We investigate efficient numerical methods for nonlinear Hamiltonian systems. Three polynomial spectral methods (including spectral Galerkin, Petrov-Galerkin, and collocation methods). Our main results include the ene...
We investigate efficient numerical methods for nonlinear Hamiltonian systems. Three polynomial spectral methods (including spectral Galerkin, Petrov-Galerkin, and collocation methods). Our main results include the energy and symplectic structure preserving properties and error estimates. We prove that the spectral Petrov-Galerkin method preserves the energy exactly and both the spectral Gauss collocation and spectral Galerkin methods are energy conserving up to spectral accuracy. While it is well known that collocation at Gauss points preserves symplectic structure, we prove that the Petrov-Galerkin method preserves the symplectic structure up to a Gauss quadrature error and the spectral Galerkin method preserves the symplectic structure to spectral accuracy. Furthermore, we prove that all three methods converge exponentially (with respect to the polynomial degree) under sufficient regularity assumption. All these aforementioned properties make our methods possible to simulate the long time behavior of the Hamiltonian system. Numerical experiments indicate that our algorithms are efficient.
具有毛细阻滞效果的CCBE(covers with capillary barrier effects)防护系统,由细粒土和粗粒土构建而成,铺设在坡面上可以有效防止坡土的深度开裂。两层土体的孔隙结构差异在两层土的交界面处形成毛细阻滞效果,进而构建了一种简易的蓄排...
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具有毛细阻滞效果的CCBE(covers with capillary barrier effects)防护系统,由细粒土和粗粒土构建而成,铺设在坡面上可以有效防止坡土的深度开裂。两层土体的孔隙结构差异在两层土的交界面处形成毛细阻滞效果,进而构建了一种简易的蓄排水系统,有利于植物护坡。人们定义CCBE层中粗粒土内的输水距离来描述CCBE防护系统的蓄排水能力。影响坡面CCBE防护结构的蓄排水能力的因素有很多,主要探究气温及其变化对它的影响。数值计算结果发现,日均气温越高,对CCBE防护结构的蓄排水能力的影响就越大,输水距离也越大;日均温差对CCBE防护结构输水距离的影响较复杂,大概在4℃日均温差时,CCBE防护结构的输水距离达到最大。研究成果可以为防坡土防裂的CCBE防护系统的设计提供参考依据。
Hong Kong University of Science and Technology Grain boundaries are the interfaces of grains with different orientations in polycrystalline materials. Energetic and dynamic properties of grain boundaries play essentia...
Hong Kong University of Science and Technology Grain boundaries are the interfaces of grains with different orientations in polycrystalline materials. Energetic and dynamic properties of grain boundaries play essential roles in the mechanical and plastic behaviors of the materials. These properties of grain boundaries strongly depend on their microscopic structures. We present continuum models for the energy and dynamics of grain boundaries based on the continuum distribution of the line defects (dislocations or disconnections) on them. The long-range elastic interaction between the line defects is included in the continuum models to maintain stable microstructure on grain boundaries during the evolution. The continuum models is able to describe both normal motion and tangential translation of the grain boundaries due to both coupling and sliding effects that were observed in atomistic simulations and experiments.
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