Séminaire

Vendredi 8 Mars 2024 à 11h00.

Nonreciprocal interactions - drops of active liquids and arrested coarsening

''After briefly introducing the recent effort of physicists and mathematicians alike to break Newton's third law to make systems active [1], we discuss particular continuum models featuring nonreciprocal interactions that break the gradient dynamics structure of well-known models. First, a thin-film model for partially wetting drops on solid substrates is made active by incorporating a nonreciprocal coupling to a polarisation field in the form of self-propulsion and active stress [2]. We show that the employed polarisation-surface coupling results in (hysteretic) transitions between resting and moving dops, the splitting of drops, and chiral motion. Second, we introduce a nonreciprocal Cahn-Hilliard model [3,4], show that all its linear stability thresholds may be mapped onto the ones of a Turing-type reaction-diffusion system [4], and indicate how nonreciprocity arrests or suppresses coarsening, and gives rise to localised and/or oscillatory states [4]. Finally, we argue that the nonrecipocal Cahn-Hilliard model is of universal importance as it corresponds to an important amplitude equation, namely, for a conserved Hopf instability that itself plays an important role in a classification of linear instabilities based on three features: small- vs large-scale, stationary vs. oscillatory, and with vs. without conservation law [5]. The talk concludes with a brief outlook.

[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 381, 20220087 (2023).
[5] T. Frohoff-Hülsmann and U. Thiele, Phys. Rev. Lett. 131, 107201 (2023).

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