Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of t...Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.展开更多
The surface undulating shapes of rock joints have been described qualitatively or experimental quantitatively for a long time. The non determined describing method can not fit quantitative evaluation of mechani...The surface undulating shapes of rock joints have been described qualitatively or experimental quantitatively for a long time. The non determined describing method can not fit quantitative evaluation of mechanical parameters of rock joints in engineering. In this paper, relative amplitude ( R A) is chosen as a quantitative describing index of surface measurement of 1 023 surface undulating curves which conducted by profile curve device(PCD). We discuss the nonuniformity,anisotropy and unhomogeneity of surface undulating shapes of joints. A new method that analyzes the complexity of surface undulating shapes of rock joints directional statistically in various rock joints is also put forward.展开更多
In order to design the production with complex external shapes, a newmethod is put forward using non-uniform rational B-spline(NURBS)curves to unifythe description of complex curves composed of several segments with d...In order to design the production with complex external shapes, a newmethod is put forward using non-uniform rational B-spline(NURBS)curves to unifythe description of complex curves composed of several segments with different degrees,and then these complex curves are used to construct NURBS skinning surface. Somekinds of skills are used to dispose the knot of NURBS curves and surfaces for practicalproblems. Finally, the method is verified by several complex examples.展开更多
The original idea and shaping principle of locus shaping method for processing the aspheric optical parts are introduced, and the partial structure of the machine tool designed is described. The method has the advanta...The original idea and shaping principle of locus shaping method for processing the aspheric optical parts are introduced, and the partial structure of the machine tool designed is described. The method has the advantage of high efficiency and low cost compared to the numerical control method. And it is proven that the method is feasible.展开更多
A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam sha...A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam shaped curve separatrix cycle for a special type of cubic system and obtains their accurate domain in parameter space.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10872114,10672089, 10832005,and 11072125)
文摘Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.
文摘The surface undulating shapes of rock joints have been described qualitatively or experimental quantitatively for a long time. The non determined describing method can not fit quantitative evaluation of mechanical parameters of rock joints in engineering. In this paper, relative amplitude ( R A) is chosen as a quantitative describing index of surface measurement of 1 023 surface undulating curves which conducted by profile curve device(PCD). We discuss the nonuniformity,anisotropy and unhomogeneity of surface undulating shapes of joints. A new method that analyzes the complexity of surface undulating shapes of rock joints directional statistically in various rock joints is also put forward.
文摘In order to design the production with complex external shapes, a newmethod is put forward using non-uniform rational B-spline(NURBS)curves to unifythe description of complex curves composed of several segments with different degrees,and then these complex curves are used to construct NURBS skinning surface. Somekinds of skills are used to dispose the knot of NURBS curves and surfaces for practicalproblems. Finally, the method is verified by several complex examples.
文摘The original idea and shaping principle of locus shaping method for processing the aspheric optical parts are introduced, and the partial structure of the machine tool designed is described. The method has the advantage of high efficiency and low cost compared to the numerical control method. And it is proven that the method is feasible.
文摘A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam shaped curve separatrix cycle for a special type of cubic system and obtains their accurate domain in parameter space.
