SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Pattern Formation, Delay and Nonlinear Stochastic Systems

DY 4.3: Vortrag

Montag, 27. März 2023, 10:00–10:15, ZEU 250

A missing amplitude equation — •Tobias Frohoff-Hülsmann1 and Uwe Thiele1,21Institute of Theoretical Physics, WWU Münster — 2Center for Nonlinear Science (CeNoS), WWU Münster

Amplitude (or envelope) equations describe the spatiotemporal dynamics of the essential linear mode(s) in the vicinity of a stability threshold and represent universal equations for spatially extended systems [3]. They are determined by the type of linear instability, the symmetries and whether or not conservation laws are present [5, 6]. For systems without conservation laws these equations are well studied, e.g. the complex Ginzburg-Landau equation [1]. However, the presence of conservation laws is highly relevant for a wide spectrum of pattern forming systems, e.g. for certain reaction diffusion (RD) systems [2, 4]. Here, we review the basic types of linear instabilities in the presence of conservation laws and show that there are relevant cases for which the amplitude equation is still unknown. We focus on such a missing case and derive an amplitude equation relevant for practically important RD systems.

[1] I. S. Aranson and L. Kramer. Rev. Mod. Phys., 74:99-143, 2002.

[2] C. Beta, N. S. Gov, and A. Yochelis. Cells, 9:1533, 2020.

[3] M. C. Cross and P. C. Hohenberg. Rev. Mod. Phys., 65:851-1112, 1993.

[4] J. Halatek and E. Frey. Nature Phys., 14:507-514, 2018.

[5] P. C. Matthews and S. M. Cox. Nonlinearity, 13:1293-1320, 2000.

[6] F. Bergmann, L. Rapp, and W. Zimmermann. Phys. Rev. E, 98:020603, 2018.

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