In the design of revetment engineering under wave action, to resist the wave action, the pattern of top layer-filter layer-core （subsoil） is often adopted. In general, the structure of top layer is usually single di...In the design of revetment engineering under wave action, to resist the wave action, the pattern of top layer-filter layer-core （subsoil） is often adopted. In general, the structure of top layer is usually single discrete blocks, typically accropode blocks, four-leg square hollow blocks and barrier boards, and also acropode, riprap, paved rock blocks or concrete slabs with smaller waves. Such top layer has been provided with many research findings on its stability and is widely used in engineering. Setting a filter layer between the top layer and the lower dike core mainly has two functions： （1） giving certain permeability, to minimize the hydrodynamic load directly acting on the lower foundation soil; （2） giving certain hydraulic tightness, to prevent fine sediment of the lower foundation soil from being washed out. This paper is focused on a special filter layer with geotextile as its upper structure and coarse aggregate as its lower structure. By simulating geotextile with different permeability and coarse aggregate with different size, the pressure of top of cover layer and the down side of the geotextile is tested under wave actions, and compared with theoretical analysis, in this way, how the permeability of geotextile impacts the stability of top layer is studied. The research shows that when the filter layer under the geotextile has high permeability and the geotextile＇s permeability gets poorer, the uplift force to geotextile and the top layer will be increased under wave action, which will cause damage to the top layer when it is greater than the vertical component of the underwater gravity along the slope surface.展开更多
We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula,the previously developed relativistic Kappa-type(KT) distribution and the regular Kappa dist...We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula,the previously developed relativistic Kappa-type(KT) distribution and the regular Kappa distribution of energetic electrons.We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter θ2 increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist.展开更多
The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper w...The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.展开更多
文摘In the design of revetment engineering under wave action, to resist the wave action, the pattern of top layer-filter layer-core （subsoil） is often adopted. In general, the structure of top layer is usually single discrete blocks, typically accropode blocks, four-leg square hollow blocks and barrier boards, and also acropode, riprap, paved rock blocks or concrete slabs with smaller waves. Such top layer has been provided with many research findings on its stability and is widely used in engineering. Setting a filter layer between the top layer and the lower dike core mainly has two functions： （1） giving certain permeability, to minimize the hydrodynamic load directly acting on the lower foundation soil; （2） giving certain hydraulic tightness, to prevent fine sediment of the lower foundation soil from being washed out. This paper is focused on a special filter layer with geotextile as its upper structure and coarse aggregate as its lower structure. By simulating geotextile with different permeability and coarse aggregate with different size, the pressure of top of cover layer and the down side of the geotextile is tested under wave actions, and compared with theoretical analysis, in this way, how the permeability of geotextile impacts the stability of top layer is studied. The research shows that when the filter layer under the geotextile has high permeability and the geotextile＇s permeability gets poorer, the uplift force to geotextile and the top layer will be increased under wave action, which will cause damage to the top layer when it is greater than the vertical component of the underwater gravity along the slope surface.
基金supported by the National Natural Science Foundation of China(Grant Nos.41531072,41274165,41404130,41204114&41504125)
文摘We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula,the previously developed relativistic Kappa-type(KT) distribution and the regular Kappa distribution of energetic electrons.We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter θ2 increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist.
文摘The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.
