{"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 separation","topic_ref":"6a008dc19304a289e116a6d6e6371cc6de0ef3d1a904e572d5454f039b2ac217"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"23e3c67b6362926e0d406b608a68f30537caececca686a00b04d0dee1637f418","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"b4efaa5c5e4059a22bdaa1a7fc62eaf228fcc6860307594f478ae547924dddb9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sj5SrnVYxvf8jtn7ruNdyWdLn7ZQ3o5540XzLKExvQP7mZoFcNyowZ0tdfjzw00Laq-Ioqv37NzoY0L0BgeLAw"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEItO-qXF5AWaIr2qGn_GLq8ij8xoYDB1lPR4rlR5JN3bnwILTzBK8WBRSAT0PzrozqvGChuyHTTIGQHcFqjiQ1VgFoCPEgOiIXryMTtCXiD94VM8-BLR5vc5eR9UWI6LfOxKI-YAEI8CBJx2uqmAQquoUSuFJZ-nKp63F0nKv-DK_i4FhDsLSn3gjwIAL8h-Ee78B025AVUbOn3HFt_da7LmYC555hxDMxEsq5CPAgaaKnY4tLIKX7Amwj0BGCzNk0uQbtxP_VHg7Yx2h-l0UI8SBE9JBSeaxZ_ym70s6DMr6dtIgZGwis9uV00YisuztiwQjwICiraB_7UgXCeuS2UG4RwGVUB0TTDW9SPZX6Cm6ovyuOCPEg4rqGLBuUkm_3jUcKp88ZZh3m3UlQLzvNY7ka68qj80wI8SCDmR0G6GV1bT7GyRXBqEjvzcE3qRopJxP_SHiWmwBlpQjxIFf8EhaVa-ubjpYx3wEAcKGxkzfUQq6B-8jimpRd8IqnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIibo0xOJ0ScqJrw12osemqBBsltLmSS6vWdVzfwbDsgLwIIm-2bnLoT5TXnzig51jAjWKv3IEb-abHuiWe6UlSWT4CPAg-f0AhBoKal4MtdoknxP8sz372TGIROyIg88daPJqX-cI8SDej6t4apCChhl-PdhyuVHucBycm-X55W7RxRCYeRhleQjwIDEwI_zgUJ7ddxJIXbKU2DeboaEN0oFf2dGEhaVI-WdGCPEgjca0ZeQgOJcxY8BRnLB6wbZw3Ro6GxBmRUKFfEyxRMcI8CChAv4LOJnvOEtdil6BJ06e3eFXbz4Mb8k4PK_czyvjaQjxIBmAhLdCMSm2ddB2_krLA_5x8y1ELLq8OxJ5esJ22HqrCPEg6l9bg5rJBhgK-4vMedKGYUZmbiRuOWgDBBHADwTF2sYI8CBxK_WraVEkFPQAC7yAevXyyf-CupxAva0AtHIOkj6nkwjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"]},"log":{"leaf_index":"721","tree_size":"2123","proof":["1e257aadf1a576d50dd53c24313c148e9d005a61f002b7e7a8cdca5e0f648531","28038f37d8a8705ac32d97ba12ffd06eeca231be76cd0e63f8c4b3d8d678cbed","1ea5f881ff7addcad780f5cc86785953163e1f390223b1dc246a680ed4b01640","da786098ece189405292305d7fc05f70b71e2b9cc1e46213f5c5182cd73d8be2","fa391078908c8893c717e570f197bae58284e749861b49658ebb9ac19b00b15a","bc697c85aef569beb137d21149857109f6b78ca56a9d7bd58b1a54a27f69de09","9ceb7141714e1a5cff68eddb8ff80f1132e12a14a4af60003b260e34e05ac85f","d97790880ce7eee58b6c6e03ccf30015dc44f92dce8c62e40fecdc66aed452a4","9f0db5cb2ee9169ea5d56ed30f68fa386251991cc487135832bf8c105dc92c96","14108339881e6713df1e6d34582069c609e80460dc60638e661361aa4403ff51","ec3fa24572dee1df200ec665f3e3244d925b199f0f84e225b820c3b66bd7b094","addcf2e0ff7974e4aa99af5e30d409f90d9f4311a4d85f5baf3e125eeb45b4c1"],"checkpoint":"pubphys.com/log/v1\n2123\npXVcluz7BF4vgChQs6lShuU0386gCH0RxrC1sxyE3rI=\n\n— pubphys.com/log/v1 JFPwIOLzsUD22XoTVyTfk/FMVj/u3f3DxZk4V/Ws10KVSS+8WQSwhunQ//EAhyS9Td5CyM0E++85GMezmKd8240j9Q8=\n","promise":null},"orcid_key_evidence":[],"attesting":null}