Abstract

After briefly reviewing the recent effort of physicists and mathematicians alike to break Newton'sthird law to make systems active [1], we introduce particular continuum models featuring suchnonreciprocal interactions that destroy the gradient dynamics structure of well-known models.First, a thin-fi lm model for partially wetting drops on solid substrates is made active byincorporating a nonreciprocal coupling to a polarisation fi eld in the form of self-propulsion andactive stress [2]. We show that the employed polarisation-surface coupling results in (hysteretic)transitions between resting and moving drops, the splitting of drops, and chiral motion. Second, weintroduce a nonrecipocal Cahn-Hilliard model [3,4], show that all its linear stability thresholds maybe mapped onto the ones of a Turing reaction-diffusion system [4], and indicate how thenonreciprocal interactions arrest and stop coarsening, and give rise to localised and/or oscillatorystates [4]. Finally, we argue that the nonrecipocal Cahn-Hilliard model indeed is of universalimportance as it corresponds to the last missing amplitude equation out of eight that should existif considering a classifi cation of linear instabilities of uniform constant states based on threefeatures: small- vs large-scale, stationary vs. oscillatory, and with vs. without conservation law [5].The talk ends with a brief outlook.

References

[1] Y. X. Chen and T. Kolokolnikov, J. R. Soc. Interface 11, 20131208 (2014); A. V. Ivlev, J. Bartnick,M. Heinen, C. R. Du, V. Nosenko, and H. Löwen, Phys. Rev. X 5, 011035 (2015); M. Fruchart, R.Hanai, P. B. Littlewood, and V. Vitelli, Nature 592, 363 (2021); M. J. Bowick, N. Fakhri, M. C.Marchetti, and S. Ramaswamy, Phys. Rev. X 12, 010501 (2022).

[2] S. Trinschek, F. Stegemerten, K. John, and U. Thiele, Phys. Rev. E 101, 062802 (2020); F. Stegemerten, K. John, and U. Thiele, Soft Matter 18, 5823 (2022).

[3] Z. H. You, A. Baskaran, and M. C. Marchetti, Proc. Natl. Acad. Sci. U. S. A. 117, 19767 (2020); S.Saha, J. Agudo-Canalejo, and R. Golestanian, Phys. Rev. X 10, 041009 (2020);

[4] T. Frohoff-Hülsmann, J. Wrembel, and U. Thiele, Phys. Rev. E 103, 042602 (2021); T. Frohoff-Hülsmann and U. Thiele, IMA J. Appl. Math. 86, 924 (2021); T. Frohoff-Hülsmann, U. Thiele, and L.M. Pismen, Philos. Trans. R. Soc. A, to appear, http://arxiv.org/abs/2211.08320 (2023).

[5] T. Frohoff-Hülsmann and U. Thiele, http://arxiv.org/abs/2301.05568 (2022).

Please contact phweb@ust.hk should you have questions about the talk.