Local <Emphasis Type="Italic">Tb</Emphasis> theorem with <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> testing conditions and general measures: square functions

Local Tb theorems with L ^p type testing conditions, which are not scale invariant, have been studied widely in the case of the Lebesgue measure. In the non-homogeneous world local Tb theorems have only been proved assuming scale invariant (L ^∞ or BMO) testing conditions. In this paper, for the first time, we overcome these obstacles in the non-homogeneous world, and prove a nonhomogeneous local Tb theorem with L ² type testing conditions. This paper is in the setting of the vertical and conical square functions defined using general measures and kernels. On the technique side, we demonstrate a trick of inserting Calderón–Zygmund stopping data of a fixed function into the construction of the twisted martingale difference operators. This built-in control of averages is an alternative to Carleson embedding.     

The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

In part 1 (Gouin, [13]), we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.Received: 5 June 2001, Accepted: 24 May 2003, Published online: 29 July 2003PACS: 02.90, 47.50, 66.20, 68.03, 68.08     

Rhodium‐Catalyzed Stereoselective Amination of Thioethers with N‐Mesyloxycarbamates: DMAP and Bis(DMAP)CH2Cl2 as Key Additives

A stereoselective Rh‐catalyzed intermolecular amination of thioethers using a readily available chiral N‐mesyloxycarbamate to produce sulfilimines in excellent yields and diastereomeric ratio is described. A catalytic mixture of 4‐dimethylaminopyridine (DMAP) and bis(DMAP)CH₂Cl₂ proved pivotal in achieving high selectivity. The X‐ray crystal structure of the (DMAP)₂?[Rh₂{(S)‐nttl}₄] complex was obtained and mechanistic studies suggested a Rh^II‐Rh^III complex as the catalytically active species.     

An Electrochemically and Thermally Switchable Donor–Acceptor [c2]Daisy Chain Rotaxane

Although motor proteins are essential cellular components that carry out biological processes by converting chemical energy into mechanical motion, their functions have been difficult to mimic in artificial synthetic systems. Daisy chains are a class of rotaxanes which have been targeted to serve as artificial molecular machines because their mechanically interlocked architectures enable them to contract and expand linearly, in a manner that is reminiscent of the sarcomeres of muscle tissue. The scope of external stimuli that can be used to control the musclelike motions of daisy chains remains limited, however, because of the narrow range of supramolecular motifs that have been utilized in their templated synthesis. Reported herein is a cyclic daisy chain dimer based on π‐associated donor–acceptor interactions, which can be actuated with either thermal or electrochemical stimuli. Molecular dynamics simulations have shown the daisy chain’s mechanism of extension/contraction in the ground state in atomistic detail.     

Organocatalyzed Step‐Growth Polymerization through Desymmetrization of Cyclic Anhydrides: Synthesis of Chiral Polyesters

The polymerization of prochiral bis‐anhydrides with diols catalyzed by a cinchona alkaloid was shown to provide chiral polyesters in good yields and with high levels of stereocontrol. The structures of the polyesters were determined by ¹H and ¹³C NMR analyses, whereas their size was estimated by both size‐exclusion chromatography (SEC) and MALDI‐TOF mass spectrometry, which indicated that moderate degrees of polymerization were attained through this step‐growth polymerization. The enantioselectivity of the process was evaluated by using chiral HPLC analysis of the bis‐lactones resulting from a controlled chemoselective degradation of the polyesters. The best stereocontrol was reached for oligomers formed from bis‐anhydride and diol monomers bearing rigid aromatic spacers between the reactive functional groups. In this case, average enantioselectivities were comparable to those observed during ring‐opening of simple anhydrides with similar alcohols. In contrast, the use of more flexible spacers between reactive entities generally led to lower levels of stereocontrol.     

