Average of a function

We now specialize the Fokker-Planck equation to the case of Brownian motion in Section 11.1. In this case, the variable y is the velocity v of the Brownian particle. We also note that the average of a function of the velocity v at time t, given that v = vo at t = t0, is simply expressed in terms of the transition probability by... 

If one can approximate the average of a function of momentum and position coordinates by a function of the average momentum and position. 

In fact, one is frequently interested in some observable property , which is (experimentally) a time average of a function of the phase variables B(r, o) ) the latter is often a sum of pair terms b(rjj,0)j,0)j) so that is given by... 

The theoretical formulation of heat and mass transfer in porous media is usually obtained by a change in scale. We can pass from a microscopic view where the size of tlie representative volume is small with regards to pores, to a microscopic view where the size of the representative volume CO is large with regard to the pores. Moreover, the heat and mass transfer equations can be deduced from Whitaker s theory. The macroscopic equations can be obtained by averaging the classical fluid mechanics, dififiision and transfer equations over the averaging volume co[m ]. The average of a function/is ... 

Averages of the Sedimentation Coefficient The average of a function X(M) is defined as... 

Hint One way to compute an average of a function, f t), is to integrate over the time interval and divide by the interval width. That is,... 

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