Capillary wave turbulence on a spherical fluid surface in low gravity

We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container which is submitted to random forcing. The surface wave amplitude displays power-law spectrum over two decades in frequency, corresponding to wavelength from $mm$ to a few $cm$. This spectrum is found in roughly good agreement with wave turbulence theory. Such a large scale observation without gravity waves has never been reached during ground experiments. When the forcing is periodic, two-dimensional spherical patterns are observed on the fluid surface such as subharmonic stripes or hexagons with wavelength satisfying the capillary wave dispersion relation

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

towards formal validation of trust and security in the internet of services

Service designers and developers, while striving to meet the requirements posed by application scenarios, have a hard time to assess the trust and security impact of an option, a minor change, a combination of functionalities, etc., due to the subtle and unforeseeable situations and behaviors that can arise from this panoply of choices. This often results in the release of flawed products to end-users. This issue can be significantly mitigated by empowering designers and developers with tools that offer easy to use graphical interfaces and notations, while employing established verification techniques to efficiently tackle industrial-size problems. The formal verification of trust and security of the Internet of Services will significantly boost its development and public acceptance

A multi-element psychosocial intervention for early psychosis (GET UP PIANO TRIAL) conducted in a catchment area of 10 million inhabitants: study protocol for a pragmatic cluster randomized controlled trial

Multi-element interventions for first-episode psychosis (FEP) are promising, but have mostly been conducted in non-epidemiologically representative samples, thereby raising the risk of underestimating the complexities involved in treating FEP in 'real-world' services

Umbilical defect dynamics in an inhomogeneous nematic liquid crystal layer

Electrically driven nematic liquid crystals layers are ideal contexts for studying the interactions of local topological defects, umbilical defects. In homogeneous samples the number of defects is expected to decrease inversely proportional to time as a result of defect-pair interaction law, so-called coarsening process. Experimentally, we characterize the coarsening dynamics in samples containing glass beads as spacers and show that the inclusion of such imperfections changes the exponent of the coarsening law. Moreover, we demonstrate that beads that are slightly deformed alter the surrounding molecular distribution and attract vortices of both topological charges, thus, presenting a mainly quadrupolar behavior. Theoretically, based on a model of vortices diluted in a dipolar medium, a 23 exponent is inferred, which is consistent with the experimental observations

Thermally-induced nonlinear spatial shaping of femtosecond pulses in nematic liquid crystals

International audienc

Coarsening dynamics of umbilical defects in inhomogeneous medium

Non-equilibrium systems with coexistence of equilibria exhibit a rich and complex defects dynamics in order to reach a more stable configuration. Nematic liquid crystals layer with negative dielectric constant and homeotropic anchoring under the influence of a voltage are the ideal context for studying the interaction of gas of topological vortices. The number of vortices decreases with time. Experimentally, we show that the presence of imperfections drastically changes this coarsening law. Imperfections are achieved by considering glass beads inside the nematic liquid crystal sample. Depending on the disorder of these imperfections, the system exhibits different statistical evolution of the number of umbilical defects. The coarsening dynamics is persistent and is characterized by power laws with different exponents