This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequflibrium transitions induced by the cross- correlated noises are studied. The stationary solutions of the Fokker-Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.
Point defect states in two-dimensional phononic crystal of a hollow mercury cylinder in a water host are studied. An improved plane expansion method combined with the supercell technique is used to calculate the band gaps and the pressure distribution at the defect position. The sonic pressure of defect modes shows that the waves are localized at or near the defect. As the filing fraction increases, more defect modes appear in the band gaps.
