Circulatory bubble dynamics: From physical to biological aspects

Bubbles can form in the body during or after decompression from pressure exposures such as those undergone by scuba divers, astronauts, caisson and tunnel workers. Bubble growth and detachment physics then becomes significant in predicting and controlling the probability of these bubbles causing mechanical problems by blocking vessels, displacing tissues, or inducing an inflammatory cascade if they persist for too long in the body before being dissolved. By contrast to decompression induced bubbles whose site of initial formation and exact composition are debated, there are other instances of bubbles in the bloodstream which are well-defined. Gas emboli unwillingly introduced during surgical procedures and ultrasound microbubbles injected for use as contrast or drug delivery agents are therefore also discussed. After presenting the different ways that bubbles can end up in the human bloodstream, the general mathematical formalism related to the physics of bubble growth and detachment from decompression is reviewed. Bubble behavior in the bloodstream is then discussed, including bubble dissolution in blood, bubble rheology and biological interactions for the different cases of bubble and blood composition considered.     

Equidistant hypersurfaces of the bidisk

The following are notes on the geometry of the bidisk, H ² × H ². In particular, we examine the properties of equidistant surfaces in the bidisk.     

Bis(diethoxyselenophosphinoyl) triselenide and bis(diisopropoxyselenophosphinoyl) diselenide

The title compounds, bis(diethoxyselenophosphinoyl) triselenide, [P(OEt)₂Se]Se₃[P(OEt)₂Se], and bis­(diisopropoxy­selenophosphinoyl) diselenide, [P(OⁱPr)₂Se]Se₂[P(OⁱPr)₂Se], comprise an Se₃ chain or an Se₂ chain bridging two (RO)₂PSe groups.     

An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients

In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading to a stochastic maximum principle of semi-couple forward–backward stochastic differential equation with non-smooth coefficients. The proof is based on the approximation of the Lipschitz coefficients by smooth ones and the approximation of the infinite horizon adjoint process.     

Diels-Alder cycloaddition of o-quinonedimethides and alkylidene-5H-furan-2-ones: new and rapid access to lambertellol cores and arthrinone derivatives

An efficient synthesis of deoxy-lambertellols was reported through a highly chemo- and diastereoselective intermolecular Diels-Alder cycloaddition between trans-1,2-disiloxybenzocyclobutenes and 2-methylprotoanemonine. Such transformation with δ-substituted γ-alkylidenebutenolides, to prepare new analogues of these tricyclic spirolactones, which would be very difficult to prepare by other ways, was also studied.     

Water soluble polymeric nanogels by xanthate-mediated radical crosslinking copolymerisation

Branched water-soluble copolymers were obtained by direct radical crosslinking copolymerisation of acrylic acid or acrylamide and N,N'-methylenebisacrylamide at high solid content in the presence of an O-ethylxanthate as a reversible chain transfer agent.     

Modélisation et simulation numérique du changement de phase liquide–vapeur en cavitéModeling and numerical simulation of liquid–vapor phase change in an enclosed cavity

A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio (${\rho }_l/{\rho }_v?1000$) flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006).