Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω _d is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r ^α ) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with n = πr ² particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and Redig. Yuval Peres is partially supported by NSF grant DMS-0605166.     

Femtosecond electronic relaxation of excited metalloporphyrins in the gas phase

A systematic study of the ultrafast decay of metalloporphyrins containing various transition metals with partially filled 3d shells and zinc (3d filled) is reported here after excitation in the second excited state of the system (Soret band). Both time-of-flight mass spectrometry and velocity map imaging have been used for detection. A general biexponential decay with a short time constant tau1 approximately 100 fs is observed for the transition metal porphyrins, followed by a tau2 approximately 1 ps time decay. This evolution is interpreted as a porphyrin-to-metal charge transfer, tau1, followed by a back transfer, tau2, which leads to an excited state (d,d*) localized on the metal. These conclusions stem from the different behaviors of zinc and the transition metal porphyrins. A porphyrin-to-metal charge transfer model is chosen to describe the relaxation mechanism, based upon the fact that transition metalloporphyrins can accept electrons on the metal site, in contrast to zinc porphyrins.     

Comparison of various detection limit estimates for volatile sulphur compounds by gas chromatography with pulsed flame photometric detection

This paper addresses the variations that presently exist regarding the definition, determination, and reporting of detection limits for volatile sulphur compounds by gas chromatography with pulsed flame photometric detection (GC-PFPD). Gas standards containing hydrogen sulphide (H(2)S), carbonyl sulphide (COS), sulphur dioxide (SO(2)), methyl mercaptan (CH(3)SH), dimethyl sulphide (DMS), carbon disulphide (CS(2)), and dimethyl disulphide (DMDS) in concentrations varying from 0.36ppb (v/v) up to 1.5ppm (v/v) in nitrogen were prepared with permeation tubes and introduced in the gas chromatograph using a 0.25-ml gas sampling loop. After measuring the PFPD response versus concentration, the method detection limit (MDL), the Hubaux-Vos detection limit (x(D)), the absolute instrument sensitivity (AIS), and the sulphur detectivity (D(s)) were determined for each sulphur compound. The results show that the MDL determined by the US Environmental Protection Agency procedure consistently underestimates the minimum concentrations of volatile sulphur compounds that can be practically distinguished from the background noise with the PFPD. The Hubaux-Vos detection limits and the AIS values are several times higher than the MDL, and provide more conservative estimates of the lowest concentrations that can be reliably detected. Sulphur detectivities are well correlated with AIS values but only poorly correlated with MDL values. The AIS is recommended as a reliable and cost-effective measure of detection limit for volatile sulphur compounds by GC-PFPD, since the AIS is easier and faster to determine than the MDL and the Hubaux-Vos detection limit. In addition, this study confirmed that the PFPD response is nearly quadratic with respect to concentration for all volatile sulphur compounds.     

Structural and spectroscopic characterization of copper(II) complexes of a new bisamide functionalized imidazole tripod and evidence for the formation of a mononuclear end-on Cu-OOH species

A new polyimidazole tripod N,N-bis((1-methyl-4-pivalamidoimidazol-2-yl)methyl)-N'-((1-methylimidazol-2-yl)methyl)amine (L2) has been synthesized and shown to form intramolecular hydrogen bonds with different axial ligands bonded to Cu(II) in the solid state. The same hydrogen-bonding property of L2 appears responsible for the stabilization of a Cu(II)-OOH species in solution. The crystal structures of L2 and three of its Cu(II) complexes are reported. The [Cu(L2)X]ClO4 complexes, 4-6 (X- = Cl-, OH-, or N3-) have distorted trigonal bipyramidal geometries in the solid state and have been characterized further by UV-vis absorption, electron paramagnetic resonance (EPR) spectroscopy, and cyclic voltammetry. The reaction of [Cu(L2)OH](ClO4) (5) with H2O2 and tert-butyl hydroperoxide in methanol generates [Cu(L2)OOH](ClO4) (7) and [Cu(L2)OO(t)Bu](ClO4) (8) which have been characterized by different spectroscopic methods. The compound [Cu(L2)OO(t)Bu]+ displays a band at 395 nm (epsilon = 950 M(-1) cm(-1)) assigned to an alkylperoxo pi*(sigma) --> Cu ligand-to-metal charge transfer (LMCT) transition, while [Cu(L2)OOH]+ displays a peroxo pi*(sigma) --> Cu charge-transfer transition at 365 nm with epsilon = 1300 M(-1) cm(-1), a mass ion at m/z 593.4, and nu(O-O) stretch (resonance Raman) at 854 cm(-1) that shifts to lower energy by 46 cm(-1) upon 18O substitution.     