Benzothiophene or Benzofuran Bridges in Diaryl Ethenes: Two‐Step Access by Pd‐Catalyzed CH Activation and Theoretical/Experimental Studies on Their Photoreactivity

A series of terarylenes incorporating benzothiophene ( BT )/benzofuran ( BF ) as the central ethene unit was synthesised by using sequential Pd‐catalysed C?H activation reactions. This new methodology allows the easy modification of the nature of the pendant heteroarene groups. Diaryl ethene (DAE) derivatives with thiophene, thiazole, pyrrole, isoxazole and pyrazole rings were prepared. A large number of asymmetrical DAEs are easily accessible by this new method in both the BT and BF series. The study of their photochromic properties in solution revealed that the nature of the heteroarene and of the central unit drastically modify their photochromic behaviour. TD‐DFT calculations were performed to assess the nature of the relevant excited states.     

Core–Shell Nanoreactors for Efficient Aqueous Biphasic Catalysis

Water‐borne phosphine‐functionalized core‐cross‐linked micelles ( CCM ) consisting of a hydrophobic core and a hydrophilic shell were obtained as stable latexes by reversible addition–fragmentation chain transfer (RAFT) in water in a one‐pot, three‐step process. Initial homogeneous aqueous‐phase copolymerization of methacrylic acid (MAA) and poly(ethylene oxide) methyl ether methacrylate (PEOMA) is followed by copolymerization of styrene (S) and 4‐diphenylphosphinostyrene (DPPS), yielding P(MAA‐co‐PEOMA)‐b‐P(S‐co‐DPPS) amphiphilic block copolymer micelles ( M ) by polymerization‐induced self‐assembly (PISA), and final micellar cross‐linking with a mixture of S and diethylene glycol dimethacrylate. The CCM were characterized by dynamic light scattering and NMR spectroscopy to evaluate size, dispersity, stability, and the swelling ability of various organic substrates. Coordination of [Rh(acac)(CO)₂] (acac=acetylacetonate) to the core‐confined phosphine groups was rapid and quantitative. The CCM and M latexes were then used, in combination with [Rh(acac)(CO)₂], to catalyze the aqueous biphasic hydroformylation of 1‐octene, in which they showed high activity, recyclability, protection of the activated Rh center by the polymer scaffold, and low Rh leaching. The CCM latex gave slightly lower catalytic activity but significantly less Rh leaching than the M latex. A control experiment conducted in the presence of the sulfoxantphos ligand pointed to the action of the CCM as catalytic nanoreactors with substrate and product transport into and out of the polymer core, rather than as a surfactant in interfacial catalysis.     

Stability of spherical isothermal liquid-vapor interfaces

This paper reconsiders the Laplace and Korteweg theories of isothermal material interfaces. After rederiving the classical instability results for a large droplet of liquid (vapor) imbedded in a vapor (liquid) we consider the stability of microscopic droplets. On this scale the revised Laplace and Korteweg theories predict critical stability of the droplet.

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Sommario In questo lavoro si riconsiderano le teorie di Laplace e di Korteweg sulle interfacce materiali isoterme. Dopo aver dedotto, con metodi nuovi, i risultati classici d'instabiltà per gocce di grande raggio di liquido (o vapore) immerse nel loro vapore (o liquido), si passa a considerare la stabilità di gocce microscopiche. Su questa scala le teorie di Laplace e di Korteweg, opportunamente riformulate, predicono la stabilità critica delle gocce.

     

Quenching and Propagation in KPP Reaction-Diffusion Equations with a Heat Loss

We consider a reaction-diffusion system of KPP type in a shear flow and with a non-zero heat-loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagation speed in terms of the exponential decay of the initial data. We prove the existence of travelling fronts for all speeds c>max(0,c*) in the case Le=1, where c* ∈ ℝ. This seems to be one of the first non-perturbative results on the existence of fronts for the thermo-diffusive system in higher dimensions.     

Image analysis of oil film interferometry — a method of measuring wall shear stress distributions

A method is described of measuring a wall shear stress distribution that varies in the direction of the flow. Variations in the height of a very thin oil film moving under the boundary layer generate interference fringes, which are recorded and digitised using image processing equipment.The evolution of the film surface in space and time can be reconstructed from the interference fringe patterns and used to calculate the shear stress field. This reconstruction is achieved by comparing the picture data with images that were calculated for prescribed heights that are adjusted iteratively, until the calculated intensities match the data.The method is applied to a flow approaching a step, and the results are compared with pulsed-wire measurements.