Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a CubicQuintic GinzburgLandau Equation Using the Center Manifold Theorem
- Title
- Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a CubicQuintic GinzburgLandau Equation Using the Center Manifold Theorem
- Creator
- Siddheshwar P.G.; Sushma T.S.
- Description
- The differential geometric method of the center manifold theorem is applied to the magnetic-Lorenz model of ferrofluid convection in an electrically non-conducting ferrofluid. The analytically intractable tri-modal nonlinear autonomous system (magnetic-Lorenz model) is reduced to an analytically tractable uni-modal cubicquintic GinzburgLandau equation. The inadequacy of the cubic GinzburgLandau equation and the need for the cubicquintic one is shown in the paper. The heat transport is quantified using the solution of the cubicquintic equation and the effect of ferrofluid parameters on it is demonstrated. The stable and unstable regions in the conductive regime and the conductive-convective regime is depicted using a bifurcation diagram. The noticeable discrepancy between the results of the two models is highlighted and the quintic non-linearity effects are delineated. 2021, Foundation for Scientific Research and Technological Innovation.
- Source
- Differential Equations and Dynamical Systems, Vol-32, No. 1, pp. 151-169.
- Date
- 2024-01-01
- Publisher
- Springer
- Subject
- Center manifold; Electroconvection; Ferrofluid convection; GinzburgLandau; GlukhovskyDolzhansky system; Lorenz model; Quintic
- Coverage
- Siddheshwar P.G., Department of Mathematics, CHRIST (Deemed to be University), Hosur Road Campus, Bengaluru, 560029, India; Sushma T.S., Department of Mathematics, B.N.M. Institute of Technology, Bengaluru, 560070, India, Department of Mathematics (VTU RC), CMR Institute of Technology, Bengaluru, India
- Rights
- Restricted Access
- Relation
- ISSN: 9713514
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Siddheshwar P.G.; Sushma T.S., “Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a CubicQuintic GinzburgLandau Equation Using the Center Manifold Theorem,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 24, 2025, https://archives.christuniversity.in/items/show/13833.