We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solution...We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.展开更多
Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in wh...Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in which backgrounds are themselves moving, such as rippling water and swaying trees. In this paper, a novel background modeling method is proposed for dynamic scenes by combining both tensor representation and swarm intelligence. We maintain several video patches, which are naturally represented as higher order tensors,to represent the patterns of background, and utilize tensor low-rank approximation to capture the dynamic nature. Furthermore, we introduce an ant colony algorithm to improve the performance. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and moving objects can be perfectly separated from the complex dynamic background.展开更多
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11071086,11371152,11401439 and 11128102)+3 种基金the Natural Science Foundation of Guangdong Province(Grant No.S2012010010408)the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No.2014KQNCX162)the University Special Research Foundation for Ph.D Program(Grant No.20104407110002)the Science Foundation for Young Teachers of Wuyi University(Grant No.2014zk06)
文摘We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301137 and 11371036)the National Science Foundation of Hebei Province of China (Grant No. A2014205100
文摘Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in which backgrounds are themselves moving, such as rippling water and swaying trees. In this paper, a novel background modeling method is proposed for dynamic scenes by combining both tensor representation and swarm intelligence. We maintain several video patches, which are naturally represented as higher order tensors,to represent the patterns of background, and utilize tensor low-rank approximation to capture the dynamic nature. Furthermore, we introduce an ant colony algorithm to improve the performance. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and moving objects can be perfectly separated from the complex dynamic background.
