... nonlinearity. Then, Fokker-Planck equation is used to study the probability density distribution of the process. Because the exact solution of Fokker-Planck equation is difficult to solve, the approximate results are calculated by the path integral solution. The innovation of this paper is to apply this method...

...-grained soil sieve consolidation self-weight consolidation liquid clay sedimentation test settlement sedimentation water content density distribution elevation concentration hydraulic consolidation consolidation test dredged soil water management interface effective stress characteristic...

... In this paper, structural optimization is addressed through a density distribution process. The recent increase in information technologies dedicated to optimal design, associated with the progress of the numerical tools, allows significant improvement in the design optimization of mechanical...

... - dividing the given domain into sub domains -- plays an important role in preprocessing step, while triangles are widely used on planar domains mainly for its easily conforming to the boundary. It is essential that a mesh based on an appropriate density distribution, which depends on the appropriate nodal...

... in irregular waves by use of both their spectrum and probability. It is shown that the linear theory of water wave is applicable to the evaluation of the absorbed power in air chambers. Turbine performances in irregular waves are easily shown with the probability density distribution, that is, Gauss...

...). The initial density distribution R(z) is given by the following expression: R(z) = Roo - (Roo - Ro) exp(z) (25) where Roo is the free-stream density and Ro is the free-surface density. The values Roo = 1. Ro = 0.99 are used. and the corre- sponding profile is shown in Figure 3. The flow (24) has one...