Numerical simulation in the frequency-space domain has inherent advantages, such as： it is possible to simulate wave propagation from multiple sources simultaneously; there are no cumulative errors; only the interest...Numerical simulation in the frequency-space domain has inherent advantages, such as： it is possible to simulate wave propagation from multiple sources simultaneously; there are no cumulative errors; only the interesting frequencies can be selected; and it is more suitable for wave propagation in viscoelastic media. The only obstacle to using the method is the requirement of huge computer storage. We extend the compressed format for storing the coefficient matrix. It can reduce the required computer storage dramatically. We get the optimal coefficients by least-squares method to suppress the numerical dispersion and adopt the perfectly matched layer （PML） boundary conditions to eliminate the artificial boundary reflections. Using larger grid intervals decreases computer storage requirements and provides high computational efficiency. Numerical experiments demonstrate that these means are economic and effective, providing a good basis for elastic wave imaging and inversion.展开更多
Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum,we exclusively utilize the period of motion of an outgoing wave,which is shown to be related to the vibrational fr...Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum,we exclusively utilize the period of motion of an outgoing wave,which is shown to be related to the vibrational frequency of the perturbed black hole,to study area spectra of a non-rotating BTZ black hole and a rotating BTZ black hole.It is found that the area spectra and entropy spectra for both space times are equally spaced.In addition,we find that though the entropy spectra of the 3-dimensional BTZ black holes take the same form as those of the 4-dimensional black holes,the area spectra depend on the dimension of space times.Our result confirms that the entropy spectrum of a black hole is more fundamental than the area spectrum.展开更多
基金supported by the 863 Program (Grant no.2006AA09Z323)the 973 Program (Grant No.2006CB202402)
文摘Numerical simulation in the frequency-space domain has inherent advantages, such as： it is possible to simulate wave propagation from multiple sources simultaneously; there are no cumulative errors; only the interesting frequencies can be selected; and it is more suitable for wave propagation in viscoelastic media. The only obstacle to using the method is the requirement of huge computer storage. We extend the compressed format for storing the coefficient matrix. It can reduce the required computer storage dramatically. We get the optimal coefficients by least-squares method to suppress the numerical dispersion and adopt the perfectly matched layer （PML） boundary conditions to eliminate the artificial boundary reflections. Using larger grid intervals decreases computer storage requirements and provides high computational efficiency. Numerical experiments demonstrate that these means are economic and effective, providing a good basis for elastic wave imaging and inversion.
基金supported by the National Natural Science Foundation of China (Grant Nos.10773002,10875012 and 11175019)the Team Research Program of Hubei University for Nationalities (Grant No.MY2011T006)Beijing Postdoctoral Research Foundation (Grant No.71006015201201)
文摘Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum,we exclusively utilize the period of motion of an outgoing wave,which is shown to be related to the vibrational frequency of the perturbed black hole,to study area spectra of a non-rotating BTZ black hole and a rotating BTZ black hole.It is found that the area spectra and entropy spectra for both space times are equally spaced.In addition,we find that though the entropy spectra of the 3-dimensional BTZ black holes take the same form as those of the 4-dimensional black holes,the area spectra depend on the dimension of space times.Our result confirms that the entropy spectrum of a black hole is more fundamental than the area spectrum.
