Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Pattern Formation
DY 22.4: Vortrag
Dienstag, 10. März 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 +