Jerky active matter: a phase field crystal model with translational and orientational memory

Abstract

Most field theories for active matter neglect effects of memory and inertia. However, recent experiments have found inertial delay to be important for the motion of self-propelled particles. A major challenge in the theoretical description of these effects, which makes the application of standard methods very difficult, is the fact that orientable particles have both translational and orientational degrees of freedom which do not necessarily relax on the same time scale. In this work, we derive the general mathematical form of a field theory for soft matter systems with two different time scales. This allows to obtain a phase field crystal model for active particles with translational and orientational memory. Notably, this theory is of third order in temporal derivatives and can thus be seen as a spatiotemporal jerky dynamics. We obtain the phase diagram of this model, which shows that, unlike in the passive case, the linear stability of the liquid state depends on the damping coefficients. Moreover, we investigate sound waves in active matter. It is found that, in active fluids, there are two different mechanisms for sound propagation. For certain parameter values and sufficiently high frequencies, sound mediated by polarization waves experiences less damping than usual passive sound mediated by pressure waves of the same frequency. By combining the different modes, acoustic frequency filters based on active fluids could be realized.

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

“…Moreover, one could extend the derivation by incorporating also the nematic order parameter (as done in previous derivations for passive models [80][81][82][83]), particle inertia (as done for a singlespecies model in Refs. [87,88]), or by considering a mixture of two different active species. After the ≈ sign in Eq.…”

“…The active PFC model, an extension of the PFC model to active matter which was proposed and derived from DDFT in Refs. [26,84], has also been extended, allowing one to describe systems on curved surfaces [85], self-spinning particles [86], particles with inertia [87,88], particles with nonreciprocal interactions [89], and mixtures of active and passive particles [12,89] -an extension suggested already in the first article on active PFC models [26]. Further investigations of active PFC models can be found in Refs.…”

Active Brownian motion with memory delay induced by a viscoelastic medium

“…Moreover different combinations of friction and memory kernel as well as colored noise can be considered for future work [96][97][98][99][100], for instance, Mittag-Leffler noise [101,102] or power-law memory [103,104]. Finally the collective behavior of many interacting active particles in a viscoelastic medium [105][106][107][108][109][110][111] needs to be explored more and will be an important area of future research.…”

From a microscopic inertial active matter model to the Schrödinger equation

“…However, recent experiments [21][22][23] have found that the inertia of active particles is important in a variety of contexts. Moreover, theoretical and experimental studies have found a number of remarkable effects associated with inertial active matter [24], ranging from self-sustained temperature gradients [25] through restored equilibrium crystallization [26] to damping-dependent phase boundaries [27].…”

“…Field theories for inertial active matter have been derived in Refs. [27,33,34] as extensions of the active phase field crystal (PFC) model [35][36][37][38]. Active PFC models can be derived as an approximation of dynamical density functional theory (DDFT) [39], and have two disadvantages compared to AMB+.…”