The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct m...The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.展开更多
We derive a closed form expression for the regularized Stokeslet in two space dimensions with periodic boundary conditions in the x-direction and a solid plane wall at y=0.To accommodate the no-slip condition on the w...We derive a closed form expression for the regularized Stokeslet in two space dimensions with periodic boundary conditions in the x-direction and a solid plane wall at y=0.To accommodate the no-slip condition on the wall,a system of images for the regularized Stokeslets was used.The periodicity is enforced by writing all elements of the image system in terms of a Green’s function whose periodic extension is known.Although the formulation is derived in the context of regularized Stokeslets,the expression for the traditional(singular)Stokeslet is easily found by taking the limit as the regularization parameter approaches zero.The new formulation is validated by comparing results of two test problems:the Taylor infinite waving sheet and the motion of a cylinder moving near a wall.As an example of an application,we use our formulation to compute the motion and flow generated by cilia using a model that does not prescribe the motion so that the beat period and synchronization of neighboring cilia are a result of the forces developed along the cilia.展开更多
The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incid...The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incidence. The reflection characteristics of the anechoic layers with cavities and locally resonant scatterers are discussed. The backing is a steel plate followed by an air half space. Under this approximate zero transmission backing condition, the reflection reduction is induced by the absorption enhancement. The absorption mechanism is explained by the scattering/absorption cross section of the isolated scatterer. Three types of resonant modes which can induce efficient absorption are revealed. Due to the fact that the frequencies of the resonant modes are related to the size of the scatterers, anechoic layers with scatterers of mixed size can broaden the absorption band. A genetic optimization algorithm is adopted to design the anechoic layer with scatterers of mixed size at a desired frequency band from 2 kHz to l0 kHz for normal incidence, and the influence of the incident angle is also discussed.展开更多
文摘The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
基金Thework of the authorswas supported in part by theNational Science Foundation(NSF)Grant No.DMS-1043626.
文摘We derive a closed form expression for the regularized Stokeslet in two space dimensions with periodic boundary conditions in the x-direction and a solid plane wall at y=0.To accommodate the no-slip condition on the wall,a system of images for the regularized Stokeslets was used.The periodicity is enforced by writing all elements of the image system in terms of a Green’s function whose periodic extension is known.Although the formulation is derived in the context of regularized Stokeslets,the expression for the traditional(singular)Stokeslet is easily found by taking the limit as the regularization parameter approaches zero.The new formulation is validated by comparing results of two test problems:the Taylor infinite waving sheet and the motion of a cylinder moving near a wall.As an example of an application,we use our formulation to compute the motion and flow generated by cilia using a model that does not prescribe the motion so that the beat period and synchronization of neighboring cilia are a result of the forces developed along the cilia.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1100429 and 51275519)
文摘The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incidence. The reflection characteristics of the anechoic layers with cavities and locally resonant scatterers are discussed. The backing is a steel plate followed by an air half space. Under this approximate zero transmission backing condition, the reflection reduction is induced by the absorption enhancement. The absorption mechanism is explained by the scattering/absorption cross section of the isolated scatterer. Three types of resonant modes which can induce efficient absorption are revealed. Due to the fact that the frequencies of the resonant modes are related to the size of the scatterers, anechoic layers with scatterers of mixed size can broaden the absorption band. A genetic optimization algorithm is adopted to design the anechoic layer with scatterers of mixed size at a desired frequency band from 2 kHz to l0 kHz for normal incidence, and the influence of the incident angle is also discussed.
