Qualitative analysis and analytical solution for higher dimensional gas-filled hyper-spherical bubbles in an ideal fluid

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-23 DOI:10.1016/j.aml.2024.109392

Yupeng Qin , Zhen Wang , Li Zou

{"title":"Qualitative analysis and analytical solution for higher dimensional gas-filled hyper-spherical bubbles in an ideal fluid","authors":"Yupeng Qin , Zhen Wang , Li Zou","doi":"10.1016/j.aml.2024.109392","DOIUrl":null,"url":null,"abstract":"<div><div>The present work concerns with the higher dimensional Rayleigh–Plesset equation for describing the nonlinear dynamics of gas-filled hyper-spherical bubbles in an ideal fluid. A strict qualitative analysis is made by means of the bifurcation theory of dynamic system, indicating that the bubble oscillation type is periodic. An analytical approach based on elliptic function is suggested to construct parametric analytical solution with arbitrary space dimension <span><math><mi>N</mi></math></span>, polytropic exponent <span><math><mi>κ</mi></math></span> and surface tension <span><math><mi>σ</mi></math></span> to the normalized higher dimensional Rayleigh–Plesset equation. The new obtained analytical solution extends the known ones for arbitrary (or some special cases of) <span><math><mi>N</mi></math></span> and <span><math><mi>κ</mi></math></span> without considering the effect of surface tension. In addition, we also discuss the dynamic characteristics for the oscillating hyper-spherical bubbles.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109392"},"PeriodicalIF":2.9000,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924004129","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

The present work concerns with the higher dimensional Rayleigh–Plesset equation for describing the nonlinear dynamics of gas-filled hyper-spherical bubbles in an ideal fluid. A strict qualitative analysis is made by means of the bifurcation theory of dynamic system, indicating that the bubble oscillation type is periodic. An analytical approach based on elliptic function is suggested to construct parametric analytical solution with arbitrary space dimension

N

, polytropic exponent

κ

and surface tension

σ

to the normalized higher dimensional Rayleigh–Plesset equation. The new obtained analytical solution extends the known ones for arbitrary (or some special cases of)

N

and

κ

without considering the effect of surface tension. In addition, we also discuss the dynamic characteristics for the oscillating hyper-spherical bubbles.

查看原文本刊更多论文

理想流体中高维气体填充超球形气泡的定性分析和解析解

本研究涉及描述理想流体中充满气体的超球形气泡非线性动力学的高维瑞利-普莱塞特方程。通过动态系统的分岔理论进行了严格的定性分析，表明气泡的振荡类型是周期性的。提出了一种基于椭圆函数的分析方法，为归一化高维瑞利-普莱塞特方程构建了具有任意空间维数 N、多向指数 κ 和表面张力 σ 的参数分析解。在不考虑表面张力影响的情况下，新得到的解析解扩展了已知的任意（或某些特殊情况）N 和 κ 的解析解。此外，我们还讨论了振荡超球形气泡的动态特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.