We investigate the potential of fabricating thermally stable refractive index contrasts using femtosecond (fs) near-infrared (IR) radiation in aluminosilicate glasses. A set of pure SiO 2-Al 2 O 3 glasses are manufactured, characterized (density and Raman) and investigated after being irradiated by fs laser within the Type II regime. The formation of nanogratings is identified and studied using quantitative birefringence measurements. Their thermal stability is then investigated through 30min step isochronal annealing (up to 1250°C). For both SiO 2 and 50SiO 2-50Al 2 O 3 compositions, the normalized birefringence does not decrease when tested up to 1100°C, while for the 4,6 mol% GeO 2-SiO 2 erased for 20% at 1000°C.

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This paper provides mathematical and numerical analysis of a one-dimensional model of turbulent flow generating the anomalous cascade of the inviscid conserved quantity. The model is based on the generalized Constantin–Lax–Majda–DeGregorio (gCLMG) equation with viscous dissipation under a large-scale forcing. Suppose that the forcing function and the initial data are random variables defined on a certain probability space. Then, the equation is regarded as a random partial differential equation. We prove the global existence of a unique solution to the gCLMG equation, from which a stochastic process is defined. In addition, by approximating the solutions numerically by Galerkin approximation of random variables with generalized polynomial chaos, we confirm the existence of a steady distribution. We find that the steady distribution reproduces qualitatively the same cascades of the energy and the enstrophy spectra as those of a turbulent flow generated by randomly moving pulse (Matsumoto and Sakajo 2016 Phys. Rev. E 93 053101). We also investigate the structure functions, showing intermittency.