建立了全光纤电流互感器（fiber-optical current transformer,FOCT）温度特性的数学模型。该模型充分考虑传感光纤的弯曲特性,结合光纤线性双折射的分布参数模型从本质上解释了温度对线性双折射的影响机理：由于传感环的弯曲性,温度变...建立了全光纤电流互感器（fiber-optical current transformer,FOCT）温度特性的数学模型。该模型充分考虑传感光纤的弯曲特性,结合光纤线性双折射的分布参数模型从本质上解释了温度对线性双折射的影响机理：由于传感环的弯曲性,温度变化会导致光纤横截面上的受力不对称,进而引起线性双折射;单位长度光纤的线性双折射相位差与温度变化量成正比,与光纤弯曲半径成反比。并结合光纤Verdet常数的温度特性综合量化了温度对FOCT的影响。采用COMSOL有限元分析方法实现光场、磁场、温度场、应力场的耦合并分析求解。仿真结果表明：双折射效应会使光波旋转角变小;光纤横截面上的应力差与温度变化量成正比,与光纤弯曲半径成反比;温度波动将引起线性双折射,进而使光波旋转角减小;结合Verdet常数得到了温度波动时FOCT的综合误差,与理论分析结果吻合。最后设计并搭建FOCT实验平台,进行线性度测试和温度循环测试。测试结果表明：实验误差与理论误差变化趋势基本一致;温度波动越大,FOCT误差漂移越严重,必须采取补偿措施,故提出一系列改善FOCT温度稳定性的方法。仿真与实验结果验证了理论分析的正确性。展开更多
The variation of in situ stress before and after earthquakes is an issue studied by geologists. In this paper, on the basis of the fault slip dislocation model of Wenchuan Ms8.0 earthquake, the changes of co-seismic d...The variation of in situ stress before and after earthquakes is an issue studied by geologists. In this paper, on the basis of the fault slip dislocation model of Wenchuan Ms8.0 earthquake, the changes of co-seismic displacement and the distribution functions of stress tensor around the Longmen Shan fault zone are calculated. The results show that the co-seismic maximum surface displacement is 4.9 m in the horizontal direction and 6.5 m in the vertical direction, which is almost consistent with the on-site survey and GPS observations. The co-seismic maximum horizontal stress in the hanging wall and footwall decreased sharply as the distance from the Longmen Shan fault zone increased. However, the vertical stress and minimum horizontal stress increased in the footwall and in some areas of the hanging wall. The study of the co-seismic displacement and stress was mainly focused on the long and narrow region along the Longmen Shan fault zone, which coincides with the distribution of the earthquake aftershocks. Therefore, the co-seismic stress only affects the aftershocks, and does not affect distant faults and seismic activities. The results are almost consistent with in situ stress measurements at the two sites before and after Wenchuan Ms8.0 earthquake. Along the fault plane, the co-seismic shear stress in the dip direction is larger than that in the strike direction, which indicates that the faulting mechanism of the Longmen Shan fault zone is a dominant thrust with minor strike-slipping. The results can be used as a reference value for future studies of earthquake mechanisms.展开更多
In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. ...In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.展开更多
文摘建立了全光纤电流互感器（fiber-optical current transformer,FOCT）温度特性的数学模型。该模型充分考虑传感光纤的弯曲特性,结合光纤线性双折射的分布参数模型从本质上解释了温度对线性双折射的影响机理：由于传感环的弯曲性,温度变化会导致光纤横截面上的受力不对称,进而引起线性双折射;单位长度光纤的线性双折射相位差与温度变化量成正比,与光纤弯曲半径成反比。并结合光纤Verdet常数的温度特性综合量化了温度对FOCT的影响。采用COMSOL有限元分析方法实现光场、磁场、温度场、应力场的耦合并分析求解。仿真结果表明：双折射效应会使光波旋转角变小;光纤横截面上的应力差与温度变化量成正比,与光纤弯曲半径成反比;温度波动将引起线性双折射,进而使光波旋转角减小;结合Verdet常数得到了温度波动时FOCT的综合误差,与理论分析结果吻合。最后设计并搭建FOCT实验平台,进行线性度测试和温度循环测试。测试结果表明：实验误差与理论误差变化趋势基本一致;温度波动越大,FOCT误差漂移越严重,必须采取补偿措施,故提出一系列改善FOCT温度稳定性的方法。仿真与实验结果验证了理论分析的正确性。
基金supported by the Sinoprobe Deep Exploration in China(SinoProbe-07)research funds of the Institute of Geomechanics,Chinese Academy of Geological Sciences(Grant No.DZLXJK201105)National Basic Research Program of China(973 Program)(Grant No.2008CB425702)
文摘The variation of in situ stress before and after earthquakes is an issue studied by geologists. In this paper, on the basis of the fault slip dislocation model of Wenchuan Ms8.0 earthquake, the changes of co-seismic displacement and the distribution functions of stress tensor around the Longmen Shan fault zone are calculated. The results show that the co-seismic maximum surface displacement is 4.9 m in the horizontal direction and 6.5 m in the vertical direction, which is almost consistent with the on-site survey and GPS observations. The co-seismic maximum horizontal stress in the hanging wall and footwall decreased sharply as the distance from the Longmen Shan fault zone increased. However, the vertical stress and minimum horizontal stress increased in the footwall and in some areas of the hanging wall. The study of the co-seismic displacement and stress was mainly focused on the long and narrow region along the Longmen Shan fault zone, which coincides with the distribution of the earthquake aftershocks. Therefore, the co-seismic stress only affects the aftershocks, and does not affect distant faults and seismic activities. The results are almost consistent with in situ stress measurements at the two sites before and after Wenchuan Ms8.0 earthquake. Along the fault plane, the co-seismic shear stress in the dip direction is larger than that in the strike direction, which indicates that the faulting mechanism of the Longmen Shan fault zone is a dominant thrust with minor strike-slipping. The results can be used as a reference value for future studies of earthquake mechanisms.
基金Supported by National Natural Science Foundation of China (10571046, 10571053, and 10871066)Program for New Century Excellent Talents in University (NCET-06-0712)+2 种基金Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal Universitythe Project of Scientific Research Fund of Hunan Provincial Education Department (09K025)the Key Scientific Research Topic of Jiaxing University (70110X05BL)
文摘In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.
