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We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present real physical systems that can produce this kind of random time-series. We report the results of real experiments with nonlinear circuits containing direct evidence for this new phenomenon. In particular, we show that a Josephson junction coupled to a chaotic circuit can generate unpredictable dynamics. Some applications are discussed.

Herein, we report the synthesis of a double hydrazone capable of undergoing photochemical E/Z isomerization through the imine double bonds. The bis(hydrazone) 1-E,E can be considered as a "two-arm" system in which the controlled movement of each arm is obtained by photo-modulation, making possible the appearance of two isolable metastable isomeric states 1-E,Z and 1-Z,Z. Such states are characterized by very specific structural, optical, and electrochemical properties. The latter allows the reversible return from either 1-E,Z or 1-Z,Z to the 1-E,E state. Our results are of great importance in the further development of molecular machines and photochemically controlled reactions by introducing for the first time double hydrazones as tunable photochemical switches.

We investigate, at a laboratory scale, the collapse of cylindrical shells of radius R and thickness t induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that the silos sustain filling heights significantly above an estimation obtained by coupling standard shell-buckling and granular stress distribution theories. Two effects contribute to stabilize the structure: (i) below the critical filling height, a dynamical stabilization due to granular wall friction prevents the localized shell-buckling modes to grow irreversibly; (ii) above the critical filling height, collapse occurs before the downward sliding motion of the whole granular column sets in, such that only a partial friction mobilization is at play. However, we notice also that the critical filling height is reduced as the grain size d increases. The importance of grain size contribution is controlled by the ratio d= ffiffiffiffiffi Rt p . We rationalize these antagonist effects with a novel fluid-structure theory both accounting for the actual status of granular friction at the wall and the inherent shell imperfections mediated by the grains. This theory yields new scaling predictions which are compared with the experimental results.

We study experimentally the collective motion of grains inside a U shaped tube undergoing vertical oscillations, and we develop a very simple quantitative model that captures relevant features of the observed behaviour. The height difference between the granular columns grows with time when the system is shaken at sufficiently low frequencies. The system exhibits two types of growth: exponentially divergent (type I) and exponentially saturating (type II), depending on the size of the grains. The type I growth can be quenched by removing the air whereas the type II behavior can occur in the absence of air. There is a good agreement between the model proposed and our experimental results.

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