By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is de...By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.展开更多
Using the standard truncated Painlev expansion, the residual symmetry of the(2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. S...Using the standard truncated Painlev expansion, the residual symmetry of the(2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived by utilizing the obtained symmetries. The symmetries of the system are also derived through the Clarkson-Kruskal direct method, and several types of explicit reduction solutions relate to the trigonometric or the hyperbolic functions are obtained. Finally, some special solitons are depicted from one of the solutions.展开更多
With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we invest...With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.展开更多
In this paper,we investigate a(2+1)-dimensional variable-coefficient modified dispersive waterwave system in fluid mechanics.We prove the Painlevéintegrability for that system via the Painlevéanalysis.We fin...In this paper,we investigate a(2+1)-dimensional variable-coefficient modified dispersive waterwave system in fluid mechanics.We prove the Painlevéintegrability for that system via the Painlevéanalysis.We find some auto-B?cklund transformations for that system via the truncated Painlevéexpansions.Bilinear forms and N-soliton solutions are constructed,where N is a positive integer.We discuss the inelastic interactions,elastic interactions and soliton resonances for the two solitons.We also graphically demonstrate that the velocities of the solitons are affected by the variable coefficient of that system.展开更多
By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system....By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.展开更多
Harvesting ambient mechanical energy is a key technology for realizing self-powered electronics. With advantages of stability and durabilid, a liquid-solid-based triboelectric nanogenerator （TENG） has recently drawn...Harvesting ambient mechanical energy is a key technology for realizing self-powered electronics. With advantages of stability and durabilid, a liquid-solid-based triboelectric nanogenerator （TENG） has recently drawn much attention. However, the impacts of liquid properties on the TENG performance and the related working principle are still unclear. We assembled herein a U-tube TENG based on the liquid-solid mode and applied 11 liquids to study the effects of liquid properties on the TENG output performance. The results confirmed that the key factors influencing the output are polarity, dielectric constant, and affinity to fluorinated ethylene propylene （FEP）. Among the 11 liquids, the pure water-based U-tube TENG exhibited the best output with an open-circuit voltage （Voc） of 81.7 V and a short-circuit current （Isc） of 0.26 μA for the shaking mode （0.5 Hz）, which can further increase to 93.0 V and 0.48 μA, respectively, for the horizontal shifting mode （1.25 Hz）. The U-tube TENG can be utilized as a self-powered concentration sensor （component concentration or metal ion concentration） for an aqueous solution with an accuracy higher than 92%. Finally, an upgraded sandwich-like water-FEP U-tube TENG was applied to harvest water-wave energy, showing a high output with Voc of 350 V, Isc of 1.75 μA, and power density of 2.04 W/m3. We successfully lighted up 60 LEDs and powered a temperature-humidity meter. Given its high output performance, the water-FEP U-tube TENG is a very promising approach for harvesting water-wave energy for self-powered electronics.展开更多
