Energy continued flux functions

Equations [88] and [89] provide the differential equations for the mass and energy flux vectors in Region II. Invoking the continuity of mass and energy fluxes at the interface of Regions I and II, the scalar mass and energy flux functions at the sphere of influence are given by... 

In many systems found in nature, there is a continuous flux of matter and energy so that the system cannot reach equilibrium. Equilibrium statistical mechanics says nothing about the rate of a process. Chemical reaction rates will be discussed in Chapter 8. The nonequilibrium processes to be discussed here are transport processes like diffusion, heat transfer, or conductivity, where the statistics are expressed as time-evolving probability distributions. Transport processes are due to random motion of molecules and are therefore called stochastic. The equations are partial differential equations describing the time evolution of a probability function rather than properties of equilibrium. 

An unresolved difficulty with Monte Carlo calculations which continues to cause concern Is the iiablllty to com-txite accurately the error estimates for the differential quantities (such as flux, fission densities, etc.) as a function of region and energy group. While there is no indication of error in computing the differential quantities themselves, the standard assumption when computing the statistical error that the "sample estimates" are independent is often not valid. To be correct, the statistical error calculation must take into account the correlation between "sample estimates." There is currently no general method to do this. While research on this problem continues, error estimates computed by standard techniques should be used with caution. 

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