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
Let {Si}li=1 be an iterated function system （IFS） on Rd with attractor K. Let π be the canonical projection. In this paper, we define a new concept called ＂projection pressure＂ Pπ（φ） for φ ∈（Rd） under cer...Let {Si}li=1 be an iterated function system （IFS） on Rd with attractor K. Let π be the canonical projection. In this paper, we define a new concept called ＂projection pressure＂ Pπ（φ） for φ ∈（Rd） under certain arlene IFS, and show the variational principle about the projection pressure. Furthermore, we check that the unique zero root of ＂projection pressure＂ still satisfies Bowen＇s equation when each Si is the similar map with the same compression ratio. Using the root of Bowen＇s equation, we can get the Hausdorff dimension of the attractor K.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 National Natural Science Foundation of China (Grant No.10971100)National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
文摘Let {Si}li=1 be an iterated function system （IFS） on Rd with attractor K. Let π be the canonical projection. In this paper, we define a new concept called ＂projection pressure＂ Pπ（φ） for φ ∈（Rd） under certain arlene IFS, and show the variational principle about the projection pressure. Furthermore, we check that the unique zero root of ＂projection pressure＂ still satisfies Bowen＇s equation when each Si is the similar map with the same compression ratio. Using the root of Bowen＇s equation, we can get the Hausdorff dimension of the attractor K.
