Computer simulations of the statistical behaviour of active particles
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
We introduce a new model of activity to study the structural and dynamical properties of mixtures of active and passive particles with molecular dynamics simulations. The limit of no activity corresponds to the passive continuous Asakura-Oosawa model. This model, which has an entropy-driven phase separation, consists of two particle types: colloids and polymers. In this thesis the colloids are made self-propelled by introducing an active force, which acts in the direction of mean velocity of the surrounding colloids, similar to the well-known Vicsek model. The addition of activity is shown to facilitate phase separation. Different thermostats are applied to study their influence on the active non-equilibrium system. Using an integral equation theory approach, a mapping of the active onto a passive model is performed. The resulting potential is studied via molecular dynamics simulations and facilitates phase separation as well.
The active model exhibits a second order phase transition from a disordered phase to an ordered state in which most of the colloids align. We apply the subbox method to determine the critical point of the system from simulations in the canonical ensemble, using an order parameter that depends on fluctuations of the particle number. This approach is shown to work with an equilibrium model. Extensive simulations are performed to determine the critical point of the active model. This is done by assuming initially that the law of rectilinear diameter still applies in a non-equilibrium system. The first determination of the critical point is then improved iteratively. We show that the law of rectilinear diameter is not followed close to the critical point and provide a simulation approach to account for this. An explanation of how the activity could influence the position of the critical point is given by using an order parameter known from the Vicsek model.
With the knowledge of the critical point two critical exponents of the active system are calculated. From the phase diagram we determine the critical exponent of the magnetisation, which is in good agreement with the 3D Ising universality of the underlying passive system. However, the critical exponent of the correlation length differs somewhat from the corresponding exponent in the 3D Ising universality class.