Ring expansions of a spirocyclohexadienone system

The unexpected rearrangement of spirocyclohexadienone 2 under acidic or basic conditions is reported.     

PEO‐Covered Nanoparticles by Emulsion Inversion Point (EIP) Method

This study reports the first PEO‐coated polymer nanoparticles synthesis by miniemulsion polymerization of nano‐emulsions prepared by the low‐energy emulsification method called EIP. The surfactant used was Brij 98, a PEO based non ionic commercial surfactant. The partial phase diagram of the system water/Brij 98/styrene was first determined. The Emulsion Inversion Point technique was then used on the water/Brij 98/styrene system to the formation of styrene‐in‐water nano‐emulsions. After miniemulsion polymerization, particle sizes as low as 36 nm were obtained. To the best of our knowledge, this method had not been used for polymerizable system up to now.

     

Multi-scale interactions in a compressible boundary layer

The properties of spectral subranges of scales in a boundary layer at Mach=2.3 and friction Reynolds number Reτ = 570 are investigated by analysing DNS data. One major aim is to examine whether footprinting and modulation of small-scale near-wall motions by outer large structures, observed at high Reynolds numbers, also pertain to this low-Reynolds-number case, or whether the logarithmic layer simply contains a continuous hierarchy of motions without specific outer scales playing a distinctive role. To this end, the spectrum of scales is decomposed into modes by application of the “Empirical Mode Decomposition”. The properties of different scales are then investigated by means of spectra, maps of isotropy/anisotropy parameters, the premultiplied derivative of the second-order structure function, correlation coefficients and joint probability density function (PDF), the last constructed from conditionally sampled data for the small-scale motions within the large-scale footprints. A clear commonality is identified between interactions in high-Reynolds-number channel flow and the present low-Reynolds-number boundary layer.     

2D FT-ICR MS of Calmodulin: A Top-Down and Bottom-Up Approach

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry (2D FT-ICR MS) allows data-independent fragmentation of all ions in a sample and correlation of fragment ions to their precursors through the modulation of precursor ion cyclotron radii prior to fragmentation. Previous results show that implementation of 2D FT-ICR MS with infrared multi-photon dissociation (IRMPD) and electron capture dissociation (ECD) has turned this method into a useful analytical tool. In this work, IRMPD tandem mass spectrometry of calmodulin (CaM) has been performed both in one-dimensional and two-dimensional FT-ICR MS using a top-down and bottom-up approach. 2D IRMPD FT-ICR MS is used to achieve extensive inter-residue bond cleavage and assignment for CaM, using its unique features for fragment identification in a less time- and sample-consuming experiment than doing the same thing using sequential MS/MS experiments.

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Tetrathiafulvalene‐Fused Porphyrins via Quinoxaline Linkers: Symmetric and Asymmetric Donor–Acceptor Systems

A tetrathiafulvalene (TTF) donor is annulated to porphyrins (P) via quinoxaline linkers to form novel symmetric P–TTF–P triads 1 a – c and asymmetric P–TTF dyads 2 a , b in good yields. These planar and extended π‐conjugated molecules absorb light over a wide region of the UV/Vis spectrum as a result of additional charge‐transfer excitations within the donor–acceptor assemblies. Quantum‐chemical calculations elucidate the nature of the electronically excited states. The compounds are electrochemically amphoteric and primarily exhibit low oxidation potentials. Cyclic voltammetric and spectroelectrochemical studies allow differentiation between the TTF and porphyrin sites with respect to the multiple redox processes occurring within these molecular assemblies. Transient absorption measurements give insight into the excited‐state events and deliver corresponding kinetic data. Femtosecond transient absorption spectra in benzonitrile may suggest the occurrence of fast charge separation from TTF to porphyrin in dyads 2 a , b but not in triads 1 a – c . Clear evidence for a photoinduced and relatively long lived charge‐separated state (385 ps lifetime) is obtained for a supramolecular coordination compound built from the ZnP–TTF dyad and a pyridine‐functionalized C₆₀ acceptor unit. This specific excited state results in a (ZnP–TTF)^?+ ??? (C₆₀py)^?? state. The binding constant of Zn^II ??? py is evaluated by constructing a Benesi–Hildebrand plot based on fluorescence data. This plot yields a binding constant K of 7.20×10⁴ M ^?1, which is remarkably high for bonding of pyridine to ZnP.