Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for...Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.展开更多
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to...This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.展开更多
We present multicomponent flow models derived from the kinetic theory of gases and investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations. We address the Cau...We present multicomponent flow models derived from the kinetic theory of gases and investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations. We address the Cauchy problem for smooth solutions as well as the existence of deflagration waves, also termed anchored waves. We further discuss related models which have a similar hyperbolic-parabolic structure, notably the Saint- Venant system with a temperature equation as well as the equations governing chemical equilibrium flows. We next investigate multicomponent ionized and magnetized flow models with anisotropic transport fluxes which have a different mathematical structure. We finally discuss numerical algorithms specifically devoted to complex chemistry flows, in particular the evaluation of multicomponent transport properties, as well as the impact of multicomponent transport.展开更多
Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the c...Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the complex flow mechanism in s-shaped intake, particular attention was given to examining the effect of centerline curvature on the performance and flowfield of an ultra-compact S-shaped intake. In order to validate the multi-block model, the computational results for Royal Aircraft Establishment intake 2129-M2129 which had modest centerline cur- vature distribution were corrected with available experimental test data. The numerical simulation results agreed fairly well with the experimental data, and the computational method was then used to investigate the effects of different centerline curvature distributions on performance and flow field in compact S-shaped intake. Detailed analyses of the flow visualization had exposed the different flow topologies between the cases with different cen- terline curvature. It was found that different centerline curvature distributions changed the initial location and the size of separation bubble, as well as the strength of two counter-rotating vortices at the entrance of engine.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction nu...A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co- exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuber- culosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.展开更多
In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit a...In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.展开更多
We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes. In the case of free surface incompressible flows, the FS-model is formally obtained, using form...We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes. In the case of free surface incompressible flows, the FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the P-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope with the transition between a free surface state and a pressured （i.e., compressible） state, we propose a mixed model, the PFS-model, taking into account changes of section and slope variation.展开更多
基金supported by the Natural Science Foundation(NSF)of Zhejiang Province(No.LQ13A01 0019)NSF of China(No.61473340)NSF of Zhejiang University of Science and Technology(No.F701108G14)
文摘Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.
基金the Natural Science Foundation of China (No. 50075029)
文摘This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.
文摘We present multicomponent flow models derived from the kinetic theory of gases and investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations. We address the Cauchy problem for smooth solutions as well as the existence of deflagration waves, also termed anchored waves. We further discuss related models which have a similar hyperbolic-parabolic structure, notably the Saint- Venant system with a temperature equation as well as the equations governing chemical equilibrium flows. We next investigate multicomponent ionized and magnetized flow models with anisotropic transport fluxes which have a different mathematical structure. We finally discuss numerical algorithms specifically devoted to complex chemistry flows, in particular the evaluation of multicomponent transport properties, as well as the impact of multicomponent transport.
文摘Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modem vehicles. In this paper a series of steady numerical simulation were carried out to investigate the complex flow mechanism in s-shaped intake, particular attention was given to examining the effect of centerline curvature on the performance and flowfield of an ultra-compact S-shaped intake. In order to validate the multi-block model, the computational results for Royal Aircraft Establishment intake 2129-M2129 which had modest centerline cur- vature distribution were corrected with available experimental test data. The numerical simulation results agreed fairly well with the experimental data, and the computational method was then used to investigate the effects of different centerline curvature distributions on performance and flow field in compact S-shaped intake. Detailed analyses of the flow visualization had exposed the different flow topologies between the cases with different cen- terline curvature. It was found that different centerline curvature distributions changed the initial location and the size of separation bubble, as well as the strength of two counter-rotating vortices at the entrance of engine.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
文摘A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co- exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuber- culosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.
文摘In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.
文摘We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes. In the case of free surface incompressible flows, the FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the P-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope with the transition between a free surface state and a pressured （i.e., compressible） state, we propose a mixed model, the PFS-model, taking into account changes of section and slope variation.
