{"title":"带有分岔的交通流模型的微观推导","authors":"P. Cardaliaguet, N. Forcadel","doi":"10.1007/s00205-023-01948-8","DOIUrl":null,"url":null,"abstract":"<div><p>The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random parameters are used as a statistical description of the road taken by a vehicle and its law of motion. The limit model is a deterministic and scalar Hamilton–Jacobi on a network with a flux limiter, the flux-limiter describing how much the bifurcation or the local perturbation slows down the vehicles. The proof of the existence of this flux limiter—the first one in the context of stochastic homogenization—relies on a concentration inequality and on a delicate derivation of a superadditive inequality.\n</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"248 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Microscopic Derivation of a Traffic Flow Model with a Bifurcation\",\"authors\":\"P. Cardaliaguet, N. Forcadel\",\"doi\":\"10.1007/s00205-023-01948-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random parameters are used as a statistical description of the road taken by a vehicle and its law of motion. The limit model is a deterministic and scalar Hamilton–Jacobi on a network with a flux limiter, the flux-limiter describing how much the bifurcation or the local perturbation slows down the vehicles. The proof of the existence of this flux limiter—the first one in the context of stochastic homogenization—relies on a concentration inequality and on a delicate derivation of a superadditive inequality.\\n</p></div>\",\"PeriodicalId\":55484,\"journal\":{\"name\":\"Archive for Rational Mechanics and Analysis\",\"volume\":\"248 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Rational Mechanics and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00205-023-01948-8\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-023-01948-8","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Microscopic Derivation of a Traffic Flow Model with a Bifurcation
The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random parameters are used as a statistical description of the road taken by a vehicle and its law of motion. The limit model is a deterministic and scalar Hamilton–Jacobi on a network with a flux limiter, the flux-limiter describing how much the bifurcation or the local perturbation slows down the vehicles. The proof of the existence of this flux limiter—the first one in the context of stochastic homogenization—relies on a concentration inequality and on a delicate derivation of a superadditive inequality.
期刊介绍:
The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.