This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and ext...This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.展开更多
In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlin...In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The P1D controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.展开更多
基金Supported by the National Natural Science Foundation of China(21206009)Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHR201107123)Program for Doctoral Fund in Beijing University of Civil Engineering and Architecture(101102307)
文摘This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072168 and 11102127)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100032120006)the Research Program of Application Foundation and Advanced Technology of Tianjin, China (Grant Nos. 12JCYBJC12500 and 11JCYBJC05800)
文摘In this paper, the Pad6 approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The P1D controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.
