Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909752394514432 |
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| author | Frohoff-Hülsmann, Tobias Thiele, Uwe |
| author_facet | Frohoff-Hülsmann, Tobias Thiele, Uwe |
| contents | Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs.\ small-scale instability, stationary vs.\ oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05568 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation Frohoff-Hülsmann, Tobias Thiele, Uwe Pattern Formation and Solitons Soft Condensed Matter Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs.\ small-scale instability, stationary vs.\ oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation. |
| title | Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation |
| topic | Pattern Formation and Solitons Soft Condensed Matter |
| url | https://arxiv.org/abs/2301.05568 |