The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures（denoted as S45, H60, S90, and D） of two-dimensi...The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures（denoted as S45, H60, S90, and D） of two-dimensional granular system is simulated by the discrete element method. The velocity vtof obtained by the time of flight method and the velocity vc obtained from the stiffness tensor of the system are compared. Different sound velocities reflect various packing structures and force distributions within the system. The compression wave velocities of H60 and S90 are nearly the same, and transmit faster than that of D packing structure, while the sound velocity of S45 is the smallest. The shear wave velocities of S45 and H60 are nearly the same, and transmit faster than that of D packing structure. The compression wave velocity is sensitive to the volume fraction of the structure, however, the shear wave velocity is more sensitive to the geometrical structure itself. As the normal stress p is larger than 1 MPa, vtof and vc are almost equal, and the stiffness tensors of various structures explain the difference of sound velocities. When the normal stress is less than 1 MPa, with the coordination number unchanged, the law vtof ∝ p^1/4 still exists. This demonstrates that apart from different power laws between force and deformation as well as the change of the coordination number under different stresses, there are other complicated causes of vtof∝ p^1/4, and an explanation of the deviation from vtof ∝ p^1/6 is given from the perspective of dissipation.展开更多
In this paper, an epidemic model of a vector-borne disease, namely, malaria, is consi- dered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the di...In this paper, an epidemic model of a vector-borne disease, namely, malaria, is consi- dered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the disease-free equilibrium is proved under certain conditions. It is shown that the model exhibits the phenomenon of backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium. Further, it is proved that the unique endemic equilibrium is globally asymptotically stable under certain conditions.展开更多
In this paper, the global properties of a mathematical modeling of hepatitis C virus （HCV） with distributed time delays is studied. Lyapunov functionals are constructed to establish the global asymptotic stability o...In this paper, the global properties of a mathematical modeling of hepatitis C virus （HCV） with distributed time delays is studied. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states. It is shown that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically stable. If the basic reproduction number R0 is larger than unity, then the infected steady state is globally asymptotically stable.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11547009)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11602062)+1 种基金the Natural Science Foundation of Guizhou Province,China(Grant No.2012/2166)the Research Foundation of Guizhou University for Talent Introduction,China(Grant No.2011/02)
文摘The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures（denoted as S45, H60, S90, and D） of two-dimensional granular system is simulated by the discrete element method. The velocity vtof obtained by the time of flight method and the velocity vc obtained from the stiffness tensor of the system are compared. Different sound velocities reflect various packing structures and force distributions within the system. The compression wave velocities of H60 and S90 are nearly the same, and transmit faster than that of D packing structure, while the sound velocity of S45 is the smallest. The shear wave velocities of S45 and H60 are nearly the same, and transmit faster than that of D packing structure. The compression wave velocity is sensitive to the volume fraction of the structure, however, the shear wave velocity is more sensitive to the geometrical structure itself. As the normal stress p is larger than 1 MPa, vtof and vc are almost equal, and the stiffness tensors of various structures explain the difference of sound velocities. When the normal stress is less than 1 MPa, with the coordination number unchanged, the law vtof ∝ p^1/4 still exists. This demonstrates that apart from different power laws between force and deformation as well as the change of the coordination number under different stresses, there are other complicated causes of vtof∝ p^1/4, and an explanation of the deviation from vtof ∝ p^1/6 is given from the perspective of dissipation.
文摘In this paper, an epidemic model of a vector-borne disease, namely, malaria, is consi- dered. The explicit expression of the basic reproduction number is obtained, the local and global asymptotical stability of the disease-free equilibrium is proved under certain conditions. It is shown that the model exhibits the phenomenon of backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium. Further, it is proved that the unique endemic equilibrium is globally asymptotically stable under certain conditions.
文摘In this paper, the global properties of a mathematical modeling of hepatitis C virus （HCV） with distributed time delays is studied. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states. It is shown that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically stable. If the basic reproduction number R0 is larger than unity, then the infected steady state is globally asymptotically stable.
