Dynamical patterns in nematic active matter on a sphere

Abstract

Using simulations of self-propelled agents with short-range repulsion and nematic alignment, we explore the dynamical phases of a dense active nematic confined to the surface of a sphere. We map the nonequilibrium phase diagram as a function of curvature, alignment strength, and activity. Our model reproduces several phases seen in recent experiments on active microtubule bundles confined the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a polar band wrapping around an equator, with large empty spherical caps corresponding to two +1 defects at the poles. Upon further increasing activity, the bands fold onto themselves, and the system eventually transitions to a turbulent state marked by the proliferation of pairs of topological defects. We highlight the key role of the nematic persistence length in controlling pattern formation in these confined systems with positive Gaussian curvature.

Dynamically generated patterns in dense suspensions of active filaments

“…Here we simply note that the extensile nematic system, such as in the experiments of Sancez et al [20], is driven by pair forcing of filaments opposite to each other [47]. Unidirectional forcing, as implemented here, has been shown by two of us to lead to a mix of polar and nematic properties [28], a result that we recover here. In experiments, filaments are surrounded by a fluid that mediates long-range hydrodynamic interactions.…”

“…In our simulations, defect motion is very slow and is driven by filaments sliding along their contour. It is straightforward to properly identify and track the defects, e.g., by using a version of the algorithm proposed by Zapotocky et al [28,62], as outlined in Appendix B. However, at the time scales accessible to our simulations, defects move over very short distances, insufficient to extract meaningful information about their dynamics.…”

Linearly forced fluid flow on a rotating sphere

“…Conceptually, our analysis supports the view that non-equilibrium approaches can provide analytical insights into the dynamics of planetary flows (Delplace et al 2017) and atmospheres (Marston 2011(Marston , 2012. Moreover, in view of the recent successful application of phenomenological GNS models to active fluids (Dunkel et al 2013;S lomka & Dunkel 2017b), the results of this study can also help advance the understanding of active matter propagation on curved surfaces (Sanchez et al 2012;Sknepnek & Henkes 2015;Zhang et al 2016;Henkes et al 2018;Nitschke et al 2019) and in rotating frames (Löwen 2019).…”

Extensile motor activity drives coherent motions in a model of interphase chromatin

“…3B, bottom row ), which coarsen with time as the chain continues to unfurl and which are separated by sparse disorganized regions. The dynamics near the boundary in this case bears resemblance to that of active 2D nematics on spherical surfaces [24][25][26], yet is fundamentally different due to the strong hydrodynamic and mechanical couplings that exist with the nucleus interior.…”