{"title":"湍流中贝叶斯嗅觉搜索的最优轨迹:低信息限制及超越。","authors":"R A Heinonen, L Biferale, A Celani, M Vergassola","doi":"10.1103/physrevfluids.10.044601","DOIUrl":null,"url":null,"abstract":"<p><p>In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, randomized encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasi-optimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics [1-3]. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior \"casting\") followed by a return to the starting location. The zigzag motion generates characteristic <math> <mrow><msup><mi>t</mi> <mrow><mn>1</mn> <mo>/</mo> <mn>2</mn></mrow> </msup> </mrow> </math> scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential <math><mrow><mi>p</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> <mo>∼</mo> <mtext>exp</mtext> <mo>(</mo> <mo>-</mo> <mi>k</mi> <msqrt><mi>T</mi></msqrt> <mo>)</mo></mrow> </math> for some <math><mrow><mi>k</mi> <mo>></mo> <mn>0</mn></mrow> </math> , in agreement with Monte Carlo results. We also discuss what happens as the wind speed becomes smaller.</p>","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":"10 4","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12369886/pdf/","citationCount":"0","resultStr":"{\"title\":\"Optimal trajectories for Bayesian olfactory search in turbulent flows: The low information limit and beyond.\",\"authors\":\"R A Heinonen, L Biferale, A Celani, M Vergassola\",\"doi\":\"10.1103/physrevfluids.10.044601\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, randomized encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasi-optimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics [1-3]. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior \\\"casting\\\") followed by a return to the starting location. The zigzag motion generates characteristic <math> <mrow><msup><mi>t</mi> <mrow><mn>1</mn> <mo>/</mo> <mn>2</mn></mrow> </msup> </mrow> </math> scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential <math><mrow><mi>p</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> <mo>∼</mo> <mtext>exp</mtext> <mo>(</mo> <mo>-</mo> <mi>k</mi> <msqrt><mi>T</mi></msqrt> <mo>)</mo></mrow> </math> for some <math><mrow><mi>k</mi> <mo>></mo> <mn>0</mn></mrow> </math> , in agreement with Monte Carlo results. We also discuss what happens as the wind speed becomes smaller.</p>\",\"PeriodicalId\":20160,\"journal\":{\"name\":\"Physical Review Fluids\",\"volume\":\"10 4\",\"pages\":\"\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12369886/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review Fluids\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevfluids.10.044601\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/4/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review Fluids","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevfluids.10.044601","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/9 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
Optimal trajectories for Bayesian olfactory search in turbulent flows: The low information limit and beyond.
In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, randomized encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasi-optimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics [1-3]. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior "casting") followed by a return to the starting location. The zigzag motion generates characteristic scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential for some , in agreement with Monte Carlo results. We also discuss what happens as the wind speed becomes smaller.
期刊介绍:
Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.