Equilibrium schemes for scalar conservation laws with stiff sources

We consider a simple model case of stiff source terms in hyperbolic conservation laws, namely, the case of scalar conservation laws with a zeroth order source with low regularity. It is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced CFL condition and refined meshes required because of the lack of accuracy on equilibrium states. The source term should be taken into account in the upwinding and discretized at the nodes of the grid. In order to solve numerically the problem, we introduce a so-called equilibrium schemes with the properties that (i) the maximum principle holds true; (ii) discrete entropy inequalities are satisfied; (iii) steady state solutions of the problem are maintained. One of the difficulties in studying the convergence is that there are no estimates for this problem. We therefore introduce a kinetic interpretation of upwinding taking into account the source terms. Based on the kinetic formulation we give a new convergence proof that only uses property (ii) in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions. The computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that, in comparison with an usual upwind scheme, the corresponding equilibrium version is far more accurate. Furthermore, numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients.

     

Visible light-induced water oxidation on mesoscopic alpha-Fe2O3 films made by ultrasonic spray pyrolysis

Alpha-Fe(2)O(3) films having a mesoscopic leaflet type structure were produced for the first time by ultrasonic spray pyrolysis (USP) to explore their potential as oxygen-evolving photoanodes. The target of these studies is to use translucent hematite films deposited on conducting fluorine doped tin oxide (FTO) glass as top electrodes in a tandem cell that accomplishes the cleavage of water into hydrogen and oxygen by sunlight. The properties of layers made by USP were compared to those deposited by conventional spray pyrolysis (SP). Although both types of films show similar XRD and UV-visible and Raman spectra, they differ greatly in their morphology. The mesoscopic alpha-Fe(2)O(3) layers produced by USP consist mainly of 100 nm-sized platelets with a thickness of 5-10 nm. These nanosheets are oriented mainly perpendicularly to the FTO support, their flat surface exposing (001) facets. The mesoscopic leaflet structure has the advantage that it allows for efficient harvesting of visible light, while offering at the same time the very short distance required for the photogenerated holes to reach the electrolyte interface before recombining with conduction band electrons. This allows for water oxidation by the valence band holes even though their diffusion length is only a few nanometers. Distances are longer in the particles produced by SP favoring recombination of photoinduced charge carriers. Open-circuit photovoltage measurements indicate a lower surface state density for the nanoplatelets as compared to the round particles. These factors explain the much higher photoactivity of the USP compared to the SP deposited alpha-Fe(2)O(3) layers. Addition of hydrogen peroxide to the alkaline electrolyte further improves the photocurrent-voltage characteristics of films generated by USP indicating the hole transfer from the valence band of the semiconductor oxide to the adsorbed water to be the rate-limiting kinetic step in the oxygen generation reaction.     

A Fused Benzocyclooctene Ring System via an Aromatic Cope Rearrangement: Thermal Reactions of trans‐1‐Aryl‐2‐ethenylcyclobutanecarbonitriles

The results of an aromatic Cope rearrangement of a trans‐1‐aryl‐2‐ethenylcyclobutanecarbonitrile are reported (Scheme). The use of this rearrangement for the construction of the fused benzocyclooctene ring system and a preliminary study of the electronic requirements to favor such a transformation are also described.     

Hopf monads

We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. In particular, any monoidal adjunction between autonomous categories gives rise to a Hopf monad. We extend many fundamental results of the theory of Hopf algebras (such as the decomposition of Hopf modules, the existence of integrals, Maschke's criterium of semisimplicity, etc.) to Hopf monads. We also introduce and study quasitriangular and ribbon Hopf monads (again defined in a non-braided setting).     

Fundamentals of Plasma Polymerization

The plasma polymerization of ethylene is used as an example through which to discuss the elementary steps involved in forming a polymer in an electric discharge. The relationship of the experimentally controlled variables to the rate of formation of first generation active species is discussed. These species are related, in turn, to the overall rate of polymerization through a simple model. Two asymptotic conditions are discussed which correspond to minimal and total conversion of monomer to polymer. The dependence of polymer deposition rate on monomer flow rate predicted by the model is found to correspond very closely to that observed experimentally. The predicted effect of gas pressure on polymer deposition rate also agrees with that found experimentally.     

Synthesis of NMP/RAFT inifers and preparation of block copolymers

Two different initiator/transfer agents (inifers) containing an alkoxyamine and a dithiobenzoate were synthetized and used to trigger out either reversible addition‐fragmentation chain transfer (RAFT) polymerization or nitroxide‐mediated polymerization (NMP). α‐Dithiobenzoate‐ω‐alkoxyamine‐difunctional polymers were produced in both cases which were subsequently used as precursors in the formation of block copolymers. This synthetic approach was applied to N‐isopropylacrylamide (NIPAM) or polyethylene oxide methacrylate (EOMA) to form α,ω‐heterodifunctional homopolymers via RAFT at 60°C which were chain extended with styrene by activating the alkoxyamine moiety at 120°C. Under such temperature conditions, it is proposed that a tandem NMP/RAFT polymerization is initiated producing a simultaneous growth of polystyrene blocks at both chain‐ends. Self‐assembled nanostructures of these amphiphilic block copolymers were evidenced by scanning electron microscopy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012