Response function approach, geometrical

The second broad area in Section 6.2 is concerned with particles. For the separation of particles from a fluid or fractionation of particles, one can adopt an Eulerian appmach to determine the particle concentration variation as observed by an observer located at a fixed coordinate (jqy,z). In such an approach, the fluid velocity is also what is determined by an observer at (jqy,z) as a function of time. However, an alternative approach, the Lagrangian approach, is frequently preferred and will be adopted often. The Lagrangian description of particle motion is obtained by an observer who rides on the particle. The geometrical coordinates (jqy,z) of the particle/observer change with time as the particle changes its location in the device in response to fluid motion and other forces, external and/or diffusive, acting on the particle. In such an approach, the coordinates (x,y,z) of a particle are dependent variables whose values as a function of time in the separation device are of interest. These equations, called trajectory equations, are also provided in Section 6.2. 

The physical inconsistency on the evaluation of the geometric GSMs, in the nonstationary case, as the moments of the one-sided EPSD function was pointed out by Corotis et al. (1972). In fact they discovered that for the case of the transient response of an oscillator subjected to stationary Gaussian white noise processes, the second GSM does not exist because it is unbounded. At same time in the stationary case, this GSM, which is the limit of the transient as the time approaches infinity, is finite. The first that considered the problem of spectral characteristics from a nongeometric point of view was Di Paola (1985). The basic idea... 

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