Analysis of the Kleiser-Schumann method

Summary The Kleiser-Schumann algorithm for the approximation of the Stokes problem by Fourier/Legendre polynomials is analized. Stability when the degree of the polynomials increases is established, whereas error estimates in Sobolev spaces are proven.The research of this author has been partially supported by the U.S. Army through its European Research Office under contract No. DAJA-84-C-0035     

Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements

Summary A generalized Stokes problem is addressed in the framework of a domain decomposition method, in which the physical computational domain is partitioned into two subdomains ₁ and ₂.Three different situations are covered. In the former, the viscous terms are kept in both subdomains. Then we consider the case in which viscosity is dropped out everywhere in . Finally, a hybrid situation in which viscosity is dropped out only in ₁ is addressed. The latter is motivated by physical applications.In all cases, correct transmission conditions across the interface between ₁ and ₂ are devised, and an iterative procedure involving the successive resolution of two subproblems is proposed.The numerical discretization is based upon appropriate finite elements, and stability and convergence analysis is carried out.We also prove that the iteration-by-subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size.This work was partially supported by CIRA S.p.A. under the contract Coupling of Euler and Navier-Stokes equations in hypersonic flowsDeceased     

Water soluble molecular switches of fluorescence based on the Ni(III)/Ni(II) redox change

The water soluble Ni(II) complexes of the cyclam derivatives with 1,3-benzodioxole and 1,2,3-trimethoxybenzene display the fluorescent emission typical of the covalently linked fluorophores, which results from a charge transfer excited state. On oxidation to Ni(III), the fluorescence is completely quenched due to the occurrence of an electron transfer (eT) process from the excited fluorogenic fragment Fl to the oxidized metal. Thus, fluorescence can be switched off/on at will, for several cycles, by consecutively oxidizing and reducing the metal center, in controlled potential electrolysis experiments both in acetonitrile and in aqueous 0.1 M HClO4. Occurrence of an eT process from Fl to Ni(III) ultimately depends upon the easy oxidation of Fl to Fl+, whereas failure of the occurrence of an eT process from Ni(II) to Fl has to be ascribed to the particular resistance of Fl fragments to the reduction.     

Toward block copolymers from nonliving isospecific single‐site catalytic systems

Ethene/1‐olefin blocky copolymers were obtained through nonliving insertion copolymerizations promoted by an isospecific single site catalyst. Propene or 4‐methyl‐1‐pentene were copolymerized with ethene with metallocenes endowed with different stereospecificity in propene polymerization: (i) aspecific “constrained geometry” half‐sandwich complex, {η¹:η⁵‐([tert‐butyl‐amido)dimethylsilyl](2,3,4,5‐tetramethyl‐1‐cyclopentadienyl)}titanium dichloride [Me₂Si(Me₄Cp)(N‐^tBu)TiCl₂] ( CG ), (ii) moderately isospecific rac‐ethylenebis(indenyl)zirconium dichloride [rac‐(EBI)ZrCl₂] ( EBI ), (iii) slightly more isospecific hydrogenated homologue, rac‐ethylenebis(tetrahydroindenyl)zirconium dichloride [rac‐(EBTHI)ZrCl₂] ( EBTHI ), (iv) highly iso‐specific rac‐[methylenebis(3‐tert‐butyl‐1‐indenyl)]zirconium dichloride [rac‐H₂C‐(3‐^tBuInd)₂ZrCl₂] ( TBI ), (v) most isospecific rac‐[isopropylidene‐bis(3‐tert‐butyl‐cyclopentadienyl)]zirconium dichloride [rac‐Me₂C‐(3‐^tBuCp)₂ZrCl₂] ( TBC ). Copolymerizations were described by a 2^nd order Markovian copolymerization model and data are proposed to correlate the formation of 1‐olefin sequences with catalytic site isospecificity, made by the cooperation of organometallic complex and growing chain. Blocky copolymers were prepared over wide ranges of compositions: with any of the isospecific metallocenes when 4‐methyl‐1‐pentene was the 1‐olefin and only with the highly isospecific ones ( TBI , TBC ) when propene was the comonomer. A penultimate unit effect was observed with TBI as the metallocene, whereas a 1^st order Markov model described the ethene/propene copolymerization from TBC . A moderately isospecific metallocene, such as EBI , is shown to be able to prepare blocky ethene copolymers with 4‐methyl‐1‐pentene. These results pave the way for the synthesis of new ethene based materials. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2063–2075, 2010     

Probability-fidelity tradeoffs for targeted quantum operations

We present probability-fidelity tradeoffs for a varying quantum operation with fixed input-output states and for a varying inversion of a fixed quantum operation.     

A two-channel molecular dosimeter for the optical detection of copper(II)

A cyclam-like macrocycle with an integrated push-pull chromophore selectively detects Cu2+ inclusion through both orange-to-yellow colour change and quenching of the green fluorescence.     

Silica-supported metallocenes: stereochemical comparison between homogeneous and heterogeneous catalysis

Propylene was polymerized in the presence of the isospecific Et(Ind)₂ZrCl₂ (Et: ethylene, Ind: indenyl) and the aspecific (Ind)₂ZrCl₂ complexes in solution and anchored to SiO₂ and SiO₂/MAO (MAO: methylaluminoxane) supports. From the stereochemical analysis of the polypropene samples obtained it can be deduced that (i) the same active species is formed when a metallocene is in solution and when it is anchored to the SiO₂/MAO support and (ii) a completely different active species is formed when the metallocene is anchored to the silica. The fact that both systems Et(Ind)₂ZrCl₂ SiO₂ and (Ind)₂ZrCl₂ SiO₂ produce the same prevailingly isospecific polymer suggests that only isospecific centers are formed in this case, independently of the metallocene stereochemical structure.