dr. Szymon Starzonek

Active Glasses: Investigating Large-Scale Dynamics and Phase Transitions in Models of Confluent Soft Matter

A central challenge of modern condensed-matter physics is to describe materials that live far from equilibrium. Classical thermodynamics explains phase transitions in passive systems — crystallization, the glass transition — but once the constituents become active, drawing energy from their surroundings to move on their own, the rules governing structure and dynamics change fundamentally.

This project develops a physical theory of active glasses in the confluent regime: active matter that completely fills space, leaving no gaps between its elements. This space-filling topology characterizes foams, dense emulsions, and — most strikingly — epithelial tissues. Here the transition between a solid-like (jammed) and a fluid-like state is governed not by density, but by the shape of the elements and their motor activity. Is this a classical thermodynamic transition, or a new kind of critical phenomenon set by the topology of the cellular network?

To answer this, the project brings together liquid-crystal physics and the statistical mechanics of disordered systems. Cell deformation is captured by Minkowski tensors from integral geometry, which allow a tensorial (Q-tensor) order parameter to be defined for irregular, deformable cells. Large-scale GPU simulations of the Active Vertex Model — reaching systems of order one million cells — enable finite-size scaling and the precise determination of critical exponents.

Its central hypothesis is that stress relaxation in active glasses is governed by topological defects: ±1/2 disclinations that act as local centers of mechanical stress, with fluidization proceeding through defect-pair unbinding — an active counterpart of Kosterlitz–Thouless–Halperin–Nelson–Young melting, driven by activity rather than heat.

Beyond basic physics, the resulting framework aims to provide rigorous tools for the mechanics of living tissues, treating them as materials with programmable viscoelastic properties — with implications for biomimetic smart materials and the biophysics of development.

Grant no. 2025/59/D/ST3/03546