Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions

This paper is devoted to the analysis of non-negative solutions for a generalisation of the classical parabolic-elliptic Patlak–Keller–Segel system with d ≥ 3 and porous medium-like non-linear diffusion. Here, the non-linear diffusion is chosen in such a way that its scaling and the one of the Poisson term coincide. We exhibit that the qualitative behaviour of solutions is decided by the initial mass of the system. Actually, there is a sharp critical mass M _c such that if solutions exist globally in time, whereas there are blowing-up solutions otherwise. We also show the existence of self-similar solutions for . While characterising the possible infinite time blowing-up profile for M  =  M _c , we observe that the long time asymptotics are much more complicated than in the classical Patlak–Keller–Segel system in dimension two. This paper is under the Creative Commons licence Attribution-NonCommercial-ShareAlike 2.5.     

The cylinder over the Koras–Russell cubic threefold has a trivial Makar-Limanov invariant

In 1996 Makar-Limanov established that the Koras–Russell cubic threefold

Refractive-index saturation-mediated multiple line emission in polymer thin-film distributed-feedback lasers

We report experimental and theoretical investigations of multiple laser-line emission in a distributed-feedback dye laser pumped by two coherent optical beams. We have used a Lloyd interferometer configuration with second- and third-order Bragg reflections to study the interaction between the two incident pumps in an organic thin film. We demonstrated theoretically that the number of laser emission lines can be interpreted with reference to the saturation effect in the refractive index.     

Naturally Derived Silicone Surfactants Based on Saccharides and Cysteamine

Silicone surfactants are widely used in many industries and mostly rely on poly(ethylene glycol) (PEG) as the hydrophile. This can be disadvantageous because commercial PEG examples vary significantly in polydispersity—constraining control over surface activity of the surfactant—and there are environmental concerns associated with PEG. Herein, we report a three-step synthetic method for the preparation of saccharide-silicone surfactants using the natural linker, cysteamine, and saccharide lactones. The Piers–Rubinsztajn plus thiol-ene plus amidation process is attractive for several reasons: if employed in the correct synthetic order, it allows for precise tailoring of both hydrophobe and hydrophile; it permits the ready utilization of natural hydrophiles cysteamine and saccharides in combination with silicones, which have significantly better environmental profiles than PEG; and the products exhibit interesting surface activities.     

Determination of Chlorinated Solvent Sorption by Porous Material—Application to Trichloroethene Vapor on Cement Mortar

Experiments have been performed to investigate the sorption of trichloroethene (TCE) vapor by concrete material or, more specifically, the cement mortar component. Gas-flow experiments were conducted using columns packed with small pieces of cement mortar obtained from the grinding of typical concrete material. Transport and retardation of TCE at high vapor concentrations (500 mg L \(^{-1})\) was compared to that of a non-reactive gas tracer (Sulfur Hexafluoride, SF \(_{6})\) . The results show a large magnitude of retardation (retardation factor \(=\) 23) and sorption (sorption coefficient \(=\) 10.6 cm \(^{3}\)  g \(^{-1})\) for TCE, compared to negligible sorption for SF \(_{6}\) . This magnitude of sorption obtained with pollutant vapor is much bigger than the one obtained for aqueous-flow experiments conducted for water-saturated systems. The considerable sorption exhibited for TCE under vapor-flow conditions is attributed to some combination of accumulation at the air-water interface and vapor-phase adsorption, both of which are anticipated to be significant for this system given the large surface area associated with the cement mortar. Transport of both SF \(_{6}\) and TCE was simulated successfully with a two-region physical non-equilibrium model, consistent with the dual-medium structure of the crushed cement mortar. This work emphasizes the importance of taking into account sorption phenomena when modeling transport of volatile organic compounds through concrete material, especially in regard to assessing vapor intrusion.     

Electrochemical cleavage of sulfonamides: an efficient and tunable strategy to prevent β-fragmentation and epimerization

The electrochemical reduction of sensitive sulfonamides is described. The addition of a benzoyl group on the nitrogen atom facilitates the reductive cleavage of sulfonamides preventing β-fragmentation and epimerization. This strategy was successfully applied to the cyclopropylamine and to α-amino stannanes.     

Design of amphoteric mixed oxides of zinc and Group 3 elements (Al, Ga, In): migration effects on basic features

The design of new amphoteric catalysts is of great interest for several industrial processes, especially those covering dehydration and dehydrogenation phenomena. Adsorption microcalorimetry was used to monitor the design of mixed oxides of zinc with Group 3 elements (aluminium, gallium, indium) with amphoteric character and enhanced specific surface area. Acid-base features were found to evolve non-linearly with the relative amounts of metal, and the strengths of the created acidic or basic sites were measured by adsorption microcalorimetry. A panel of bifunctional catalysts of various acid-base (amounts, strengths) and redox character was obtained. Besides, special interest was given to In-Zn mixed oxides for their enhanced basicity: this series of catalysts displays important basic features of high strength (q(diff) (SO? ads.) > 200 kJ mol(SO?)?1 in substantial amounts (1 - 2 μmol m(catalyst)?2), whose impact on efficiency or selectivity in catalytic dehydration/dehydrogenation can be valuable.     

Pickering Emulsion Stabilized by Catalytic Polyoxometalate Nanoparticles: A New Effective Medium for Oxidation Reactions

Decyl‐, dodecyl‐, and tetradecyltrimethylammonium cations were combined with the catalytic polyoxometalate [PW₁₂O₄₀]^3? anion to give spherical and monodisperse nanoparticles that are able to stabilize emulsions in the presence of water and an aromatic solvent. This triphasic liquid/solid/liquid system, based on a catalytic surfactant, is particularly efficient as a reaction medium for epoxidation reactions that involve hydrogen peroxide. The reactions proceed at competitive rates with straightforward separation of the phases by centrifugation. Such catalytic “Pickering” emulsions combine the advantages of heterogeneous catalysis and biphasic catalysis without the drawbacks (e.g., catalyst leaching or separation time).     

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on Z$Z$ that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs.     

Energetic and spectral properties of triple photon downconversion in a phase-matched KTiOPO4 crystal

We measured the spectrum and energy of infrared triple photons generated in a phase-matched KTiOPO4 crystal pumped by picosecond beams at 532 and 1662 nm. The experimental data are in good agreement with our model, taking into account the spectral linewidths of the incident beams as well as a parasitic Kerr effect.