Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Pattern Formation

DY 22.4: Talk

Tuesday, March 10, 2026, 10:15–10:30, ZEU/0118

The 3-Components Problem — •Davide Toffenetti¹, Beatrice Nettuno¹, Henrik Weyer², and Erwin Frey¹ — ¹Ludwig Maximilian University of Munich (LMU), Munich, Germany — ²KITP, UC Santa Barbara, USA

Our work develops a general framework that connects reaction-diffusion systems with active-matter theories. Earlier studies showed that two-component mass-conserving reaction-diffusion (2cMcRD) systems can be mapped onto Model-B-type dynamics [1], which leads to the coarsening of patterns. We extend this idea by introducing a minimal three-component mass-conserving reaction-diffusion (3cMcRD) model. Using adiabatic elimination, we derive an effective active description for the total-mass dynamics, reminiscent of the well-known AMB+ theory. We validate the mapping through extensive numerical simulations.

Only 3cMcRD systems and their associated effective active theory produce finite-wavelength patterns such as dots, stripes, and foam-like structures, in contrast to the coarsening dynamics of 2cMcRD models. Employing a local quasi-steady-state approximation, we further determine the thresholds separating distinct pattern-forming regimes. In particular, we analyze how fingering instability emerges from an initially flat interface, marking the transition to foam-like patterns.

Our approach naturally generalizes to systems with more than three components and and to more general active-matter theories.

[1] Weyer, Brauns & Frey (2023). Phys. Rev. E 108, 064202.

Keywords: pattern formation; active matter; foams; reaction diffusion; active model B +