Electromagnetic liquid pistons for capillarity-based pumping

The small scales associated with lab-on-a-chip technologies lend themselves well to capillarity-dominated phenomena. We demonstrate a new capillarity-dominated system where two adjoining ferrofluid droplets can behave as an electronically-controlled oscillator or switch by an appropriate balance of magnetic, capillary, and inertial forces. Their oscillatory motion can be exploited to displace a surrounding liquid (akin to an axial piston pump), forming electromagnetic "liquid pistons." Such ferrofluid pistons can pump a precise volume of liquid via finely tunable amplitudes (cf. pump stroke) or resonant frequencies (cf. pump speed) with no solid moving parts for long-term operation without wear in a small device. Furthermore, the rapid propagation of electromagnetic fields and the favorable scaling of capillary forces with size permit micron sized devices with very fast operating speeds (～kHz). The pumping dynamics and performance of these liquid pistons is explored, with experimental measurements showing good agreement with a spherical cap model. While these liquid pistons may find numerous applications in micro- and mesoscale fluidic devices (e.g., remotely activated drug delivery), here we demonstrate the use of these liquid pistons in capillarity-dominated systems for chip-level, fast-acting adaptive liquid lenses with nearly perfect spherical interfaces.     

Electronic Properties of Vinylene-Linked Heterocyclic Conducting Polymers: Predictive Design and Rational Guidance from DFT Calculations

The band structure and electronic properties in a series of vinylene-linked heterocyclic conducting polymers are investigated using density functional theory (DFT). In order to accurately calculate electronic band gaps, we utilize hybrid functionals with fully periodic boundary conditions to understand the effect of chemical functionalization on the electronic structure of these materials. The use of predictive first-principles calculations coupled with simple chemical arguments highlights the critical role that aromaticity plays in obtaining a low band gap polymer. Contrary to some approaches which erroneously attempt to lower the band gap by increasing the aromaticity of the polymer backbone, we show that being aromatic (or quinoidal) in itself does not ensure a low band gap. Rather, an iterative approach which destabilizes the ground state of the parent polymer toward the aromatic ? quinoidal level crossing on the potential energy surface is a more effective way of lowering the band gap in these conjugated systems. Our results highlight the use of predictive calculations guided by rational chemical intuition for designing low band gap polymers in photovoltaic materials.     

Chemical composition of the essential oil from Corsican Mentha aquatica--combined analysis by GC(RI), GC-MS and 13C NMR spectroscopy

The essential oil (EO) of M. aquatica L. growing wild in Corsica was isolated by dry vapor distillation and submitted to combined analysis by column chromatography over silica gel, GC(RI), GC-MS and 13C NMR spectroscopy. The composition was dominated byoxygenated monoterpenes and characterized by the occurrence of menthofuran (50.7%) as the major component. In parallel, seven laboratory-distilled oil samples isolated from individual plants collected in Corsica were analyzed by GC(RI) and 13C NMR spectroscopy. Onlyquantitative differences were observed between the samples. Beside the usual terpenes, various p-menthane lactones (mintlactone, isomintlactone, hydroxymintlactone, menthofurolactone and epimenthofurolactone) have been identified in all the oil samples.     

Ensemble and Single Molecule Studies on the Use of Metallic Nanostructures to Enhance the Intrinsic Emission of Enzyme Cofactors

We present a strategy for enhancing the intrinsic emission of the enzyme cofactors flavin adenine dinucleotide (FAD), flavin mononucleotide (FMN) and nicotinamide adenine dinucleotide (NADH). Ensemble studies show that silver island films (SIFs) are the optimal metal enhanced fluorescence (MEF) substrates for flavins and gave emission enhancements of over 10-fold for both FAD and FMN. A reduction in the lifetime of FAD and FMN on SIFs was also observed. Thermally evaporated aluminum films on quartz slides were found to be the optimal MEF substrate for NADH and gave a 5-fold increase in the emission intensity of NADH. We present finite-difference time-domain (FDTD) calculations that compute the enhancement in the radiated power emitting from an excited state dipole emitting in the wavelength range of NADH in close proximity to an aluminum nanoparticle, and a dipole emitting in the emission wavelength of flavins next to a silver nanoparticle. These calculations confirm that aluminum serves as the optimal MEF substrate for NADH and silver was the optimal MEF substrate for flavins. This is because the plasmon resonance properties of aluminum lie in the UV-blue regime and that of silver lie in the visible region. We also present the results of single molecule studies on FMN which show SIFs can both significantly enhance the intrinsic emission from single FMN molecules, significantly reduce their lifetimes and also significantly reduce FMN blinking. This is the first report of the observation of MEF from cofactors both at the ensemble and single molecule level. We hope this study will serve as a platform to encourage the future use of metallic nanostructures to study cofactors using their intrinsic fluorescence to directly monitor enzyme binding reactions without the need of extrinsic labeling of the molecules.     

Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump

Particle image velocimetry (PIV) measurements at varying resolutions focus on the flow structures in the tip region of a water-jet pump rotor, including the tip-clearance flow and the rollup process of a tip leakage vortex (TLV). Unobstructed views of these regions are facilitated by matching the optical refractive index of the transparent pump with that of the fluid. High-magnification data reveal the flow non-uniformities and associated turbulence within the tip gap. Instantaneous data and statistics of spatial distributions and strength of vortices in the rotor passage reveal that the leakage flow emerges as a wall jet with a shear layer containing a train of vortex filaments extending from the tip of the blade. These vortices are entrained into the TLV, but do not have time to merge. TLV breakdown in the aft part of the blade passage further fragments these structures, increasing their number and reducing their size. Analogy is made between the circumferential development of the TLV in the blade passage and that of the starting jet vortex ring rollup. Subject to several assumptions, these flows display similar trends, including conditions for TLV separation from the shear layer feeding vorticity into it.     

An algebraic slice in the coadjoint space of the Borel and the Coxeter element

Let g be a complex simple Lie algebra and b a Borel subalgebra. The algebra Y of polynomial semi-invariants on the dual b^? of b is a polynomial algebra on rank g generators (Grothendieck and Dieudonné (1965–1967)) [16]. The analogy with the semisimple case suggests there exists an algebraic slice to coadjoint action, that is an affine translate y+V of a vector subspace of b^? such that the restriction map induces an isomorphism of Y onto the algebra R[y+V] of regular functions on y+V. This holds in type A and even extends to all biparabolic subalgebras (Joseph (2007)) [20]; but the construction fails in general even with respect to the Borel. Moreover already in type C(2) no algebraic slice exists.Very surprisingly the exception of type C(2) is itself an exception. Indeed an algebraic slice for the coadjoint action of the Borel subalgebra is constructed for all simple Lie algebras except those of types B(2m), C(n) and F(4).Outside type A, the slice obtained meets an open dense subset of regular orbits, even though the special point y of the slice is not itself regular. This explains the failure of our previous construction.     

An extension of Alexandrov?s theorem on second derivatives of convex functions

If f is a function of n variables that is locally L¹ approximable by a sequence of smooth functions satisfying local L¹ bounds on the determinants of the minors of the Hessian, then f admits a second order Taylor expansion almost everywhere. This extends a classical theorem of A.D. Alexandrov, covering the special case in which f is locally convex.     

Finite groups with all subgroups not contained in the Frattini subgroup permutable

Let G be a finite group. A subgroup H of G is a permutable subgroup of G if HK = KH for all subgroups K of G. It will be shown that if all subgroups not contained in the Frattini subgroup are permutable in a group G, then all subgroups are permutable in G.     

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements D^J_MM￠(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ ^J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ ^J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.