With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is ...With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter （OWSC） could withstand the force of an incoming tsunami. Several tools are used to provide an answer： an analytical 3D model developed within the framework of linear theory, a numerical model based on the non-linear shallow water equations and empirical formulas. Numerical results show that run-up and draw-down can be amplified under some circumstances, leading to an OWSC lying on dry ground t展开更多
We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear sec...We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter.The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations.A non-oscillatory finite volume method for the relaxation system is developed.The method is uniformly accurate for all relaxation rates.Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation.Our method demonstrated the capability of accurately capturing soliton wave phenomena.展开更多
Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have ...Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.展开更多
The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost su...The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.展开更多
基金support provided by the Science Foundation Ireland(SFI)under the project High-end computational modeling for wave energy systemsthe Framework Program for Research,Technological Development,and Innovation of the Cyprus Research Promotion Foundation under the Project AΣTI/0308(BE)/05+1 种基金the Irish Research Council for Science Engineering and Technology(IRCSET)Aquamarine Power and by the European Union’s Seventh Framework Programme for research,technological development and demonstration under the grant agreement ASTARTE No.603839
文摘With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter （OWSC） could withstand the force of an incoming tsunami. Several tools are used to provide an answer： an analytical 3D model developed within the framework of linear theory, a numerical model based on the non-linear shallow water equations and empirical formulas. Numerical results show that run-up and draw-down can be amplified under some circumstances, leading to an OWSC lying on dry ground t
文摘We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter.The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations.A non-oscillatory finite volume method for the relaxation system is developed.The method is uniformly accurate for all relaxation rates.Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation.Our method demonstrated the capability of accurately capturing soliton wave phenomena.
基金supported by a grant from the Simons Foundation(Grant No.601950 YM)
文摘Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.
基金supported by National Natural Science Foundation of China (Grant No.11971192)。
文摘The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.
