Swirl effects on variable-density jet mixing in confined flows

An experimental investigation on swirl effects on inhomogeneous confined jet mixing in a combustor configuration is reported. The confined swirling flow was simulated by a swirler with a central jet mounted in a cyclindrical tube. Helium and air jets set at different velocities were injected into the confined swirling air flow. The resulting flow fields due to two vane swirlers with constant vane angles of 35° and 66° were compared. Results show that the 35° vane swirler produces a solid-body rotation core with a slope about twice that created by the 66° vane swirler. It is the behavior of this solid-body rotation core that determines jet mixing rather than the swirler vane angle. Consequently, the coaxial jet decays much faster, the mixing is more intense, and the turbulence intensities are higher for the 35° vane swirler. In view of these results, combustor designers should be more concerned with behavior of the solid-body rotation core produced by the swirler, instead of the swirler vane angle.     

On Lipschitz extension from finite subsets

We prove that for every n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X, a Banach space (Z, \({\left\| \right\|_Z}\)) and a 1-Lipschitz function f: S → Z such that the Lipschitz constant of every function F: X → Z that extends f is at least a constant multiple of \(\sqrt {\log n} \). This improves a bound of Johnson and Lindenstrauss [JL84]. We also obtain the following quantitative counterpart to a classical extension theorem of Minty [Min70]. For every α ∈ (1/2, 1] and n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X and a function f: S → ?₂ that is α-Hölder with constant 1, yet the α-Hölder constant of any F: X → ?₂ that extends f satisfies \({\left\| F \right\|_{Lip\left( \alpha \right)}} > {\left( {\log n} \right)^{\frac{{2\alpha - 1}}{{4\alpha }}}} + {\left( {\frac{{\log n}}{{\log \log n}}} \right)^{{\alpha ^2} - \frac{1}{2}}}\). We formulate a conjecture whose positive solution would strengthen Ball’s nonlinear Maurey extension theorem [Bal92], serving as a far-reaching nonlinear version of a theorem of König, Retherford and Tomczak-Jaegermann [KRTJ80]. We explain how this conjecture would imply as special cases answers to longstanding open questions of Johnson and Lindenstrauss [JL84] and Kalton [Kal04].     

Synthetic Approaches towards the Sulfonamide Substituted‐1,5‐Diarylimidazole‐2‐thiones as Selective Cyclooxygense‐2 inhibitors

A new series of sulfonamide substituted 1,5‐diarylimidazole, possessing C‐2 alkylthio moiety, were synthesized for their cyclooxygense‐2 (COX‐2) inhibitory activity starting from condensation of N,N‐dibenzylaminosulfonylphenacylamine hydrochloride ( 2 ) and corresponding isothiocyanate in the presence of Et₃N, followed by alkylation in the basic medium. In concomitant with these intermediates, 2‐arylamino‐5‐arylthiazole derivatives 5 were also produced. The ratio of these two products was variable with different isothiocyanates. Final debenzylation was achieved using concentrated sulfuric acid to give the title sulfonamides 8 .     

Odd-even effects on the structure, stability, and phase transition of alkanethiol self-assembled monolayers

Molecular dynamics simulations were conducted to predict the structural properties and phase transition temperatures of n-alkanethiols CH(3)(CH(2))(n-1)SH (Cn, 4 ≤ n ≤ 22) self-assembled monolayers (SAMs) on Au (111) surfaces. We studied the effects of chain length on the structural properties, including tilt and orientation angles, and on phase transition temperature. We found clear dependence of the structural properties, on both the number of carbon atoms, n; and on n being odd or even. Alkanethiols with n ≤ 7 show liquid-like behavior and large rotational mobility, whereas those with n ≥ 12 are well-ordered and stable. For 12 ≤ n ≤ 15, odd-even effects are observed, where for n = odd, larger tilt angles, oriented in the direction of their next next nearest neighbor (NNNN), and for n = even, lower tilt angles, mostly tilted toward next nearest neighbor (NNN), were observed. For 15 ≤ n ≤ 19, we find tilt angle and orientation to be independent of n. For all alkanethiols, a gradual decrease of the tilt angle occurred by increasing the temperature from 300 to 420 K. Order-disorder phase transitions occurred at a certain temperature. This was signified by abrupt instabilities in the tilt orientation angle. This transition temperature showed an enhancement of ～67-100 °C over the melting point of the corresponding n-alkane bulk system. This enhancement depended on n, and was larger for n = odd. Overall, we found that odd alkanethiols show better structural and thermal stability, and smaller gauche defects.     

One-pot synthesis of aliphatic and aromatic 2H-indazolo[2,1-b]phthalazine-triones catalyzed by N-halosulfonamides under solvent-free conditions

N, N, N′, N′-Tetrabromobenzene-1,3-disulfonamide and poly(N-bromo-N-ethylbenzene-1,3-disulfonamide) were used as efficient catalysts for the one-pot synthesis of aliphatic and aromatic 2H-indazolo[2,1-b]phthalazine-triones in excellent yields from aldehydes, phthalhydrazide, and dimedone at 80-100 °C under solvent-free conditions.     

Fabrication of superhydrophobic polymethylsilsesquioxane nanostructures on cotton textiles by a solution-immersion process

Superhydrophobic cotton textiles are prepared by a simple, one-step and inexpensive phase separation method under ambient conditions by which a layer of polymethylsilsesquioxane (PMSQ) nanostructures is covered onto the cellulose fibers. By changing the silane precursor concentration, PMSQ nanostructures with various shapes, morphologies and sizes were fabricated. Nanostructures were characterized using SEM, EDS, and attenuated total reflectance FTIR. The wettability of the modified cellulose surfaces was characterized with contact-angle goniometry and sliding angle technique, respectively. The water contact angle of modified cotton is measured to be higher than 150°, which is high enough to exhibit the lotus effect as a result of the superhydrophobicity. Tunable water-repellent properties of the fabric are also demonstrated, with sliding contact angles varying from "sticky" to "slippery" depending upon different nanostructures on the surface of the fibers. It is expected that this simple technique will accelerate the large-scale production of superhydrophobic cellulosic materials with new industrial applications.     

Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times

Methodology and Computing in Applied Probability - We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their...     

Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.     

Quantum Hall ferrimagnetism in lateral quantum dot molecules

We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.