TrialGibbsMorph
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class TrialGibbsMorph : public feasst::TrialFactoryNamed
Attempt to change the identity of two particles of different types in different configurations. This trial is only valid for rigid particles.
The limiting distribution in the Gibbs ensemble with changing number of particles is given by
\(\frac{\Pi_{n}}{\Pi_{o}} = V_1^{N_{ni1}-N_{oi1}} V_2^{N_{ni2}-N_{oi2}}e^{-\beta\Delta (U_1+U_2)}\)
See (https://doi.org/10.33011/livecoms.6.1.3289)
The transition probabilities are as follows.
Forward
\(\pi_{o \rightarrow n}\)
Choose particle of type i in domain 1
\(1/N_{i1}\)
Choose particle of type j in domain 2
\(1/N_{j2}\)
Exchange the types of the particles and rotate both of them
\(P_{\omega i2}\mathrm{d}\boldsymbol{\omega}\) \(P_{\omega j1}\mathrm{d}\boldsymbol{\omega}\)
Reverse
\(\pi_{n \rightarrow o}\)
Choose particle of type i in domain 2
\(1/(N_{i2}+1)\)
Choose particle of type j in domain 1
\(1/(N_{j1}+1)\)
Exchange the types of the particles and rotate both of them
\(P_{\omega i1}\mathrm{d}\boldsymbol{\omega}\) \(P_{\omega j2}\mathrm{d}\boldsymbol{\omega}\)
Application of local detailed balance yields the acceptance probability,
\(\chi = \frac{N_{i1} N_{j2}}{(N_{i2}+1)(N_{j1}+1)} \frac{P_{\omega i1}P_{\omega j2}}{P_{\omega i2}P_{\omega j1}} e^{-\beta (\Delta U_1 + \Delta U_2)}\)
Attempt TrialGibbsMorphOneWay with equal probability in either direction.
Arguments
configs: two comma-separated names of configurations to transfer between (default: “0,1”).
TrialSelectParticle arguments.
particle_type_morph: the name of the particle type to morph into (and vice versa), not equal to particle_type.