Active anti-diffusion in the nonreciprocal Cahn-Hilliard model

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• Uwe Thiele (Universität Münster)
• Wednesday 29 May 2024, 11:00-12:00
• Seminar Room 1, Newton Institute.

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ADI - Anti-diffusive dynamics: from sub-cellular to astrophysical scales

The phenomenologically introduced nonreciprocal Cahn-Hilliard (NRCH) model couples densities with mass-conserving dynamics via a nonreciprocal interaction [1]. After discussing types of nonreciprocity and their relation to a ’spurious’ gradient dynamics form (allowing for a Maxwell construction) we show that the NRCH model features conserved-Turing and conserved-Hopf instabilities beside the usual Cahn-Hilliard instability—and discuss the related  nonlinear ‘monotonically and oscillatory antidiffusive clustering phenomena’. Then, we address the model’s role as a high-codimension amplitude equation (AE) placing it within a hierarchy of AE for the eight types of instabilities of uniform steady states in homogeneous isotropic systems resulting from the combination of three features: large- vs small-scale, stationary vs oscillatory, and with vs without conservation law(s) [2]. Further, a codimension-one AE for the conserved-Hopf instability is discussed [4] and compared to [3].   [1] ZH You, A Baskaran, MC Marchetti, PNAS 117 , 19767 (2020); S Saha, J Agudo-Canalejo, R Golestanian, PRX 10 , 041009 (2020); T Frohoff-Hülsmann, J Wrembel, U Thiele, PRE 103 , 042602 (2021)   [2] T Frohoff-Hülsmann, U Thiele, PRL 131 , 107201 (2023) T Frohoff-Hülsmann, U. Thiele, and L. M. Pismen, Philos. Trans. R. Soc. A 381 , 20220087 (2023) T Frohoff-Hülsmann and U Thiele, IMA J . Appl. Math. 86, 924–943 (2021) D Greve, G Lovato, T Frohoff-Hülsmann, and U Thiele   [3] A Nepomnyashchy, S Shklyaev, J Phys  A 49 , 053001 (2016); A F örtsch, W Zimmermann, DY 4 .4, DPG Spring Meeting 2023, Dresden; A F örtsch, Thesis Bayreuth 2023. [4] D Greve, U Thiele, in preparation, 2024.

This talk is part of the Isaac Newton Institute Seminar Series series.

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