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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:07:32 +0000Finite-size effects on linear stability of pure-fluid convection
https://resolver.caltech.edu/CaltechAUTHORS:CHEpra92
Authors: {'items': [{'id': 'Chen-Yih-Yuh', 'name': {'family': 'Chen', 'given': 'Yih-Yuh'}}]}
Year: 1992
DOI: 10.1103/PhysRevA.45.3727
The linear stability of pure-fluid Rayleigh-Benard convection in a finite cell of arbitrary geometry can be formulated as a self-adjoint eigenvalue problem. This, when coupled with perturbation theory, allows one to deduce how the sidewalls affect its stability. In particular, it is shown that for almost all boundary conditions the difference between the onset Rayleigh number and its infinite-cell limit scales like L^-2 as the cell dimension L tends to infinity, and near the sidewall the temperature and velocity are of order L^-1 compared to their bulk values. The validity of replacing the true thermal boundary condition by a frequently used mathematically simpler homogeneous one is also demonstrated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fvs62-z5m74Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection
https://resolver.caltech.edu/CaltechAUTHORS:CHEjfm92
Authors: {'items': [{'id': 'Chen-Yih-Yuh', 'name': {'family': 'Chen', 'given': 'Yih-Yuh'}}]}
Year: 1992
DOI: 10.1017/S0022112092002155
The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hg2gw-qqm40Pattern formation in finite size non-equilibrium systems and models of morphogenesis
https://resolver.caltech.edu/CaltechAUTHORS:CHEnonlin94
Authors: {'items': [{'id': 'Chen-Yih-Yuh', 'name': {'family': 'Chen', 'given': 'Yih-Yuh'}}, {'id': 'Cross-M-C', 'name': {'family': 'Cross', 'given': 'M. C.'}}]}
Year: 1994
DOI: 10.1088/0951-7715/7/4/001
Two canonical pattern forming systems, the Rayleigh-Benard convection and the Turing mechanism for biological pattern formation, are compared. The similarity and fundamental differences in the mathematical structure of the two systems are addressed, with special emphasis on how the linear onset of patterns is affected by the finite size and the boundary conditions. Our analysis is facilitated by continuously varying the boundary condition, from one that admits simple algebraic solution of the problem but is unrealistic to another which is physically realizable. Our investigation shows that the size dependence of the convection problem can be considered generic, in the sense that for the majority of boundary conditions the same trend is to be observed, while for the corresponding Turing mechanism one will rely crucially on the assumed boundary conditions to ensure that a particular sequence of patterns be picked up as the system grows in size. This suggests that, although different systems might exhibit similar pattern forming features, it is still possible to distinguish them by characteristics which are specific to the individual models.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s9afb-f6m66