This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field couple...This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.展开更多
This paper applies the convolutional differentiator method, based on generalized Forsyte orthogonal polynomial (CFPD), to simulate the seismic wave propagation in two-phase media. From the numerical results we can s...This paper applies the convolutional differentiator method, based on generalized Forsyte orthogonal polynomial (CFPD), to simulate the seismic wave propagation in two-phase media. From the numerical results we can see that three types of waves, fast P-waves, S-waves and slow P-waves, can be observed in the seismic wave field. The experiments on anisotropic models demonstrate that the wavefront is elliptic instead of circular and S-wave splitting occurs in anisotropic two-phase media. The research has confirmed that the rules of elastic wave propagation in fluid-saturated porous media are controlled by Biot's theory. Experiment on a layered fault model shows the wavefield generated by the interface and the fault very well, indicating the effectiveness of CFPD method on the wavefield modeling for real layered media in the Earth. This research has potential applications to the investigation of Earth's deep structure and oil/gas exploration.展开更多
Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of ...Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.展开更多
High intensity focused ultrasound(HIFU)therapy is an effective method in clinical treatment of tumors,in order to explore the bio-heat conduction mechanism of in multi-layer media by concave spherical transducer,tempe...High intensity focused ultrasound(HIFU)therapy is an effective method in clinical treatment of tumors,in order to explore the bio-heat conduction mechanism of in multi-layer media by concave spherical transducer,temperature field induced by this kind of transducer in multi-layer media will be simulated through solving Pennes equation with finite difference method,and the influence of initial sound pressure,absorption coefficient,and thickness of different layers of biological tissue as well as thermal conductivity parameter on sound focus and temperature distribution will be analyzed,respectively.The results show that the temperature in focus area increases faster while the initial sound pressure and thermal conductivity increase.The absorption coefficient is smaller,the ultrasound intensity in the focus area is bigger,and the size of the focus area is increasing.When the thicknesses of different layers of tissue change,the focus position changes slightly,but the sound intensity of the focus area will change obviously.The temperature in focus area will rise quickly before reaching a threshold,and then the temperature will keep in the threshold range.展开更多
With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carrie...With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.展开更多
The static electromagnetic fields are studied here based on the standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are deduced. By introducing ...The static electromagnetic fields are studied here based on the standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are deduced. By introducing a set of new potential functions of order 2, several novel theoretical results were obtained: The classical potential functions of order 1 can be expressed by the new potential functions of order 2, the electric or magnetic potentials are scalar for isotropic media, and vector for anisotropic media. The amplitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.展开更多
基金Project (No. 10372088) supported by the National Natural Science Foundation of China
文摘This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.
基金supported by the National Natural Science Foundation of China(Grant No.40874045)Special Funds for Sciences and Technology Research of Public Welfare Trades(Grant Nos. 200811021 and 201011042)
文摘This paper applies the convolutional differentiator method, based on generalized Forsyte orthogonal polynomial (CFPD), to simulate the seismic wave propagation in two-phase media. From the numerical results we can see that three types of waves, fast P-waves, S-waves and slow P-waves, can be observed in the seismic wave field. The experiments on anisotropic models demonstrate that the wavefront is elliptic instead of circular and S-wave splitting occurs in anisotropic two-phase media. The research has confirmed that the rules of elastic wave propagation in fluid-saturated porous media are controlled by Biot's theory. Experiment on a layered fault model shows the wavefield generated by the interface and the fault very well, indicating the effectiveness of CFPD method on the wavefield modeling for real layered media in the Earth. This research has potential applications to the investigation of Earth's deep structure and oil/gas exploration.
基金supported by the National Natural Science Foundation of China (No.50778179)
文摘Static electromagnetic fields are studied based on standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are derived. By introducing a new set of first-order potential functions, several novel theoretical results are obtained. It is found that, for isotropic media, electric or magnetic potentials are scalar; while for anisotropic media, they are vectors. Magnitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.
基金Project(11174077)supported by the National Natural Science Foundation of ChinaProject(11JJ3079)supported by the Hunan Provincial Natural Science Foundation of ChinaProjects(12C0237,11C0844)supported by the Science Research Program of Education Department of Hunan Province,China
文摘High intensity focused ultrasound(HIFU)therapy is an effective method in clinical treatment of tumors,in order to explore the bio-heat conduction mechanism of in multi-layer media by concave spherical transducer,temperature field induced by this kind of transducer in multi-layer media will be simulated through solving Pennes equation with finite difference method,and the influence of initial sound pressure,absorption coefficient,and thickness of different layers of biological tissue as well as thermal conductivity parameter on sound focus and temperature distribution will be analyzed,respectively.The results show that the temperature in focus area increases faster while the initial sound pressure and thermal conductivity increase.The absorption coefficient is smaller,the ultrasound intensity in the focus area is bigger,and the size of the focus area is increasing.When the thicknesses of different layers of tissue change,the focus position changes slightly,but the sound intensity of the focus area will change obviously.The temperature in focus area will rise quickly before reaching a threshold,and then the temperature will keep in the threshold range.
文摘With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.
文摘The static electromagnetic fields are studied here based on the standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are deduced. By introducing a set of new potential functions of order 2, several novel theoretical results were obtained: The classical potential functions of order 1 can be expressed by the new potential functions of order 2, the electric or magnetic potentials are scalar for isotropic media, and vector for anisotropic media. The amplitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.