{"title":"质量视角下从双极欧拉-泊松系统到单极欧拉-泊松系统","authors":"Shuai Xi, Liang Zhao","doi":"10.1007/s00021-023-00838-z","DOIUrl":null,"url":null,"abstract":"<div><p>The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting <span>\\(m_e/m_i\\rightarrow 0\\)</span> and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass\",\"authors\":\"Shuai Xi, Liang Zhao\",\"doi\":\"10.1007/s00021-023-00838-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting <span>\\\\(m_e/m_i\\\\rightarrow 0\\\\)</span> and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00021-023-00838-z\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-023-00838-z","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass
The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting \(m_e/m_i\rightarrow 0\) and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.