We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the ...We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the free surface, and the outer normal derivative ？P/？n of the pressure P satisfy sup t∈[0,T]｜｜κ（t）｜｜Lp∩L^2＋∫0^T｜｜（▽V, ▽B）（t）｜｜L∞^6dt〈＋∞,inf （t,x,y）∈[0,T]×Σ_t- P/ n（t, x, y）≥c0,for some p 〉 2d and c_0〉 0, then the solution can be extended after t = T.展开更多
An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete fo...An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.展开更多
研究旨在探究振荡水柱(oscillating water column,简称OWC)防波堤前墙的受力特性。通过物理模型试验,利用狭缝开口模拟冲击式空气透平,测量前墙两侧的波浪压强和振荡水柱气室内气体压强,从而在计算前墙水平波致总力时计及波压力和气压...研究旨在探究振荡水柱(oscillating water column,简称OWC)防波堤前墙的受力特性。通过物理模型试验,利用狭缝开口模拟冲击式空气透平,测量前墙两侧的波浪压强和振荡水柱气室内气体压强,从而在计算前墙水平波致总力时计及波压力和气压力。研究结果表明,气室宽度比和狭缝开口率是影响波浪压强和气体压强的关键参数,其主要影响表现为:改变前墙两侧波浪压强的幅值,改变前墙两侧高波压区域的垂向宽度以及改变气压振荡的剧烈程度。在不同的气室结构参数和波浪参数组合下,前墙的最大水平波致力分布呈现两个高波力区域,时域分析结果表明,这两个区域的前墙水平波致力中波压分力与气压分力的峰值幅值和相位组合存在差异。文中特别强调气体压强在前墙水平波致力中的重要作用,受其主要影响,狭缝开口率小于1.50%的OWC防波堤前墙在B/L=0.15附近波浪作用下出现较大波致力。为确保OWC防波堤结构安全,设计时应根据海域波浪特征调整气室结构,避免或减少在前墙表面形成高波力区域。展开更多
本文提出在振荡水柱(oscillating water column,简称OWC)波浪能转换装置中引入双空气透平结构的概念,在由圆筒形OWC装置与带导浪墙的直立防波堤耦合形成的一体化系统中,通过配置两台U形流道结构的冲击式空气透平,数值研究了一体化系统...本文提出在振荡水柱(oscillating water column,简称OWC)波浪能转换装置中引入双空气透平结构的概念,在由圆筒形OWC装置与带导浪墙的直立防波堤耦合形成的一体化系统中,通过配置两台U形流道结构的冲击式空气透平,数值研究了一体化系统从波浪能至电能的多过程能量转换的特性,并在空气透平处于自由启动和强制启动的两种工作模式下,与采用单空气透平的一体化系统的能量转换特性进行了对比。研究结果表明,在采用双透平的一体化系统中,虽然每个透平将波浪能转换为气动能的效率略低于采用单透平的系统,但是在双透平的协同作用下,系统的一级能量和总体能量转换效率要明显优于采用单透平的系统,其中,在自由启动模式下,一级能量转换效率和总体能量转换效率的峰值分别实现约56.4%和69.4%的增长。在特定周期波浪作用下,额外空气透平的引入还使得一体化系统的总电功率输出的峰值提升约66.57%。结果还表明,双空气透平的增效机理在于可以更有效地调整气室内外空气压差与空气流量,优化气室内的气动阻尼,从而实现波浪能的高效俘获与转换。展开更多
基金Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6100257 and Y6110140)
文摘By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.
基金Supported by the National Natural Science Foundation of China under Grant No.11447017the Natural Science Foundation of Zhejiang Province under Grant Nos.LY14A010005 and LQ13A010013
文摘Using the standard truncated Painlev expansion, the residual symmetry of the(2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived by utilizing the obtained symmetries. The symmetries of the system are also derived through the Clarkson-Kruskal direct method, and several types of explicit reduction solutions relate to the trigonometric or the hyperbolic functions are obtained. Finally, some special solitons are depicted from one of the solutions.
基金the Natural Science Foundation of Zhejiang Province under Grant No.Y606128the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20070568
文摘With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.
基金the National Natural Science Foundation of China under Grant No.11772017the Fundamental Research Funds for the Central Universities
文摘In this paper,we investigate a(2+1)-dimensional variable-coefficient modified dispersive waterwave system in fluid mechanics.We prove the Painlevéintegrability for that system via the Painlevéanalysis.We find some auto-B?cklund transformations for that system via the truncated Painlevéexpansions.Bilinear forms and N-soliton solutions are constructed,where N is a positive integer.We discuss the inelastic interactions,elastic interactions and soliton resonances for the two solitons.We also graphically demonstrate that the velocities of the solitons are affected by the variable coefficient of that system.
文摘By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.
