In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or...In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.展开更多
Removal of foreign bodies from seed mixtures, or their calibration for use as planting material, as well as fraction classification of granular materials requires screening surfaces with vibratory motion. This paper p...Removal of foreign bodies from seed mixtures, or their calibration for use as planting material, as well as fraction classification of granular materials requires screening surfaces with vibratory motion. This paper presents some aspects on the working process of a sieve, made of perforated sheet and having an outer conical surface with oscillatory circular motion （alternative） on the horizontal. Results are presented for some experimental researches on the movement of material on the sieve, for various kinematical parameters of the sieve （amplitude and oscillation frequency）. A conical sieve, suspended at the upper and lower in three points, was tested for screening of rapeseeds in order to estimate the influence of oscillation frequency on the screening process. Curves were drawn for separation intensity on the sieve generating line, and by regression analysis with normal distribution law were determined the equation coefficients and the correlation with experimental data. Movement of material on the sieve and its working process, in general, was appreciated by means of the peak position of distribution curve depending on the oscillation frequency of the sieve, considering that the normal distribution law correlates very well the data obtained by experiments.展开更多
In this paper, the variation of contact angles of a droplet on grooved surfaces was studied from microscale to macroscale experimentally and theoretically. The experimental results indicated that the contact angle cha...In this paper, the variation of contact angles of a droplet on grooved surfaces was studied from microscale to macroscale experimentally and theoretically. The experimental results indicated that the contact angle changes nonlinearly with anisotropic factor. To get clear of the changing process of contact angle on grooved surfaces from microscale to macroscale, we carried out theoretical analysis with moment equilibrium method being adopted. In addition, the variation of contact angles in different directions was investigated and a mathematic model to calculate arbitrary contact angles around the elliptic contact line was suggested. For the convenience of potential applications, a symbolic contact angle was proposed to characterize the ellipsoidal cap droplet on grooved surfaces. Our results will offer help to the future design of patterned surfaces in practical applications,and deepen the understanding of wetting behavior on grooved surfaces.展开更多
Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from...Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.展开更多
The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite form...The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite's geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.展开更多
文摘In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.
文摘Removal of foreign bodies from seed mixtures, or their calibration for use as planting material, as well as fraction classification of granular materials requires screening surfaces with vibratory motion. This paper presents some aspects on the working process of a sieve, made of perforated sheet and having an outer conical surface with oscillatory circular motion （alternative） on the horizontal. Results are presented for some experimental researches on the movement of material on the sieve, for various kinematical parameters of the sieve （amplitude and oscillation frequency）. A conical sieve, suspended at the upper and lower in three points, was tested for screening of rapeseeds in order to estimate the influence of oscillation frequency on the screening process. Curves were drawn for separation intensity on the sieve generating line, and by regression analysis with normal distribution law were determined the equation coefficients and the correlation with experimental data. Movement of material on the sieve and its working process, in general, was appreciated by means of the peak position of distribution curve depending on the oscillation frequency of the sieve, considering that the normal distribution law correlates very well the data obtained by experiments.
基金supported by the National Natural Science Foundation of China(Grant Nos.U1562105,11611130019 and 11372313)the Chinese Academy of Sciences(CAS)through CAS Interdisciplinary Innovation Team Project+1 种基金the CAS Key Research Program of Frontier Sciences(Grant No.QYZDJ-SSW-JSC019)the CAS Strategic Priority Research Program(Grant No.XDB22040401)
文摘In this paper, the variation of contact angles of a droplet on grooved surfaces was studied from microscale to macroscale experimentally and theoretically. The experimental results indicated that the contact angle changes nonlinearly with anisotropic factor. To get clear of the changing process of contact angle on grooved surfaces from microscale to macroscale, we carried out theoretical analysis with moment equilibrium method being adopted. In addition, the variation of contact angles in different directions was investigated and a mathematic model to calculate arbitrary contact angles around the elliptic contact line was suggested. For the convenience of potential applications, a symbolic contact angle was proposed to characterize the ellipsoidal cap droplet on grooved surfaces. Our results will offer help to the future design of patterned surfaces in practical applications,and deepen the understanding of wetting behavior on grooved surfaces.
基金supported by the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (Grant No. NRF-2007-2-C00002)
文摘Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.
基金supported by the National Natural Science Foundation of China(Grant Nos.41174014 and D0401)
文摘The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite's geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.
