vmmc | Monte Carlo algorithm

vmmc is a C++ library typically used in Simulation applications. vmmc has no bugs, it has no vulnerabilities, it has a Strong Copyleft License and it has low support. You can download it from GitHub.

A simple C++ library to implement the "virtual-move" Monte Carlo (VMMC) algorithm of Steve Whitelam and Phill Geissler, see:. We introduce a “virtual-move” Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific (“patchy”) attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a “virtual” trial move. We determine which of its neighbours move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. Our primary goal is to make VMMC accessible to a wider audience, for whom the time required to code the algorithm poses a significant barrier to using the method. This allows the user to focus on model development. The animation below shows a comparison of the dynamics generated by traditional single-particle Monte Carlo (SPMC) and the VMMC algorithm for a periodic two-dimensional square-well fluid. The model system consists of particles interacting via strong, short-ranged isotropic interactions. Due to the suppression of collective particle rearrangements, SPMC results in the slow Ostwald ripening of isolated clusters. In contrast, VMMC facilitates the diffusion and coalescence of particle clusters, resulting in a long-time dynamics that is dominated by the motion of a single large cluster. Both trajectories represent one billion trial moves of the respective algorithms, with the system initialised with a random, non-overlapping, particle configuration in each case. The VMMC algorithm works by proposing the move of a single, randomly chosen, "seed" particle. If, following the move, the change in the energy of interaction between the particle and its neighbours is unfavourable, then those neighbours are recruited and moved in concert. This process is iterated recursively for each new recruit until no further particles show a tendency to move. The animations below illustrate example VMMC translation and rotation moves taken from a real simulation. Red indicates the most recent recruit to the cluster, orange indicates the nearest neighbour to which link formation is currently being tested, and green indicates those particles that have been accepted as part of the cluster move. The animations show how a recursive depth-first search is used to iteratively link particles to the cluster. Particles are linked according to probabilities based on the pair interaction energy differences following the forward and reverse virtual move of each recruit. Computation of the reverse move is required to enforce superdetailed balance, thus ensuring that the probability of a given particle pushing or pulling on the cluster is the same.