On convergence of solutions of fractal Burgers equation toward rarefaction waves

In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\partial^2_x)^{\alpha/2} u+uu_x=0$ with $\alpha\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\pm$ ($u_-<u_+$) as $x\to \pm\infty$, respectively, then the corresponding solution converges toward the rarefaction wave, {\it i.e.} the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.Comment: 15 page

On the spectrum of a waveguide with periodic cracks

The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small

Numerical approximation of a concrete carbonation model: study of the t\sqrt{t}-law of propagation

International audienceIn this paper, we are interested in the long time behavior of approximate solutions to a free boundary model which appears in the modeling of concrete carbonation [1]. In particular, we study the long time regime of the moving interface. The numerical solutions are obtained by an implicit in time and finite volume in space scheme. We show the existence of solutions to the scheme and, following [2, 3], we prove that the approximate free boundary increases in time following a $\sqrt{t}$-law. Finally, we supplement the study through numerical experiments

Effect of anchimeric assistance in the reaction of triphenylphosphine with α,β-unsaturated carboxylic acids

Quaternization of triphenylphosphine with maleic and cis-aconitic acids is strongly accelerated by participation of the cis-carboxyl group in stabilization of the phosphonium zwitterion intermediate by intramolecular hydrogen bonding, in spite of steric hindrance by the acid's reaction center. A similar effect for trans-isomeric acids is not observed, which can be rationalized on the basis of spatial structures of the generated zwitterions, implying an electrostatic interaction between the phosphonium center and carbonyl oxygen atom. The effect of anchimeric assistance decreases when the intramolecular hydrogen bonding disfavors attack of the phosphine on the sterically less hindered carbon atom of the C=C bond, as observed for cis-aconitic acid. © 2014 Wiley Periodicals, Inc

Probability of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips

We have studied supercurrent-assisted formation of the resistive state in nano-structured Nb and NbN superconducting films after absorption of a single photon. In amorphous narrow NbN strips the probability of the resistive state formation has a pronounced spectral cut-off. The corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the generalized hot-spot model suggests that the quantum yield for near-infrared photons increases faster than the photon nergy. Relaxation of the resistive state depends on the photon energy making the phenomenon feasible for the development of energy resolving single-photon detectors.Comment: 9 pages, 9 figures, submitted to Eur. Phys. Journa