Classical Statistical Mechanics with Nested Sampling by Robert John Nicholas Baldock

Author:Robert John Nicholas Baldock
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Algorithm 8.4 Lattice stretch MC step. This algorithm samples the surface according to the enthalpy and cell height bounded uniform pdf (8.13). is a random number uniform in [0,1].

8.6 Initialising Nested Sampling at Fixed Pressure

The configuration space for particles in a simulation cell of variable volume, where the volume is allowed to vary without limit, is not a compact space. To generate the initial live samples for nested sampling we require a compact configuration space, and therefore we must impose a maximum allowed volume on our simulation cell. A sensible way to do this is to place the boundary well inside the region corresponding to the ideal gas. Having chosen a contour well inside the ideal gas, we can safely neglect the contribution made to statistical quantities by the excluded ideal gas configurations, provided . This is described in Sect. 8.7.

From the very start of a nested sampling calculation we require samples distributed as (8.13) with , and with the added constraint . The volume bound is chosen to be so large that it is, effectively, independent of the system, comfortably within the ideal gas phase. An example value is Å3. The time for this part of the calculation scales as where corresponds to the highest volume at which the gas undergoes a phase transition. The fractional coordinates should be initialised as univariate random numbers in the interval . Lattice matrices are generated by applying Algorithms 8.3 and 8.4 in a random sequence, starting from a cube. Step lengths of 1 can be used for both these algorithms at this point. Initial volumes may be generated by repeat application of Algorithm 8.2, starting from any allowed volume. It has been found that a good choice of starting volume is the mean of the distribution : . A good choice of step length for volume initialisation has been found to be .

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.