Frictional dissipation and interfacial glass transition of polymeric solids

We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer-substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyze as resulting from an interaction-induced "interfacial glass transition" helped by pressure.     

Electrophotocatalysis with a Trisaminocyclopropenium Radical Dication

Visible‐light photocatalysis and electrocatalysis are two powerful strategies for the promotion of chemical reactions. Here, these two modalities are combined in an electrophotocatalytic oxidation platform. This chemistry employs a trisaminocyclopropenium (TAC) ion catalyst, which is electrochemically oxidized to form a cyclopropenium radical dication intermediate. The radical dication undergoes photoexcitation with visible light to produce an excited‐state species with oxidizing power (3.33 V vs. SCE) sufficient to oxidize benzene and halogenated benzenes via single‐electron transfer (SET), resulting in C?H/N?H coupling with azoles. A rationale for the strongly oxidizing behavior of the photoexcited species is provided, while the stability of the catalyst is rationalized by a particular conformation of the cis‐2,6‐dimethylpiperidine moieties.     

Locally Hausdorff tight groupoids generalised

We extend Exel’s ample tight groupoid construction to non-ample groupoids, even in the general locally Hausdorff case.

     

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Single-frequency Brillouin distributed feedback fiber laser

We demonstrate a single-frequency Brillouin distributed feedback laser (DFB). The DFB laser cavity was a 12.4 cm long fiber Bragg grating with a π-phase shift offset from the grating center. It exhibited a threshold of 30 mW and conversion efficiency from pump to Stokes wave as high as 27%. Higher-order Stokes waves were suppressed by more than 20 dB. The Stokes output of the laser could be obtained in either the forward or backward direction, simply by changing the orientation of the offset of the discrete phase shift with respect to the pump propagation direction. The DFB laser operated over a pump frequency range of 1.2 GHz, more than 60 times larger than the SBS gain bandwidth.     

On avoiding odd partial Latin squares and r-multi Latin squares

We show that for any positive integer k?4, if R is a (2k-1)×(2k-1) partial Latin square, then R is avoidable given that R contains an empty row, thus extending a theorem of Chetwynd and Rhodes. We also present the idea of avoidability in the setting of partial r-multi Latin squares, and give some partial fillings which are avoidable. In particular, we show that if R contains at most nr/2 symbols and if there is an n×n Latin square L such that δn of the symbols in L cover the filled cells in R where 0<δ<1, then R is avoidable provided r is large enough.     

valuation of options on joint minima and maxima

It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.     

A quantization property for static Ginzburg‐Landau vortices

For any critical point of the complex Ginzburg‐Landau functional in dimension 3, we prove that, for large coupling constants, ; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log , then the ball of half‐radius contains no vortex (the modulus of the solution is larger than ½). We then show how this property can be applied to describe limiting vortices as ε → 0. © 2001 John Wiley & Sons, Inc.