Order and shape dependence of mechanical relaxation in proliferating active matter

TL;DR

This work investigates how growth-driven division and mechanical interactions compete to shape orientational order in proliferating anisotropic particles, revealing that oblate growth can invert flow-alignment and disrupt microdomain formation seen with rod-like shapes. Using agent-based simulations of elliptical and rounded-rectangle particles in channel and disk geometries across varying division aspect ratios $a_d$, the study uncovers distinct relaxation pathways governed by shape: ellipses yield large-scale orientational correlations with efficient partial packing, while rods form persistent microdomains and exhibit pronounced stress anisotropies. A key mechanistic insight is the emergence of order-dependent packing fraction $φ(ξ)$ and order-dependent viscous relaxation, which together provide a compact coarse-grained description that connects particle-scale mechanics to mesoscale organization. These results offer a robust route to integrating particle-resolved dynamics with continuum theories for growing, anisotropic active matter and point to experimental tests by tuning cell shape and division orientation.

Abstract

Collective dynamics in proliferating anisotropic particle systems arise from an interplay between growth, division, and mechanical interactions, often mediated by particle shape. In classical models of prolate, rod-like growth, flow-induced alignment and division geometry reinforce one another, leading to robust nematic order under confinement. Here we introduce a complementary regime by considering smooth convex particles whose geometry can be oblate for part or all of their growth cycle, creating a tunable competition between these two alignment mechanisms. Using agent-based simulations of elliptical and rounded-rectangular particles in both channel and open-domain geometries, we systematically vary the division aspect ratio to span regimes of cooperation and competition between ordering cues. We find that oblate growth can reverse classical flow-alignment, destabilize microdomain formation in intermediate regimes, and open up new regimes with modified microdomain dynamics in free expansion and sustained orientation dynamics in channel geometry. These findings are explained by an order- and shape-dependent mechanical relaxation interpretation that is supported by explicit measurements. This sheds new light on the available relaxation pathways and therefore provides key ingredients for effective descriptions of collective anisotropic proliferation dynamics.

Figures (5)

• Figure 1: (A) Sketches of steric repulsion for elliptical and rod-shaped particles. (B), (C), (D), (E) Snapshots of particle simulations in channel geometry using either prolate or oblate particle shapes as indicated by the accompanying sketches. Particles are colored by their nematic orientation as indicated in the color wheel.
• Figure 2: (A) Central order parameter $Q_{yy}$ and (B) stresses $|\sigma_{xx}|$ and $|\sigma_{yy}|$ in channel geometry for both elliptical and (C) rod-shaped particles for varied division aspect $a_{\mathrm{d}}$. Errorbars indicate variation between different initial conditions.
• Figure 3: (A) Simulation snapshots for varied particle shapes as labelled. (B) Average instantaneous velocity deviation from the mean-field flow. (C) Average global instantaneous scalar order parameter $\xi=\sqrt{-\det Q}$. (D) Pairwise orientation statistics between touching particles. Data is split into different panels to aid readability. (E) Two-point orientation correlation for rods (top) and ellipses (bottom) as markers and approximations as a damped oscillation as solid lines. (F) Fit parameters of damped oscillator approximation.
• Figure 4: (A) Packing fraction as a function local order for varied division aspect $a_{\mathrm{d}}$ and particle model as labelled. (B) Histograms of observed order--packing pairs as heatmap over the division aspect ratio for elliptical particles. (C) Analogous to \ref{['pan:packing_heatmap_ellipse']} for rod-shaped particles.
• Figure 5: (A) Rod velocities as arrows in co-moving frame with additional visualization of velocities centered in single particle and with rescaled coordinates. (B) Analogous to \ref{['pan:local_vel_rodsketch']} for elliptical particles. (C) Local velocity variations co-aligned with nematic order and relative to co-moving frame for elliptical and rod-shaped particles as labelled. Averages over samples with lowest $10\%$ order (dashed) and highest $1\%$ order (solid). (D) Average of locally observed order (top $1\%$) (E) Ratio of velocity variations (top $1\%$) with ensemble aspect $a_{\mathrm{e}}$ added in black. (F) Viscous flux approximation according to \ref{['eq:viscflux']}.