethyl‐4‐methoxy, 2,5‐dimethyl‐4‐methoxy‐, 2,3,4‐trimethoxy‐, 2,4,5‐trimethoxy, 2,4,6‐trimethoxy, and 2,4‐dimethoxy‐3‐methyl), were synthesized by the piperidine catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and methyl cyanoacetate, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (AIBN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 283–306°C range.     

Heavy Metal Removal from Synthetic Solutions with Magnetic Beads Under Magnetic Field

The aim of this study is to prepare magnetic beads which can be used for the removal of heavy metal ions from synthetic solutions. Magnetic poly(ethylene glycol dimethacrylate‐vinyl imidazole) [m‐poly(EGDMA‐VIM)] beads were produced by suspension polymerization in the presence of magnetite Fe₃O₄ nano‐powder. The specific surface area of the m‐poly(EGDMA‐VIM) beads was found to be 63.1 m²/g with a size range of 150–200 µm in diameter and the swelling ratio was 85%. The average Fe₃O₄ content of the resulting m‐poly(EGDMA‐VIM) beads was 12.4%. The maximum binding capacities of the m‐poly(EGDMA‐VIM) beads were 32.4 mg/g for Cu²⁺, 45.8 mg/g for Zn²⁺, 84.2 mg/g for Cd²⁺and 134.5 mg/g for Pb²⁺. The affinity order on mass basis is Pb²⁺>Cd²⁺>Zn²⁺>Cu²⁺. Equilibrium data agreed well with the Langmuir model. pH significantly affected the binding capacity of the magnetic beads. Binding of heavy metal ions from synthetic wastewater was also studied. The binding capacities were 26.2 mg/g for Cu²⁺, 33.7 mg/g for Zn²⁺, 54.7 mg/g for Cd²⁺ and 108.4 mg/g for Pb²⁺. The magnetic beads could be regenerated up to about 97% by treating with 0.1 M HNO₃. These features make m‐poly(EGDMA‐VIM) beads a potential candidate for support of heavy metal removal under magnetic field.     

Electronic structure and related properties for quasi-binary (GaP)1−x (ZnSe) x crystals

The results of pseudopotential calculations of the band structure and related electronic and optical properties of quasi-binary (GaP)_1?x (ZnSe) _x crystals in the zinc blende structure are presented. Trends in bonding and ionicity are discussed in terms of electronic charge densities. Moreover, the composition dependence of the refractive index and dielectric constants are reported. The computed values are in reasonable agreement with experimental data. The results suggest that for a proper choice of the composition x, (GaP)_1?x (ZnSe) _x could provide more diverse opportunities to achieve the desired electronic and optical properties of the crystals which would improve the performances of devices fabricated on them.     

Phase modulation and ellipticity of the light transmitted through a smectic C* layer with short helix pitch

A chiral ferroelectric smectic C* liquid crystal (FLC) with the helix pitch p ₀?=?330 nm was developed to avoid any scattering of visible light when the helix is not unwound over a certain limit. Planar cells with different FLC layer thickness (16 and 44 μm) have been assembled with helix axis parallel to the glass plates and aligned along the rubbing direction. The ellipticity of the light passing through the cells vs. the electric field was investigated, and a method for evaluating the electrically controlled birefringence via ellipticity measurements has been established. We have found that the FLC cell is an optical retardation layer driven by the electric field, the effective birefringence being proportional to the square electric field. The physical origin of the electrically controlled phase shift of the light passing through the FLC layer has been analysed.     

Evaluation of Pesticide Contamination of Ground Water in Two Agricultural Areas of Portugal

In two Portuguese agricultural areas, "Beira Litoral" and "Ribatejo e Oeste", several pesticides regularly applied in vineyards, maize, potato, tomato for industry, apple, pear and rice were detected in ground water. Atrazine was the most frequently detected, being found in 70% of the total of 79 sites selected in the year 2000, followed by its metabolites desethylatrazine and desisopropylatrazine with frequencies of detection, respectively, of 56% and 48% and by simazine (37%), alachlor (25%), metolachlor (24%) and metribuzin (15%). Other pesticides and metabolites i.e. 3,4-dichloroaniline, dimethoate, f and g -endosulfan, lindane, molinate and prometryn were also detected but at lower occurrences. Pesticides were detected mainly in ground water wells used for irrigation purposes, although in some locations they were also found in water wells used for human consumption. In this study, it was also observed a seasonal variation of pesticide residues in ground water of shallow and deep wells.     

One-pot enyne ring-closing metathesis–Diels–Alder reactions for the synthesis of polycyclic sulfamides

Ring-closing metathesis (RCM) and sequential Yb(OTf)₃ promoted Diels–Alder reactions of sulfamide-linked enynes proceeded selectively in one-pot to afford a series of bicyclic and tricyclic sulfamides. Excellent levels of diastereoselectivity are observed for the cycloaddition step, with only the endo-adducts being isolated. The protocol was further extended to incorporate a one-pot RCM–cross metathesis (CM)–Diels–Alder sequence, permitting rapid access to high levels of molecular complexity from simple and easily accessible precursors.