Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource The effect of boundary conditions on the onset of chaos in RayleighBard convection using energy-conserving Lorenz models Subject The topic of the resource Chaos; FourierGalerkin; Hopf bifurcation; Lorenz model; RayleighBard convection; StuartLandau equation Description An account of the resource The influence of 16 boundary conditions on linear and nonlinear stability analyses of RayleighBard system is reported. A StuartLandau amplitude equation for the RayleighBard system between stress-free, isothermal boundary conditions is derived and the procedure used in this derivation serves as guidance for constructing an appropriate FourierGalerkin expansion for the other 15 boundary conditions to derive a generalized Lorenz model. The influence of the boundary conditions comes within the coefficients of the generalized Lorenz model. It is shown that the obtained generalized Lorenz model is energy conserving and for certain boundary conditions it retains features of the classical Lorenz model. Further, the principle of exchange of stabilities is shown to be valid for the present problem and hence it is the steady-state, linearized version of the generalized Lorenz model which yields an analytical expression for the Rayleigh number. On minimizing this expression with respect to wave number the critical Rayleigh number at which the onset of regular convective motion occurs in the form of rolls is determined for all 16 boundary conditions. It is found that these values are in good agreement with those of previous investigations leading to the conclusion that the chosen minimal FourierGalerkin expansion is a valid one. Exhibition of chaotic motion in the generalized Lorenz system at the Hopf Rayleigh number is studied. The phase-space plots which indicate a clear-cut visualization of the transition from regular convective motion to chaotic motion in the generalized Lorenz system are presented. Further, existence of a developing region for chaos (mildly chaotic motion) and windows of periodicity are captured using the bifurcation diagrams. It is concluded from the phase-space plots and the bifurcation diagrams that the generalized Lorenz model for certain sets of boundary conditions retains all the features of the classical Lorenz model. Such a conclusion cannot be made by a linear stability analysis and the need thus for a nonlinear analysis is highlighted in the paper. 2020 Elsevier Inc. Creator An entity primarily responsible for making the resource Kanchana C.; Siddheshwar P.G.; Yi Z. Source A related resource from which the described resource is derived Applied Mathematical Modelling, Vol-88, pp. 349-366. Publisher An entity responsible for making the resource available Elsevier Inc. Date A point or period of time associated with an event in the lifecycle of the resource 2020-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1016/j.apm.2020.06.062" target="_blank" rel="noreferrer noopener">https://doi.org/10.1016/j.apm.2020.06.062</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087996083&amp;doi=10.1016%2Fj.apm.2020.06.062&amp;partnerID=40&amp;md5=7ad2dc8372e77f283da13d3926bc50f0" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087996083&amp;doi=10.1016%2fj.apm.2020.06.062&amp;partnerID=40&amp;md5=7ad2dc8372e77f283da13d3926bc50f0</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 0307904X; CODEN: AMMOD Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Kanchana C., Harbin Institute of Technology, Shenzhen, Nanshan District, Shenzhen, 518055, China; Siddheshwar P.G., CHRIST(Deemed to be University), Bengaluru, 560056, India; Yi Z., Harbin Institute of Technology, Shenzhen, Nanshan District, Shenzhen, 518055, China