The mode frequencies and the quality factors for the equilateral triangular resonator (ETR), the square resonator (SR) and the rhombus resonator (RR) are numerically calculated by the finite difference time domai...The mode frequencies and the quality factors for the equilateral triangular resonator (ETR), the square resonator (SR) and the rhombus resonator (RR) are numerically calculated by the finite difference time domain technique and the Padé approximation. The numerical results show that the resonant modes confined in an equilateral triangular cavity have much higher quality factors than those in the square or the rhombus cavities. The modes in the ETR are totally confined in transverse direction while those in the SR and RR are only partly confined. For the ETR with the side length of 4μm and the refractive index of 3 2, the mode quality factor of about 5 5×10 3 at the wavelength of 1 55μm has been obtained.展开更多
Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method （FDM）. The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to dra...Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method （FDM）. The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to draw out governing equation of beam. The interactions between the dam and the soil were modeled by using a translational spring and a rotational spring. A Sommerfeld＇s radiation condition at the infinity boundary of the fluid domain was adopted. The effects of the reservoir bottom absorption and surface waves on the dam-reservoir-foundation interaction due to the earthquake were studied. To avoid the instability of solution, a semi-implicit scheme was used for the discretization of the governing equation of dam and an explicit scheme was used for the discretization of the governing equation of fluid. The results show that as the slope of upstream dam increases, the hydrodynamic pressure on the dam is reduced. Moreover, when the Timoshenko beam theory is used, the system response increases.展开更多
The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split...The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split mode wavelengths. We find that the coupled fundamental and first order WG modes can have anticrossing mode coupling as their wavelengths approach the same value in some case,which prevents the cross of the coupled mode wavelengths. The anticrossing mode coupling greatly reduces the coupled mode Q-factor,because the coupled mode field distribution transfers between the fundamental and the first order WG modes.展开更多
The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was emplo...The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling wilth finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding tc geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.展开更多
Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dime...Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.展开更多
文摘The mode frequencies and the quality factors for the equilateral triangular resonator (ETR), the square resonator (SR) and the rhombus resonator (RR) are numerically calculated by the finite difference time domain technique and the Padé approximation. The numerical results show that the resonant modes confined in an equilateral triangular cavity have much higher quality factors than those in the square or the rhombus cavities. The modes in the ETR are totally confined in transverse direction while those in the SR and RR are only partly confined. For the ETR with the side length of 4μm and the refractive index of 3 2, the mode quality factor of about 5 5×10 3 at the wavelength of 1 55μm has been obtained.
文摘Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method （FDM）. The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to draw out governing equation of beam. The interactions between the dam and the soil were modeled by using a translational spring and a rotational spring. A Sommerfeld＇s radiation condition at the infinity boundary of the fluid domain was adopted. The effects of the reservoir bottom absorption and surface waves on the dam-reservoir-foundation interaction due to the earthquake were studied. To avoid the instability of solution, a semi-implicit scheme was used for the discretization of the governing equation of dam and an explicit scheme was used for the discretization of the governing equation of fluid. The results show that as the slope of upstream dam increases, the hydrodynamic pressure on the dam is reduced. Moreover, when the Timoshenko beam theory is used, the system response increases.
文摘The mode characteristics for twin coupled microdisks are investigated by finite-difference time-domain technique. In the coupled microdisks,the same order whispering-gallery(WG) modes can form coupled modes with split mode wavelengths. We find that the coupled fundamental and first order WG modes can have anticrossing mode coupling as their wavelengths approach the same value in some case,which prevents the cross of the coupled mode wavelengths. The anticrossing mode coupling greatly reduces the coupled mode Q-factor,because the coupled mode field distribution transfers between the fundamental and the first order WG modes.
基金Project supported by Global Center of Excellence in Novel Carbon Resource Sciences,Kyushu University,Japan
文摘The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling wilth finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding tc geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.
基金supported by National Natural Science Foundation of China(Grant No.11201239)the Singapore A*STAR SERC PSF(Grant No.1321202067)
文摘Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.
