{
  "annotation_id": "c65b059c-32b9-4195-816b-11d4516f1784",
  "date_created": "2026-02-17T05:53:12.016000Z",
  "date_modified": "2026-02-17T05:53:12.016000Z",
  "file_hash": "0cbdcfb691529b720b9ef3a0ae8a8336fa77f9da0f50ee4789c5dd0754faf26f",
  "private": false,
  "record": {
    "abstract": "We derive and analyze the amplitude equation for the roll patterns in case of generalized Active Model B+ (AMB+) in the presence of chemical reactions. The generalized AMB+ differs from the original AMB+ introduced by Tjhung \\textit{et al.} [E. Tjhung \\textit{et al.}, Phys. Rev. X \\textbf{8}, 031080 (2018)] by the addition of a quadratic term, $g\\phi^2$, in the expression for the equilibrium part of the current. Also, the model includes a rotation-free active current of strength $\\lambda$ and a rotational current of strength $\\xi$. The inclusion of a chemical reaction with rate $\\Gamma$ removes the conservation constraint and introduces a preferred wavenumber that governs the pattern formation below a critical reaction rate $\\Gamma_c$. We argue for the analytical form of the amplitude equation based on symmetry considerations and explicitly derived it using multiscale analysis. By taking different limits of $g$, $\\lambda$, and $\\xi$, we recover amplitude equations for several well-known physical models as special cases and determine the nature transitions close to the onset of instability. We find that for $g = 0$, the transition is always supercritical, whereas for $g \\ne 0$, the transition between the supercritical and subcritical regimes depends sensitively on the model parameters. Further, we derive the condition for the \\textit{Eckhaus instability} from the stability analysis of the amplitude equation as well as from the phase diffusion equation, and find that it is independent of $g$.",
    "arxiv_id": "2601.07231",
    "authors": [
      "Sayantan Mondal",
      "Prasenjit Das"
    ],
    "categories": [
      "cond-mat.stat-mech",
      "cond-mat.soft"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Derivation and Analysis of Amplitude Equation for Generalized AMB+ in Presence of Chemical Reaction",
    "url": "https://arxiv.org/abs/2601.07231",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b8074b5b-56d9-41eb-8468-70626a8753ba",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}