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Experiments on the depressurization of high-pressure vessels have shown the vaporization to occur in ‘boiling shocks’ moving with the velocity of ∼10 m s −1 . This phenomenon was explained by proposing a boiling liquid model accounting for bubble fragmentation. It was shown that an explosive boiling-up was caused by a sharp increase in the interphase area due to a chain process of bubble breakup. In the present study, we use this model, with no change in its free parameters, to simulate the flow in a Laval nozzle. In a critical nozzle flow, boiling occurs to proceed in a shock-type wave as well. It is shown that the formation of boiling shocks may cause autovibrations. The investigation of the shock structure shows that the fulfillment of two conditions is necessary for its realization: Weber number must reach its critical value and the flow velocity must be less than an equilibrium speed of sound. When the conditions cannot be simultaneously realized at a steady-state regime, the flow goes over into a self-oscillation mode.

Fine particles aggregating into larger units or flocculation body is a random combination process. Increasing the size and density of flocculation body is the main approach to rapid particle removal or sedimentation in water. Aiming at the Brownian coagulation of fine particles, a new method of Taylor expansion moment construction of fractal flocs has been developed in this paper, incorporating the Taylor expansion approach based on the moment method and the fractal dimension of the floc structure originated from fractal theories. This method successfully overcomes the limit of previous moment methods that require pre-assumed particle size distribution. Results of the zero and second order moments of Brownian flocs from the proposed method are compared with those from the Laguerre method, integral moment method and finite element method. It is found that the higher accuracy and efficiency of computation have been achieved by the new method, compared to the previous ones. Effects of the fractal dimension on the zero and second order moments, geometric average volume and standard deviation are also analyzed using this method. The self-conservation characteristics of particle distribution is observed without presumption of initial distributions.

In this paper, the concept of complex hybrid synchronization in complex-variable chaotic system is introduced for the first time. Based on Lyapunov stability theory, two typical complex-variable chaotic systems are considered and corresponding controllers are designed to achieve complex hybrid synchronization. Further, a universal control method in virtue of adaptive control scheme is proposed. Numerical examples are provided to show the effectiveness of the proposed method.

In this work we investigate the numerical solution of Kaup-Kupershmit (KK) equation, KdV-KdV and generalized Hirota-Satsuma (HS) systems. The proposed numerical schemes in this paper are based on fourth-order time-stepping schemes in combination with discrete Fourier transform. We discretize the original partial differential equations (PDEs) with discrete Fourier transform in space and obtain a system of ordinary differential equations (ODEs) in Fourier space which will be solved with fourth order time-stepping methods. After transforming the equations to a system of ODEs, the linear operator in KK and HS equation is diagonal but in KDV-KDV equation is not diagonal. However for KDV-KDV system which is the focus of this paper, we show that the exponential of linear operator and related inverse matrix have definite structure which enable us to implement the methods such as diagonal case. Comparing numerical solutions with exact traveling wave solutions demonstrates that those methods are accurate and readily implemented.

This paper presents the advantages of some effective analytical approaches applied on the governing equation of transversely vibrating cantilever beams. Six studied methods are Min-Max Approach, Parameter Expansion Method, Hamiltonian Approach, Variational Iteration Method, Bubnov-Galerkin and Energy Balance Method. The powerful analytical approaches are used to obtain frequency-amplitude relationship for dynamic behavior of nonlinear vibration of cantilever beams. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the accuracy of these methods.

The movement of reinforced concrete fragments driven by internal explosions was investigated, and a model was built in consideration of the interaction and deformation harmony between steel bars and concrete for the description of fragments movement. The calculated and experimental results indicate that the model is reasonable.