The homotopy analysis method (HAM), as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differentia...The homotopy analysis method (HAM), as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation (BE) describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.展开更多
The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In th...The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.展开更多
基金Supported by the National Basic Research Program of China (Grant No. 2007CB714101)Research Fund of the State Key Laboratory for Hydroscience and Engineering in Tsinghua University (Grant No. 2008-ZY-6)
文摘The homotopy analysis method (HAM), as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation (BE) describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002077 and 11072215)
文摘The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.
