In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex loca...In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features.In addition,an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions,largely reducing the computational cost.Numerical examples demonstrate the effectiveness of the proposed method in large deformation,large rotation and dynamics simulation.展开更多
We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since ...We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible （SIS） structure. We calculate the effective reproduction number Rv for the model and describe the local-asymptotic stability of the disease-free equilibrium using Rv. We prove the existence of an endemic equilibrium for Rv 〉 1 for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.展开更多
In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the l...In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52175223,and 11802072)the Fundamental Research Funds for the Central Universities(Grant No.B210201038).
文摘In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features.In addition,an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions,largely reducing the computational cost.Numerical examples demonstrate the effectiveness of the proposed method in large deformation,large rotation and dynamics simulation.
文摘We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible （SIS） structure. We calculate the effective reproduction number Rv for the model and describe the local-asymptotic stability of the disease-free equilibrium using Rv. We prove the existence of an endemic equilibrium for Rv 〉 1 for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.
文摘In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.
