New constraints on the pion EM form factor using $ \Pi^{{ \prime}}_{}$(- Q2)

We study the constraints arising on the expansion parameters c and d of the pion electromagnetic form factor from the inclusion of pure spacelike data and the phase of timelike data along with one spacelike datum, using as input the first derivative of the QCD polarization amplitude (- Q ²) . These constraints when combined with other analyses, provide a valuable check on a determination of c due to Guo et al. and on our previous work where pionic contribution to the (g - 2) of the muon was used as the input. This work further illustrates the power of analyticity techniques in form factor analysis.     

Competition between singlet fission and charge separation in solution-processed blend films of 6,13-bis(triisopropylsilylethynyl)pentacene with sterically-encumbered perylene-3,4:9,10-bis(dicarboximide)s

The photophysics and morphology of thin films of N,N-bis(2,6-diisopropylphenyl)perylene-3,4:9,10-bis(dicarboximide) (1) and the 1,7-diphenyl (2) and 1,7-bis(3,5-di-tert-butylphenyl) (3) derivatives blended with 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-Pn) were studied for their potential use as photoactive layers in organic photovoltaic (OPV) devices. Increasing the steric bulk of the 1,7-substituents of the perylene-3,4:9,10-bis(dicarboximide) (PDI) impedes aggregation in the solid state. Film characterization data using both atomic force microscopy and X-ray diffraction showed that decreasing the PDI aggregation by increasing the steric bulk in the order 1 < 2 < 3 correlates with a decrease in the density/size of crystalline TIPS-Pn domains. Transient absorption spectroscopy was performed on ~100 nm solution-processed TIPS-Pn:PDI blend films to characterize the charge separation dynamics. These results showed that selective excitation of the TIPS-Pn results in competition between ultrafast singlet fission ((1*)TIPS-Pn + TIPS-Pn → 2 (3*)TIPS-Pn) and charge transfer from (1*)TIPS-Pn to PDIs 1-3. As the blend films become more homogeneous across the series TIPS-Pn:PDI 1 → 2 → 3, charge separation becomes competitive with singlet fission. Ultrafast charge separation forms the geminate radical ion pair state (1)(TIPS-Pn(+?)-PDI(-?)) that undergoes radical pair intersystem crossing to form (3)(TIPS-Pn(+?)-PDI(-?)), which then undergoes charge recombination to yield either (3*)PDI or (3*)TIPS-Pn. Energy transfer from (3*)PDI to TIPS-Pn also yields (3*)TIPS-Pn. These results show that multiple pathways produce the (3*)TIPS-Pn state, so that OPV design strategies based on this system must utilize this triplet state for charge separation.     

Two new polyoxovanadate clusters templated through cysteamine

Two new fully oxidized polyoxovanadate cluster-based solids (C₄N₂S₂H₁₄)₂[H₂V₁₀O₂₈]·4H₂O,1 and (C₄N₂S₂H₁₄)₅[H₄V₁₅O₄₂]₂·l0H₂O,2 are crystallized under self-assembly process in the presence of cysteamine. In both1 and2, cysteamines are oxidized forming disulphide linkages and occur as counter cations. The organic cations assemble around V₁₀O₂₈ cluster anions in1 whereas they aggregate around V₁₅O₄₂ clusters in 2· pH appears to be the structure determinant in the occurrence of decavanadate cluster in1 and pentadecavanadate in2, with the same counter cation.     

Synthesis of tertiary carbinamines

An efficient synthesis of tertiary carbinamines using a one-pot, three-component reaction employing TMSCl activation of an intermediate imine salt followed by addition of an organometallic is described. An optimized second generation chiral synthesis of select tertiary carbinamines utilizing the Ellman sulfinamine was subsequently developed on a multi-gram scale and is also described.     

Convex duality and the Skorokhod Problem. II

In this paper we consider Skorokhod Problems on polyhedral domains with a constant and possibly oblique constraint direction specified on each face of the domain, and with a corresponding cone of constraint directions at the intersection of faces. In part one of this paper we used convex duality to develop new methods for the construction of solutions to such Skorokhod Problems, and for proving Lipschitz continuity of the associated Skorokhod Maps. The main alternative approach to Skorokhod Problems of this type is the reflection mapping technique introduced by Harrison and Reiman [8]. In this part of the paper we apply the theory developed in part one to show that the reflection mapping technique of [8] is restricted to a slight generalization of the class of problems originally considered in [8]. We further illustrate the power of the duality approach by applying it to two other classes of Skorokhod Problems – those with normal directions of constraint, and a new class that arises from a model of processor sharing in communication networks. In particular, we prove existence of solutions to and Lipschitz continuity of the Skorokhod Maps associated with each of these Skorokhod Problems. Received: 17 April 1998 / Revised: 8 January 1999     

Convex duality and the Skorokhod Problem. I

The solution to the Skorokhod Problem defines a deterministic mapping, referred to as the Skorokhod Map, that takes unconstrained paths to paths that are confined to live within a given domain G⊂ℝ ⁿ . Given a set of allowed constraint directions for each point of ∂G and a path ψ, the solution to the Skorokhod Problem defines the constrained version φ of ψ, where the constraining force acts along one of the given boundary directions using the “least effort” required to keep φ in G. The Skorokhod Map is one of the main tools used in the analysis and construction of constrained deterministic and stochastic processes. When the Skorokhod Map is sufficiently regular, and in particular when it is Lipschitz continuous on path space, the study of many problems involving these constrained processes is greatly simplified. We focus on the case where the domain G is a convex polyhedron, with a constant and possibly oblique constraint direction specified on each face of G, and with a corresponding cone of constraint directions at the intersection of faces. The main results to date for problems of this type were obtained by Harrison and Reiman [22] using contraction mapping techniques. In this paper we discuss why such techniques are limited to a class of Skorokhod Problems that is a slight generalization of the class originally considered in [22]. We then consider an alternative approach to proving regularity of the Skorokhod Map developed in [13]. In this approach, Lipschitz continuity of the map is proved by showing the existence of a convex set that satisfies a set of conditions defined in terms of the data of the Skorokhod Problem. We first show how the geometric condition of [13] can be reformulated using convex duality. The reformulated condition is much easier to verify and, moreover, allows one to develop a general qualitative theory of the Skorokhod Map. An additional contribution of the paper is a new set of methods for the construction of solutions to the Skorokhod Problem. These methods are applied in the second part of this paper [17] to particular classes of Skorokhod Problems. Received: 17 April 1998 / Revised version: 8 January 1999     

Characterising chaos-hyperchaos transition using correlation dimension

Transition to hyperchaos is uaually studied by computing the spectrum of Lyapunov Exponents (LE). But such a procedure can be employed mainly when the equations governing the dynamical system are known. However, if the information available on the system is only through time series, the method becomes difficult to implement. We show that the transition to hyperchaos is followed by a sudden change in the topological structure of the underlying attractor. Our numerical results indicate that the transition to hyperchaos can be characterized accurately through the computation of correlation dimension (D ₂) from time series. We use two standard time delayed hyperchaotic systems as examples since, for such systems, D ₂ varies smoothly as a function of the time delay τ which can be used as the control parameter.