TrialAddMultiple

class TrialAddMultiple : public feasst::Trial

Attempt to add multiple particles. Typically requires the use of a reference index.

For a derivation of the acceptance criteria, see TrialComputeMove and TrialComputeAdd for reference. For adding multiple particles i, j, …, z:

Forward event [reverse event]	Probability, \(\pi_{on}\) [reverse probability, \(\pi_{no}\)]
Select insert trial [Select remove trial]	\(1/w\) \([1/w]\)
Place particle of type i [Delete particle type i]	\(1/V\) \(\left[1/(N_{i}+ \sum_{a=i}^{z}\delta_{ia})\right]\)
Place particle of type j [Delete particle type j]	\(1/V\) \(\left[1/(N_{j}+ \sum_{a=j}^{z}\delta_{ja})\right]\)
…	…
Place particle of type z [Delete particle type z]	\(1/V\) \(\left[1/(N_{z}+1)\right]\)
Accept [Accept]	\(min(1, \chi)\) \([min(1, 1/\chi)]\)

where \(\delta_{ab} = 1\) when the types of particles \(a\) and \(b\) are identical. Otherwise, \(\delta = 0\).

Application of local detailed balance yields the acceptance probability,

\(\chi = e^{-\beta\Delta U}\prod_{a=i}^z\frac{Ve^{\beta\mu_a}} {(N_a+\sum_{b=a}^{z}\delta_{ab})\Lambda^d}\)

This equation was derived from the perspective of the old state. If the new state is the perspective, \(N_a+\sum_{b=a}^{z}\delta_{ab} \rightarrow N_a-\sum_{b=i}^{a-1}\delta_{ab}\)

Arguments

• particle_type[i]: the i-th type of particle to add. The “[i]” is to be substituted for an integer 0, 1, 2, …

• TrialStage arguments.