Regensburg 2025 – scientific programme
Parts | Days | Selection | Search | Updates | Downloads | Help
DY: Fachverband Dynamik und Statistische Physik
DY 18: Pattern Formation
DY 18.1: Talk
Tuesday, March 18, 2025, 14:00–14:15, H47
Amplitude and envelope equation for the conserved-Hopf bifurcation — •Daniel Greve1 and Uwe Thiele1,2 — 1Institut für Theoretische Physik, Universität Münster, Münster, Germany — 2Center for Nonlinear Science (CeNoS), Münster, Germany
Nonreciprocal interactions and conservation laws both play an important role in out-of-equilibrium pattern formation processes, e.g., in biochemical systems.[1,2] The generic large-scale oscillatory instability in such systems -- the conserved-Hopf instability -- is a central organizing element for such processes.[3,4] After classifying this instability within an extension of the Cross-Hohenberg[5] scheme, we use weakly nonlinear multi-scale analysis to obtain aclosed form (but nonlocal) slow time evolution equation for the spatiotemporal dynamics of the amplitude of fast time oscillations for thee example of two-species nonreciprocal Cahn-Hilliard models. Analytical results then reveal a universal coarsening suppression in oscillatory phase separation. Finally, we demonstrate the agreement of the two levels of description in a comparison of numerical results for the reduced and full model.
[1] A. Dinelli, J. O'Byrne, A. Curatolo, Y. Zhao, P. Sollich, and J. Tailleur, Nat. Commun. 14, 7035 (2023). [2] F. Brauns and M. C. Marchetti, Phys. Rev. X 14, 021014 (2024). [3] A. Förtsch and W. Zimmermann, (2023), talk, DPG Spring Meeting, Dresden, and A. Förtsch, Ph.D. thesis, Bayreuth (2023). [4] T. Frohoff-Hülsmann and U. Thiele, Phys. Rev. Lett. 131, 107201 (2023). [5] M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
Keywords: nonreciprocal Cahn-Hilliard; conservation laws; envelope equation; travelling waves; Hopf bifurcation