Rotating waves within a hollow vortex core

The rotating waves within a hollow vortex core (polygonal patterns) are generated under shallow water conditions inside a cylindrical tank by a revolving disk at its bottom. We previously reported some basic features of these polygonal patterns during transition and at the equilibrium states. The present paper includes a more comprehensive investigation into the transition process of these polygonal patterns and expands the recent partial results that have been previously reported. We show that the parent wave (or the N-gon pattern) to disk frequencies ratio is around one-third (1/3) regardless of the flow conditions. A detailed insight into the transition process from the parent wave N-gon to daughter wave (N + 1)-gon is provided, which consists of two regimes, quasi-periodic and synchronized. Based on these observations, we explained the shrinking of the disk speed subintervals over which the N-gon patterns occur, when N increases.     

What is your “birthday elliptic curve”?

In this article, Ramanujan–Weber class invariants and its analogue are used to derive birthday elliptic curves.     

Novel diblock copolymer‐grafted multiwalled carbon nanotubes via a combination of living and controlled/living surface polymerizations

Diels–Alder cycloaddition reactions were used to functionalize multiwalled carbon nanotubes (MWNTs) with 1‐benzocylcobutene‐1′‐phenylethylene (BCB‐PE) or 4‐hydroxyethylbenzocyclobutene (BCB‐EO). The covalent functionalization of the nanotubes with these initiator precursors was verified by FTIR and thermogravimetric analysis (TGA). After appropriate transformations/additions, the functionalized MWNTs were used for surface initiated anionic and ring opening polymerizations of ethylene oxide and ε‐caprolactone (ε‐CL), respectively. The OH‐end groups were transformed to isopropylbromide groups by reaction with 2‐bromoisobutyryl bromide, for subsequent atom transfer radical polymerization of styrene or 2‐dimethylaminoethyl methacrylate to afford the final diblock copolymers. ¹H NMR, differential scanning calorimetry (DSC), TGA, and transmission electron microscopy (TEM) were used for the characterization of the nanocomposite materials. TEM images showed the presence of a polymer layer around the MWNTs as well as the dissociation of MWNT bundles. Consequently, this general methodology, employing combinations of different polymerization techniques, increases the diversity of diblocks that can be grafted from MWNTs. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1104–1112, 2010     

Singular finite elements for the sudden-expansion and the die-swell problems

The singular finite element method is used to solve the sudden-expansion and the die-swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden-expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die-swell problem is solved using the singular elements constructed for the stick–slip problem. The singular elements accelerate the convergence of the free surface dramatically.     

The Method of Fundamental Solutions for Stokes flows with a free surface

We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667–678, 1998     

New Calix[4]arene‐Cored Peripherally Functionalized Dendrimers: Synthesis and Conformational Characteristics

New calixarene‐based dendrimers, containing calix[4]arene as the core and different generations of Fréchet‐type poly(benzyl ether) dendrons as building blocks, which possess either Br‐atoms or COO^tBu groups at their surface were synthesized and presented herein for the first time. The new calix[4]arene‐cored dendritic macromolecules were fully characterized and found to prefer strictly the cone conformation.     

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: Binary mixtures with CO2

In Part I of this series of articles, the study of H₂S mixtures has been presented with CPA. In this study the phase behavior of CO₂ containing mixtures is modeled. Binary mixtures with water, alcohols, glycols and hydrocarbons are investigated. Both phase equilibria (vapor-liquid and liquid-liquid) and densities are considered for the mixtures involved. Different approaches for modeling pure CO₂ and mixtures are compared. CO₂ is modeled as non self-associating fluid, or as self-associating component having two, three and four association sites. Moreover, when mixtures of CO₂ with polar compounds (water, alcohols and glycols) are considered, the importance of cross-association is investigated. The cross-association is accounted for either via combining rules or using a cross-solvation energy obtained from experimental spectroscopic or calorimetric data or from ab initio calculations. In both cases two adjustable parameters are used when solvation is explicitly accounted for. The performance of CPA using the various modeling approaches for CO₂ and its interactions is presented and discussed, comparatively to various recent published investigations. It is shown that overall very good correlation is obtained for binary mixtures of CO₂ and water or alcohols when the solvation between CO₂ and the polar compound is explicitly accounted for, whereas the model is less satisfactory when CO₂ is treated as self-associating compound.     

Aspects of heterogeneous enantioselective catalysis by metals

Some aspects of metal-catalyzed heterogeneous enantioselective reactions are reviewed with specific reference to four different systems where the phenomena that control enantioselection appear to be very different. In the case of glucose electro-oxidation, it is clear that any intrinsic chirality present at the metal surface plays a vital role. With α-keto hydrogenation, achiral surfaces modified by the adsorption of chiral agents become effective enantioselective catalysts and the formation of extended arrays of chiral species appears not to be of importance: instead a 1:1 docking interaction controlled by hydrogen bonding between the adsorbed chiral modifier and the prochiral reactant determines the outcome. Hydrogen bonding also plays a central role in β-ketoester hydrogenation, but here fundamental studies indicate that the formation of ordered arrays involving the reactant and chiral ligand is of importance. Asymmetric C═C hydrogenation, though relatively little studied, has the potential for major impact in synthetic organic chemistry both on the laboratory scale and in the manufacture of fine chemicals and pharmaceuticals. The structural attributes that determine whether a given chiral ligand is effective have been identified; the ability to form strong covalent bonds with the metal surface while also resisting hydrogenation and displacement by the strongly adsorbing reactant under reaction conditions is an essential necessary condition. Beyond this, ligand rigidity in the vicinity of the chirality center coupled with resistance to SAM formation is a critically important factor whose absence results in racemic chemistry.     

Poly(sodium styrene sulfonate)-b-poly(methyl methacrylate) diblock copolymers through direct atom transfer radical polymerization: Influence of hydrophilic–hydrophobic balance on self-organization in aqueous solution

A series of poly(sodium styrene sulfonate)-b-poly(methyl methacrylate), PSSNa-b-PMMA, amphiphilic diblock copolymers have been synthesized through atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) in N,N-dimethylformamide/water mixtures, starting from a PSSNa macroinitiator. The kinetics of the polymerization was followed by ¹H NMR, while the chemical composition of the copolymers was verified by a variety of techniques, such as ¹H NMR, FTIR and TGA. The MMA content of the copolymers ranges from 0 up to 60 mol%, while the number–average molecular weight of the PSSNa macroinitiator was 9000 g/mol. The self-association of the diblock copolymers in aqueous solution was compared to the respective behavior of similar random P(SSNa-co-MMA) copolymers through optical density measurements, pyrene fluorescence probing, dynamic light scattering and surface tension measurements. It is shown that the diblock copolymers form micellar structures in water, characterized by an increasing hydrophobic character and a decreasing size as the length of the PMMA block increases. These micelle-like structures turn from surface inactive to surface active as the length of the PMMA block increases. Moreover, contrary to the MMA-rich random copolymers, the respective diblock copolymers form water insoluble polymer/surfactant complexes with cationic surfactants such as hexadecyltrimethyl ammonium bromide (HTAB), leading to materials with antimicrobial activity.