The objective of this paper is to review the lifespan model. This paper will also suggest four additional general alternative computational methods not mentioned in Kass, R.E. and Vos, P.W. [1] [2]. It is not intended...The objective of this paper is to review the lifespan model. This paper will also suggest four additional general alternative computational methods not mentioned in Kass, R.E. and Vos, P.W. [1] [2]. It is not intended to compare the four formulas to be used in computing the Gaussian curvature. Four different formulas adopted from Struik, D.J. [3] are used and labeled here as (A), (B), (C), and (D). It has been found that all four of these formulas can compute the Gaussian curvature effectively and successfully. To avoid repetition, we only presented results from formulas (B) and (D). One can more easily check other results from formulas (A) and (C).展开更多
The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate a...The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c<sup>0</sup> and contains post-Newtonian correction terms of all orders of c<sup>-2</sup>. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.展开更多
Abstract The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tens...Abstract The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tensor product.Then two new applications are investigated. Firstly, its applications to connection, an important concept in differential geometry, is considered. The structure matrix and the Christoffel matrix are introduced. The transfer formulas under coordinate transformation are expressed in matrix form. Certain new results are obtained. Secondly, the structure of finite dimensional Lie algebra, etc. are investigated under the matrix expression.These applications demonstrate the usefulness of the new matrix products.展开更多
In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations （FNBE） in order to simulate wave transformation phenomena, wave breaking, runup and nearshore ...In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations （FNBE） in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f＇mite difference scheme. A high-order upwind weighted essentially non-oscillatory （WENO） finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations （NSWE）. On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento （Italy）.展开更多
文摘The objective of this paper is to review the lifespan model. This paper will also suggest four additional general alternative computational methods not mentioned in Kass, R.E. and Vos, P.W. [1] [2]. It is not intended to compare the four formulas to be used in computing the Gaussian curvature. Four different formulas adopted from Struik, D.J. [3] are used and labeled here as (A), (B), (C), and (D). It has been found that all four of these formulas can compute the Gaussian curvature effectively and successfully. To avoid repetition, we only presented results from formulas (B) and (D). One can more easily check other results from formulas (A) and (C).
文摘The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c<sup>0</sup> and contains post-Newtonian correction terms of all orders of c<sup>-2</sup>. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.
基金Partially supported by the National Science Foundation (G.59837270)the National Key Project (G.1998020308) of China.
文摘Abstract The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tensor product.Then two new applications are investigated. Firstly, its applications to connection, an important concept in differential geometry, is considered. The structure matrix and the Christoffel matrix are introduced. The transfer formulas under coordinate transformation are expressed in matrix form. Certain new results are obtained. Secondly, the structure of finite dimensional Lie algebra, etc. are investigated under the matrix expression.These applications demonstrate the usefulness of the new matrix products.
文摘In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations （FNBE） in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f＇mite difference scheme. A high-order upwind weighted essentially non-oscillatory （WENO） finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations （NSWE）. On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento （Italy）.