文摘Harvesting ambient mechanical energy is a key technology for realizing self-powered electronics. With advantages of stability and durabilid, a liquid-solid-based triboelectric nanogenerator （TENG） has recently drawn much attention. However, the impacts of liquid properties on the TENG performance and the related working principle are still unclear. We assembled herein a U-tube TENG based on the liquid-solid mode and applied 11 liquids to study the effects of liquid properties on the TENG output performance. The results confirmed that the key factors influencing the output are polarity, dielectric constant, and affinity to fluorinated ethylene propylene （FEP）. Among the 11 liquids, the pure water-based U-tube TENG exhibited the best output with an open-circuit voltage （Voc） of 81.7 V and a short-circuit current （Isc） of 0.26 μA for the shaking mode （0.5 Hz）, which can further increase to 93.0 V and 0.48 μA, respectively, for the horizontal shifting mode （1.25 Hz）. The U-tube TENG can be utilized as a self-powered concentration sensor （component concentration or metal ion concentration） for an aqueous solution with an accuracy higher than 92%. Finally, an upgraded sandwich-like water-FEP U-tube TENG was applied to harvest water-wave energy, showing a high output with Voc of 350 V, Isc of 1.75 μA, and power density of 2.04 W/m3. We successfully lighted up 60 LEDs and powered a temperature-humidity meter. Given its high output performance, the water-FEP U-tube TENG is a very promising approach for harvesting water-wave energy for self-powered electronics.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371039 and 11425103)
文摘We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace（V, B） of the velocity at the free surface, and the outer normal derivative ？P/？n of the pressure P satisfy sup t∈[0,T]｜｜κ（t）｜｜Lp∩L^2＋∫0^T｜｜（▽V, ▽B）（t）｜｜L∞^6dt〈＋∞,inf （t,x,y）∈[0,T]×Σ_t- P/ n（t, x, y）≥c0,for some p 〉 2d and c_0〉 0, then the solution can be extended after t = T.
基金the National Key Development and Planning Project for the Basic Research (973) (Grant No.2005CB321703)the Science Funds for Creative Research Groups (Grant No.40221503)
文摘An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.
文摘研究旨在探究振荡水柱(oscillating water column,简称OWC)防波堤前墙的受力特性。通过物理模型试验,利用狭缝开口模拟冲击式空气透平,测量前墙两侧的波浪压强和振荡水柱气室内气体压强,从而在计算前墙水平波致总力时计及波压力和气压力。研究结果表明,气室宽度比和狭缝开口率是影响波浪压强和气体压强的关键参数,其主要影响表现为:改变前墙两侧波浪压强的幅值,改变前墙两侧高波压区域的垂向宽度以及改变气压振荡的剧烈程度。在不同的气室结构参数和波浪参数组合下,前墙的最大水平波致力分布呈现两个高波力区域,时域分析结果表明,这两个区域的前墙水平波致力中波压分力与气压分力的峰值幅值和相位组合存在差异。文中特别强调气体压强在前墙水平波致力中的重要作用,受其主要影响,狭缝开口率小于1.50%的OWC防波堤前墙在B/L=0.15附近波浪作用下出现较大波致力。为确保OWC防波堤结构安全,设计时应根据海域波浪特征调整气室结构,避免或减少在前墙表面形成高波力区域。
文摘本文提出在振荡水柱(oscillating water column,简称OWC)波浪能转换装置中引入双空气透平结构的概念,在由圆筒形OWC装置与带导浪墙的直立防波堤耦合形成的一体化系统中,通过配置两台U形流道结构的冲击式空气透平,数值研究了一体化系统从波浪能至电能的多过程能量转换的特性,并在空气透平处于自由启动和强制启动的两种工作模式下,与采用单空气透平的一体化系统的能量转换特性进行了对比。研究结果表明,在采用双透平的一体化系统中,虽然每个透平将波浪能转换为气动能的效率略低于采用单透平的系统,但是在双透平的协同作用下,系统的一级能量和总体能量转换效率要明显优于采用单透平的系统,其中,在自由启动模式下,一级能量转换效率和总体能量转换效率的峰值分别实现约56.4%和69.4%的增长。在特定周期波浪作用下,额外空气透平的引入还使得一体化系统的总电功率输出的峰值提升约66.57%。结果还表明,双空气透平的增效机理在于可以更有效地调整气室内外空气压差与空气流量,优化气室内的气动阻尼,从而实现波浪能的高效俘获与转换。
