This paper proposes a three-dimensional autonomous chaotic system which displays some interest dynamical behaviors such as invariable Lyapunov exponent spectrums and controllable signal amplitude. The corresponding fractional version of the proposed system is obtained. A single state controller for synchronization of this fractional-order chaotic system is developed based on the techniques of sliding mode control and adaptive control. Numerical simulations are provided to demonstrate the feasibility of the presented synchronization method.

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Previous experimental, molecular dynamics, and thermodynamic researches on the melting temperature of Au nanoparticles on tungsten substrate provide entirely different results. To account for the substrate effect upon the melting point of nanoparticles, three different substrates were tested by using a thermodynamic model: tungsten, amorphous carbon, and graphite. The results reveal that the melting point suppression of a substrate-supported Au nanoparticle is principally ruled by the free surface-to-volume ratio of the particle or the contact angle between the particle and the substrate. When the contact angle θ is less than 90°, a stronger size-dependent melting point depression compared with those for free nanoparticles is predicted; when the contact angle θ is greater than 90°, the melting temperature of the supported Au nanoparticles are somewhat higher than those for free nanoparticles.

The semiclassical approach in the framework of the non-local theory of resonance electron-molecule collisions is developed. The basic integro-differential equation of this theory is reduced to the recursion set of linear equations, the number of the equations is equal to the total number of the vibrational levels of the target molecule. The continuum of the molecule dissociative states is taken into account by the boundary condition. The semiclassical approach makes it possible to calculate the whole set of cross sections for all the channels which are accessible at the value of the total energy under consideration. These cross sections are calculated for the model systems, F2 and HCl molecules. The relation between local and non-local theories is considered. It is shown that the local theory is well founded if the molecule and resonance energy curves cross far from the equilibrium geometry and if the threshold dependence of the width of the resonance state on the electron energy is smooth enough.