A stochastic model of bubble distribution in gas–solid fluidized beds

On the basis of the Langevin equation and the Fokker-Planck equation, a stochastic model of bubble distribution in a gas-solid fluidized bed was developed. A fluidized bed with a cross section of 0.3 m×0.02 m and a height of 0.8 m was used to investigate the bubble distribution with the photographic method. Two distributors were used with orifice diameters of 3 and 6 mm and opening ratios of 6.4% and 6.8%, respectively. The particles were color glass beads with diameters of O.3, 0.5 and 0.8 mm （Geldart group B particles）. The model predictions are reasonable in accordance with the experiment data. The research results indicated that the distribution of bubble concentration was affected by the particle diameter, the fluidizing velocity, and the distributor style. The fluctuation extension of the distribution of bubble concentration narrowed as the particle diameter, fluidizing velocity and opening ratio of the distributor increased. For a given distributor and given particles the distribution was relatively steady along the bed height as the fluidizing velocity changed.

Lagrangian statistics in isotropic turbulent flows with deterministic and stochastic forcing schemes

Artificial input of energy into the flow is neces sary to create and maintain a statistically stationary isotropic turbulence for sampling in studying the statistics. Due to the nonlinear coupling among different Fourier modes through the triadic interaction, whether or not various forc ing schemes affect the statistics in turbulence is an impor tant and open question. We present detailed comparison of Lagrangian statistics of fluids particles in forced isotropic turbulent flows in 1283, 2563, and 5123 simulations, with Taylorscale Reynolds numbers in the range of 64-171, us ing a deterministic and a stochastic forcing scheme, respec tively. Several Lagrangian statistics are compared, such as velocity and acceleration autocorrelations, and moments of Lagrangian velocity increments. The differences in the La grangian statistics obtained from the two forcing schemes are shown to be small, indicating that the isotropic forcing schemes used have little effects on the Lagrangian statistics in the isotropic turbulence.

RESEARCH ANNOUNCEMENTS——Random Attractors for a Dissipative Quasi-geostrophic Dynamical System Under Stochastic Forcing

We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the

Stability of Controlled Hamilton Systems Excited by Gaussian White Noise

A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed.The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises.Some further developments,problems,and challenges in this direction are also discussed.