Pump Effect of a Capillary Discharge in Electrically Conductive Liquids

Among the configurations to generate plasma in electrically conductive liquids only the diaphragm and the capillary discharge schemes allow to generate plasma which is not in contact with one of the electrodes. Based on this concept, this work reports for the first time the development of an underwater plasma pump, in which the periodic electrical breakdown inside an asymmetrical (sub-)millimetre hole results in a net flow of aqueous solution through the hole without the use of any moving parts such as valves or diaphragms typically used in micropumps. Certain capillary geometries feature very stable flow rates and even allow altering flow direction by changing the power. By varying the hole’s dimensions, the range of time-independent flow rates covers more than one order of magnitude and as the discharge produces some of the strongest oxidants available, we believe that this concept might find application in fields as water decontamination and sterilization.     

Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach

In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily, monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore, we show that the optimal purchase is of bang-bang type.      

Transport-equilibrium schemes for computing nonclassical shocks

This Note presents a very efficient numerical strategy for computing weak solutions of a scalar conservation law which fails to be genuinely nonlinear. In such a situation, the dynamics of shock solutions turns out to be mainly driven by a prescribed kinetic function that imposes the speed of propagation of the discontinuities. We show how to enforce the validity of the kinetic criterion at the discrete level. The resulting scheme provides, in addition, sharp profiles. Numerical evidence are included. To cite this article: C. Chalons, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Orthogonally protected carbohydrate-based scaffolds

A series of orthogonally protected polyaminated carbohydrate scaffolds have been prepared on a multi-gram scale.     

A direct and rapid route to α,α-difluoroacylsilanes from trifluoroethanol

α,α-Difluoroacylsilanes were synthesised directly from a range of allyl ethers of trifluoroethanol via dehydrofluorination/metallation procedures, followed by thermal [3,3]-sigmatropic rearrangement of the intermediate vinylmetals. The scope and limitations of ether synthesis and dehydrofluorination/metallation are described.     

A Conjecture on the Hall Topology for the Free Group

The Hall topology for the free group is the coarsest topologysuch that every group morphism from the free group onto a finitediscrete group is continuous. It was shoen by M.Hall Jr thatevery finitely generated subgroup of the free group is closedfor this topology. We conjecture that if H₁, H₂,...,H_n are finitelygenerated subgroups of the free group, then the product H₁ H₂...H_n is closed. We discuss some consequences of this conjecture.First, it would give a nice and simple algorithm to computethe closure of a given rational subset of the free group. Next,it implies a similar conjecture for the free monoid, which inturn is equivalent to a deep conjecture on finite semigroupsfor the solution of which J. Rhodes has offered $100. We hopethat our new conjecture will shed some light on Rhodes' conjecture.