Mean local density

Clutch size was set to depend on age at reproduction and mean local density encountered by the individual. Mean local density was calculated as the mean of all the within-grid cell densities encountered by the individual. The number of offspring could never exceed twice the default clutch size. 

A closer inspection of the distributions of local densities. Fig. 2, shows that at the most near critical bulk density, p == 0.30 cr J, the mean local density p ) =... 

While mean local density enhancements (LDE) increase the favorable free energy of solvation, over that expected in the absence of compression, i, e. for an... 

A possible, relatively ubiquitous source of error in the standard extraction analysis used above is the neglect of the very broad distributions of local densities which exist in the compressible regime (Fig. 2). Specifically, the extraction analysis assumes that the observable of interest, A, is a function of the mean local density, i.e. A((p )). However, the ensemble average of the observable, and thus the measured value, is really... 

In Fig. 2 it was observed that not only does the mean local density (p ) exceed the bulk density for compressible state points, but also that the distribution of local densities V pi) broadens significantly as one moves towards the critical region. The effect that such broad distributions can have on dynamic processes is more complex than the effect such distributions have on static properties, eq. 8, because in the dynamic case, the nature of the effect depends upon the time scale of the dynamic process of interest. For concreteness, we again consider the case of vibrational relaxation, such that, by eq. 2, eq. 8 becomes... 

Particularly important is the pair distribution function, g Vi,r2), or simply g(ri,r2). In a homogeneous system this is only a function of the interparticle distance vector r = r2 — ri. The quantity pg(r) can be interpreted as the mean local density of particles at position r relative to a particle that is taken as reference. The quantity (r) = g(r) — 1 is called the (total) pair correlation function. If the system is also spherically symmetric, as in the... 

Now p is r-dependent, rather than z-dependent as it was in (9.2), and the relevant solution is that whidi for large r is asymptotic to the mean density p of the homogeneous fluid udiik the uniform p, hne is ft( T). We have the mean local density p(r) related to the pair-correlation function h(r) by... 

In the mean-field treatment one approximates the square average (c ) by If we choose for the description of the mean local density (cm(r)) a Gaussian function, with a radius of gyration Rg and the maximum at the center of gravity rc... 

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