{"title":"Johnson-Segalman导数中所有参数值的圆柱对称驻点问题Maxwell方程的通解","authors":"C. Chittam, S.V. Meleshko","doi":"10.1016/j.cnsns.2024.108527","DOIUrl":null,"url":null,"abstract":"<div><div>This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter <span><math><mi>α</mi></math></span>. The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"142 ","pages":"Article 108527"},"PeriodicalIF":3.4000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative\",\"authors\":\"C. Chittam, S.V. Meleshko\",\"doi\":\"10.1016/j.cnsns.2024.108527\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter <span><math><mi>α</mi></math></span>. The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.</div></div>\",\"PeriodicalId\":50658,\"journal\":{\"name\":\"Communications in Nonlinear Science and Numerical Simulation\",\"volume\":\"142 \",\"pages\":\"Article 108527\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Nonlinear Science and Numerical Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007570424007123\",\"RegionNum\":2,\"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":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424007123","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative
This paper explores two-dimensional flows near a free critical point in an incompressible viscoelastic Maxwell medium, governed by a rheological constitutive law. While stagnation point flow problems have been widely studied, general exact analytical solutions for stresses in cylindrical coordinates - more practical and suitable for certain experiments—remain undiscovered. In this study, we derive the general solution for the Maxwell model with the Johnson-Segalman convected derivative in cylindrical coordinates for an arbitrary model parameter . The analysis reveals the necessity of separately considering the upper-convected, lower-convected, and Jaumann derivatives when solving the stagnation point flow problem.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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