A two-dimensional planar crack which propagates along its self-plane is taken as the fault model. The static solution of the classic (linear elastic fracture mechanics) model for this study for three types of two-dime...A two-dimensional planar crack which propagates along its self-plane is taken as the fault model. The static solution of the classic (linear elastic fracture mechanics) model for this study for three types of two-dimensional cracks are obtained by means of degeneration method based on the dynamic solution obtained by Kostrov (1975 ). The degeneration method used in this study has two points of convenience: ① One can obtain the solutions of different types of cracks by using the unified method; ②It is avoided to use displacement potential and stress function which physical meaning is not straight. The results obtained in this paper are just the same as that obtained by previous authors who solved the equilibrium equations by means of integral transform method.It is showed that: ① The static solution cannot be separated from the dynamic one, because the static solution also has the meaning of duration time. ② Both the static and the dynamic solutions of a critical crack must satisfy the same criteria, and the evolution from static to dynamic solution must be associated with some additional disturbance. Particularly, the quantity of disturbance in some form has to be imposed when a critical crack is ready to initiate.展开更多
The stress field, controlling the developmental process of a shallow focus inland earthquake, is regarded as the superposition of the fundamental and the variational stress field, but the latter often plays an...The stress field, controlling the developmental process of a shallow focus inland earthquake, is regarded as the superposition of the fundamental and the variational stress field, but the latter often plays an important role. In this paper we focus on two kinds of problems generating the variational stress field, which is related to geotherm. One is the local high temperature region problem, which includes the situations of the heat carrying fluid intruding into the vertical or horizontal cracks and the case of existence of the static state local high temperature region. The other is the problem that the thermal energy is released as the fault emerges displacement discontinuities,during the steady state extension. The two problems can be idealized into the three dimension thermoelastic quasi static problems and their solutions can be given, respectively. Thereby,we may obtain the approximate expressions of some additional seismic precursor fields generated on the plane near the ground surface,for examples, the temperature, the body strain and the underground water, the vertical deformation and the ground tilt vector fields etc. We discuss their space time distribution feature on the plane and get some qualitative results by contrasting them with each other. lt may provide some clues for further studying the comprehensive applications of the preseismic observations.展开更多
The liquid Lane-Emden star is a free boundary problem of compressible EulerPoisson equation which describes motion of celestial bodies.This model admits a class of static solutions parametrized by its central density....The liquid Lane-Emden star is a free boundary problem of compressible EulerPoisson equation which describes motion of celestial bodies.This model admits a class of static solutions parametrized by its central density.According to Lam[9],when the central density is sufficiently small or the adiabatic constantγ∈[4/3,2],the static solutions are linearly stable.In this article,by constructing periodic solutions to the linearized equation,we prove that even though these solutions are linearly stable,they may not decay in time.Moreover we prove that if the sum of the internal energy and potential energy of this model has an minimizer,then it must be the spherically symmetric solution to the static equation,therefore demonstrating their stability from a variational point of view.展开更多
A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains Q（3）-symmetric tensor part according to irreducible decomposition. Some propertie...A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains Q（3）-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.展开更多
文摘A two-dimensional planar crack which propagates along its self-plane is taken as the fault model. The static solution of the classic (linear elastic fracture mechanics) model for this study for three types of two-dimensional cracks are obtained by means of degeneration method based on the dynamic solution obtained by Kostrov (1975 ). The degeneration method used in this study has two points of convenience: ① One can obtain the solutions of different types of cracks by using the unified method; ②It is avoided to use displacement potential and stress function which physical meaning is not straight. The results obtained in this paper are just the same as that obtained by previous authors who solved the equilibrium equations by means of integral transform method.It is showed that: ① The static solution cannot be separated from the dynamic one, because the static solution also has the meaning of duration time. ② Both the static and the dynamic solutions of a critical crack must satisfy the same criteria, and the evolution from static to dynamic solution must be associated with some additional disturbance. Particularly, the quantity of disturbance in some form has to be imposed when a critical crack is ready to initiate.
文摘The stress field, controlling the developmental process of a shallow focus inland earthquake, is regarded as the superposition of the fundamental and the variational stress field, but the latter often plays an important role. In this paper we focus on two kinds of problems generating the variational stress field, which is related to geotherm. One is the local high temperature region problem, which includes the situations of the heat carrying fluid intruding into the vertical or horizontal cracks and the case of existence of the static state local high temperature region. The other is the problem that the thermal energy is released as the fault emerges displacement discontinuities,during the steady state extension. The two problems can be idealized into the three dimension thermoelastic quasi static problems and their solutions can be given, respectively. Thereby,we may obtain the approximate expressions of some additional seismic precursor fields generated on the plane near the ground surface,for examples, the temperature, the body strain and the underground water, the vertical deformation and the ground tilt vector fields etc. We discuss their space time distribution feature on the plane and get some qualitative results by contrasting them with each other. lt may provide some clues for further studying the comprehensive applications of the preseismic observations.
基金supported by the National Key R&D Program of China(2021YFA1001700)the National Science Foundation of China(12426203,12221001)。
文摘The liquid Lane-Emden star is a free boundary problem of compressible EulerPoisson equation which describes motion of celestial bodies.This model admits a class of static solutions parametrized by its central density.According to Lam[9],when the central density is sufficiently small or the adiabatic constantγ∈[4/3,2],the static solutions are linearly stable.In this article,by constructing periodic solutions to the linearized equation,we prove that even though these solutions are linearly stable,they may not decay in time.Moreover we prove that if the sum of the internal energy and potential energy of this model has an minimizer,then it must be the spherically symmetric solution to the static equation,therefore demonstrating their stability from a variational point of view.
基金Supported by National Natural Science Foundation of China under Grant Nos.10775140,10975141Knowledge Innovation Funds of CAS under Grant No.KJCX3-SYW-S03
文摘A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains Q（3）-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.
