Population function

It is believed that population density of a consortium component species mediates population function through self-awareness mechanisms such as quorum sensing , that enable bacteria to communicate among and between species in a consortium (Miller and Bassler, 2001). 

Another way to apply the same idea can be derived from formal considerations. We now consider a double well system that correspond to the reaction 7 P and suppose that we can generate trajectories as before. Define the population function... 

A combination of physical forces and diffusion governs pore evolution. As a result, pores with a wide range of sizes appear in the membrane. This distribution of sizes is described by a pore population function that is, a probability density function, n(r, t) At any time t, there are n(r, t) Ar pores with radii between r and r +Ar. 

Here, h (x) and /jb(x) are the population functions, or characteristic functions, of regions A and B, respectively. The function h x) = 1 if its argument, x, lies in A, and vanishes otherwise. The characteristic function hg x) is similarly defined. In most cases, h x) and hg x) depend only on the configuration part r of state x, but situations may arise in whieh it is advantageous to introduce characteristic functions that depend on momenta as well. In practical applications, the stable regions A and B must be characterized carefully. We will return to this issue in Section ILF. 

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