Bounce algorithm

In this section we describe the way we have implemented electronic move in the CEIMC method. In particular we present an original algorithm for RQMC, particularly suitable for CEIMC, called the bounce algorithm. 

We have found that a minimal modification of the reptation algorithm solves both of these problems. The idea is to chose randomly the growth direction at the beginning of the Markov chain, and reverse the direction upon rejection only, the bounce algorithm. 

J. Schneider, I. Morgenstern, and J. M. Singer. Bouncing towards the optimum Improving the results of monte carlo optimisation algorithms. Phys. Rev. E,... 

Constraints should have no impact on the value of the parameter estimates themselves nor should they affect the fitting process, unless the parameter is near a boundary. A parameter may bounce into an invalid parameter space causing the algorithm to either crash, in which case widening the bounds may be necessary, or to finish the optimization process and report the parameter estimate as a boundary value. In no instance when the final parameter estimates fall on a boundary should these be considered optimal values. 

As an example of a simation in which it is important to use an algorithm which conserves angular momentum, consider a drop of a highly viscous fluid inside a lower-viscosity fluid in circular Couette flow. In order to avoid the complications of phase-separating two-component fluids, the high viscosity fluid is confined to a radius r < Ri by an impenetrable boundary with reflecting boundary conditions (i.e., the momentum parallel to the boundary is conserved in collisions). No-slip boundary conditions between the inner and outer fluids are guaranteed because collision cells reach across the boundary. When a torque is applied to the outer circular wall (with no-slip, bounce-back boundary conditions) of radius R2 > Ri, a solid-body rotation of both fluids is expected. The results of simulations with both MPC-AT-a... 

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