To investigate the superhydrophobic properties of different surface textures, nine designs of textures with micro-nanostructures were produced successfully using the laser engraving technique on the surfaces of composite insulator umbrella skirt samples made of silicon rubber. The optimal parameters of the texture designs to give rise to the best hydrophobicity were determined. The surface morphology, abrasion resistance, corrosion resistance, self-cleaning and antifouling property of the different textured surfaces as well as water droplets rolling on the textured surfaces were studied experimentally using a contact angle meter, scanning electron microscope, three-dimensional topography meter and high-speed camera system. It was found that the diamond column design with optimal parameters has the best superhydrophobicity and overall performance. The most remarkable advantage of the optimal diamond column design is its robustness and long-term superhydrophobicity after repeated de-icing in harsh conditions. The reported work is an important step towards achieving superhydrophobic surface without coating for outdoor composite insulator in practical applications.

Based on the energy flow theory of nonlinear dynamical system, the stabilities, bifurcations, possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper. It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-paramters. (a) Energy flow matrix has two negative and one positive energy flow factors, constructing an attractive local zero-energy flow surface, in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state, while forced vibrations by external forces show stable oscillations. (b) Energy flow matrix has one negative and two positive energy flow factors, spaning a divergence local zero-energy flow surface, so that the both free and forced vibrations are divergence oscillations with the system being unstable. (c) Energy flow matrix has a zero-energy flow factor and two opposite factors, which constructes a local zero-energy flow surface dividing the local phase space into stable, unstable and central subspace, and the simulation shows friction self-induced unstable vibrations for both free and forced cases. For a set of friction parameters, the system behaves a periodical oscillation, where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero. Numerical simulations have not found any possible chaotic motions of the system. It is discovered that the damping matrices of cases (a), (b) and (c) respectively have positive, negative and zero diagonal elements, resulting in the different dynamic behavour of system, which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications. Graphic

Chaotic phenomena are increasingly being observed in all fields of nature, where investigations reveal that a natural phenomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms. Chaos is normally understood as “a state of disorder”, for which there is as yet no universally accepted mathematical definition. A commonly used concept states that, for a dynamical system to be classified as chaotic, it must have the following properties: be sensitive to initial conditions, show topological transitivity, have densely periodical orbits etc. Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature. We present herein a generalised energy conservation law governing chaotic phenomena. Based on two scalar variables, viz. generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems, we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period. This implies that, as the averaging time is increased, the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows, i.e., their rates of change with time, tend to zero. Numerical simulations on reported chaotic motions, such as the forced van der Pol system, forced Duffing system, forced smooth and discontinuous oscillator, Lorenz’s system, and Rössler’s system, show the above conclusions to be correct according to the results presented herein. This discovery may indicate that chaotic phenomena in nature could be controlled because, even though their instantaneous states are disordered, their long-time averages can be predicted.

This paper presents theoretical investigations of lattice Boltzmann method (LBM) to develop a completed LBM theory. Based on H-theorem with Lagrangian multiplier method, an amended theoretical equilibrium distribution function (EDF) is derived, which modifies the current Maxwell–Boltzmann distribution (MBD) to include the total internal energy as its parameter. This modification allows the three conservation laws derived directly from lattice Boltzmann equation (LBE) without additional small-parameter expansions adopted in references. From this amended theoretical EDF, an improved LBM is developed, in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations. The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations. The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated. Analytically hand-workable examples are given to illustrate its applications and to confirm its validity. The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems, from which it is expected to further advance LBM benefiting science and engineering. Graphic abstract