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
By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The ma...By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The mainidea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation thatthe symmetrical Lucas functions satisfy.From the variable separation solution and by selecting appropriate functions,some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons areinvestigated.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
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
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
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
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 fr...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+∫^T_0||(▽V, ▽B)(t)||~6_(L∞)dt<+∞,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
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.
文摘By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The mainidea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation thatthe symmetrical Lucas functions satisfy.From the variable separation solution and by selecting appropriate functions,some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons areinvestigated.
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
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 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 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.
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+∫^T_0||(▽V, ▽B)(t)||~6_(L∞)dt<+∞,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.
