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

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

Broadening of hot-spot response spectrum of superconducting NbN nanowire single-photon detector with reduced nitrogen content

The spectral detection efficiency and the dark count rate of superconducting nanowire single-photon detectors (SNSPD) has been studied systematically on detectors made from thin NbN films with different chemical compositions. Reduction of the nitrogen content in the 4 nm thick NbN films results in a more than two orders of magnitude decrease of the dark count rates and in a red shift of the cut-off wavelength of the hot-spot SNSPD response. The observed phenomena are explained by an improvement of uniformity of NbN films that has been confirmed by a decrease of resistivity and an increase of the ratio of the measured critical current to the depairing current. The latter factor is considered as the most crucial for both the cut-off wavelength and the dark count rates of SNSPD. Based on our results we propose a set of criteria for material properties to optimize SNSPD in the infrared spectral region.Comment: 15 pages, 6 figure

Geometry-induced reduction of the critical current in superconducting nanowires

Reduction of the critical current in narrow superconducting NbN lines with sharp and rounded bends with respect to the critical current in straight lines was studied at different temperatures. We compare our experimental results with the reduction expected in the framework of the London model and the Ginsburg-Landau model. We have experimentally found that the reduction is significantly less than either model predicts. We also show that in our NbN lines the bends mostly contribute to the reduction of the critical current at temperatures well below the superconducting transition temperature