We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separat...We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
Aeromagnetic data for center-east Cameroon between the latitudes 3.5° to 4.5°N and longitudes 12° to 12.5°E are used to further study the subsurface area of this part of the geological Province of ...Aeromagnetic data for center-east Cameroon between the latitudes 3.5° to 4.5°N and longitudes 12° to 12.5°E are used to further study the subsurface area of this part of the geological Province of Central Africa and the Congo Craton. The GIS and GEOSOFT v6.5 softwares are used to treat the data. This analysis enabled us to explore our study area from surface right to the base. The Tilt Angle method is used to delineate geological structures and to estimate the depth. The Euler’s deconvolution method is used to estimate the specific depth of structural contacts. We estimate the northern boundary of the Congo Craton and southern boundary of the Pan-African starting from 3°7'N of West to 3°75'N of East. Its depth is estimated around 2.6 km for deep and 0.1 km for shallow while the direction is WSW-ENE and the NW slope varies from 30° to 60°. We obtain that main and minor lineaments exist throughout, from the surface to the base of the area with their principal direction being SW-NE. We also obtain the vertical gradient contact and the quasihorizontal contact. This is proof of the subduction of the Pan-African belt under the Congo Craton due to the intense collision which caused the rejuvenation of the crust. The main consequence of this collision is the formation of pudding and fold structures, beginning from the superficial part right to the base and which caused the intrusion of schistose, chlorite-schist, quartzite in the micaschist and the intrusions of gneiss and garnetiferous schist in the migmatite. In our study, we highlight the presence of 37 major and 523 minor lineaments that localize the circulation of minerals. The probable slope of the lineaments in the northern part of the region varies from 30° to 60° in a SE direction while in the southern part, and it varies from 30° to 60° in a NW direction.展开更多
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
The purpose of this study is to develop maneuvering models and systems of a simulator to improve the motion performance of autonomous underwater vehicles （AUVs） at the preliminary design stages in advance. The AUVs ...The purpose of this study is to develop maneuvering models and systems of a simulator to improve the motion performance of autonomous underwater vehicles （AUVs） at the preliminary design stages in advance. The AUVs simulation systems based on the standard submarine equations of motion in six-degree-of-freedom （6-DOF） integrated with the Euler-Rodriguez quaternion method for representing singularity-free AUV attitude and time-saving calculation, and with a nonlinear control model for maneuvering and depth control simulations, time-marching in the fourth-order Runge-Kutta scheme. For validation of the simulation codes, results of the ISiMI AUV open-loop tests including turning test and zigzag test as well as an AUV simulator on the basis of Euler-angle method were used to compare with the quaternion-based AUV simulator. The computational results from the proposed simulator agree well with those from both the ISiMI AUV experiments and the Euler-angle based simulations. Additionally, a new maneuvering procedure, namely ＂put-out＂ was implemented to test directional stability for a large-scale AUV in the proposed AUV simulator that can be considered for vehicles in space as well as in constrained planes.展开更多
In the process of solving Euler vectors based on GNSS horizontal movement field,the number of estimated parameters can affect Euler vector results. This issue is analyzed through theoretical deduction and practical ex...In the process of solving Euler vectors based on GNSS horizontal movement field,the number of estimated parameters can affect Euler vector results. This issue is analyzed through theoretical deduction and practical example in this paper. Firstly,the difference between the results of Euler vectors in different solving models is deduced. Meanwhile, based on GNSS horizontal movement field in the Chinese mainland from 2004 to 2007,two common models( RRM and REHSM) are used to discuss the impact of solving models on Euler vectors and the follow-up study. The result shows that the maximum value of the difference in a block's entire rotation can reach 2. 6mm /a,and should not be ignored. Therefore,the results of horizontal movement are different using different kinematic block models,and this should be paid more attention in the analysis of crustal horizontal movement.展开更多
基金supported by the National Natural Science Foundation of China(11871218,12071298)in part by the Science and Technology Commission of Shanghai Municipality(21JC1402500,22DZ2229014)。
文摘We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
文摘Aeromagnetic data for center-east Cameroon between the latitudes 3.5° to 4.5°N and longitudes 12° to 12.5°E are used to further study the subsurface area of this part of the geological Province of Central Africa and the Congo Craton. The GIS and GEOSOFT v6.5 softwares are used to treat the data. This analysis enabled us to explore our study area from surface right to the base. The Tilt Angle method is used to delineate geological structures and to estimate the depth. The Euler’s deconvolution method is used to estimate the specific depth of structural contacts. We estimate the northern boundary of the Congo Craton and southern boundary of the Pan-African starting from 3°7'N of West to 3°75'N of East. Its depth is estimated around 2.6 km for deep and 0.1 km for shallow while the direction is WSW-ENE and the NW slope varies from 30° to 60°. We obtain that main and minor lineaments exist throughout, from the surface to the base of the area with their principal direction being SW-NE. We also obtain the vertical gradient contact and the quasihorizontal contact. This is proof of the subduction of the Pan-African belt under the Congo Craton due to the intense collision which caused the rejuvenation of the crust. The main consequence of this collision is the formation of pudding and fold structures, beginning from the superficial part right to the base and which caused the intrusion of schistose, chlorite-schist, quartzite in the micaschist and the intrusions of gneiss and garnetiferous schist in the migmatite. In our study, we highlight the presence of 37 major and 523 minor lineaments that localize the circulation of minerals. The probable slope of the lineaments in the northern part of the region varies from 30° to 60° in a SE direction while in the southern part, and it varies from 30° to 60° in a NW direction.
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
文摘The purpose of this study is to develop maneuvering models and systems of a simulator to improve the motion performance of autonomous underwater vehicles （AUVs） at the preliminary design stages in advance. The AUVs simulation systems based on the standard submarine equations of motion in six-degree-of-freedom （6-DOF） integrated with the Euler-Rodriguez quaternion method for representing singularity-free AUV attitude and time-saving calculation, and with a nonlinear control model for maneuvering and depth control simulations, time-marching in the fourth-order Runge-Kutta scheme. For validation of the simulation codes, results of the ISiMI AUV open-loop tests including turning test and zigzag test as well as an AUV simulator on the basis of Euler-angle method were used to compare with the quaternion-based AUV simulator. The computational results from the proposed simulator agree well with those from both the ISiMI AUV experiments and the Euler-angle based simulations. Additionally, a new maneuvering procedure, namely ＂put-out＂ was implemented to test directional stability for a large-scale AUV in the proposed AUV simulator that can be considered for vehicles in space as well as in constrained planes.
基金sponsored by the Special Earthquake Research Project Granted by the China Earthquake Administration(201308009,201208006)
文摘In the process of solving Euler vectors based on GNSS horizontal movement field,the number of estimated parameters can affect Euler vector results. This issue is analyzed through theoretical deduction and practical example in this paper. Firstly,the difference between the results of Euler vectors in different solving models is deduced. Meanwhile, based on GNSS horizontal movement field in the Chinese mainland from 2004 to 2007,two common models( RRM and REHSM) are used to discuss the impact of solving models on Euler vectors and the follow-up study. The result shows that the maximum value of the difference in a block's entire rotation can reach 2. 6mm /a,and should not be ignored. Therefore,the results of horizontal movement are different using different kinematic block models,and this should be paid more attention in the analysis of crustal horizontal movement.
