Probability density function Monte Carlo simulation

Figure 6. Probability density function of PFDavg according to the configurations given in Table 8, obtained by Monte Carlo simulations, after smoothing.

Using a series of Monte-Carlo ealeulations, the elastic properties of the network are derived from the network ehain end-to-end distance distribution, and are assumed to arise solely as a result of allowed conformational changes in individual network chains. Figure 3.12 shows the calculation for the probability density functions p f) calculated from the simulated radial end-to-end distance distribution functions P f), where... 

The IRT model [1,2, 12, 15] is essentially a Monte Carlo algorithm which assumes the independence of reaction times (i.e. each reaction is independent of other such reactions and that the covariance of these reaction times is zero). Unlike the random flights simulation, the diffusive trajectories are not tracked but instead encounter times are generated by sampling from an appropriate probability density function conditioned on the initial separation of the pair. The first encounter takes place at the minimum of the key times generated min(h t2, fs...) and all subsequent reactions occur based on the minimum of surviving reaction times. Unlike random flights... 

Another important decision relates to the number of trials, iVtriais-Admittedly, there is no precise a-priori determination of the number of Monte Carlo moves necessary to sample the probability density. The answer is attained empirically, with test simulations. Properties must be monitored, such as the energy and the pair distribution function. When the average properties converge to stable values, the Monte Carlo simulation may be stopped. 

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