{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"edd1af6621f1e83e16e7fc296b8b08ca4e5ed6936073a940dc43c3ea1d4f6e1a","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"7b808b74cf67d236ce99c8f323ee215e8d6988b065fb82b06d6a00498a1b5e17","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"bio.active-matter.bubbly-phase-separation","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In ordinary phase separation small droplets dissolve and big ones grow until one large region of each phase remains. In active systems small gas bubbles inside the dense phase persist, and a theory that predicts their largest size and when they take over from bulk coexistence is missing.","posed_since":"","precise":"Active model $B+$ predicts reverse Ostwald ripening, which can arrest coarsening and produce a steady population of gas bubbles inside the dense phase; large $2\\mathrm{D}$ simulations of active Brownian particles (ABPs) show bubbles with a power-law size distribution up to a cutoff and, at large system size $L$ or density, microphase separation. Derive the active model $B+$ coefficients $(\\lambda,\\zeta)$ from ABP parameters and predict the bubble cutoff scale and the size or density threshold for microphase separation in $d=2\\ \\text{and}\\ 3$.","problem_ref":null,"references":"","settled_by":"A derivation of the active model $B+$ coefficients from particle parameters whose predicted bubble cutoff and microphase threshold match particle simulations over a wide range of $L$ in $d = 2\\ \\text{and}\\ 3$.","status_note":"Large 2D ABP simulations (Shi et al., PRL 2020, https://doi.org/10.1103/PhysRevLett.125.168001) found algebraically distributed bubbles and, at large L or density, microphase separation with a finite bubble cutoff; a quantitative derivation of active model B+ coefficients from particle parameters, and the 3D case, remain open (2026).","title":"Predicting the bubble cutoff and microphase threshold in active phase 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