This paper presents the development of the blood flow simulation in two dimensions over the real geometry of the femoral artery. The Navier-Stokes equations are solved using the finite element method, to obtain the di...This paper presents the development of the blood flow simulation in two dimensions over the real geometry of the femoral artery. The Navier-Stokes equations are solved using the finite element method, to obtain the distributions of the blood pressure and flow velocity in multiple instants of time and different places of the femoral artery and thus determine the current condition of the blood vessels. The velocity field shows a laminar behavior,where, the velocity is higher in the center of the artery and decreases as the blood flow approaches artery walls. In spite of all artery and blood flow properties not being considered, the values of pressure and velocity obtained are within the normal ranges. Finally the model is used to verify if there exist irregularities in the blood flow in both healthy subjects and sick patients.展开更多
In this paper we consider a class of polynomial planar system with two small parameters,ε and λ,satisfying 0<ε《λ《1.The corresponding first order Melnikov function M_(1) with respect to ε depends on λ so tha...In this paper we consider a class of polynomial planar system with two small parameters,ε and λ,satisfying 0<ε《λ《1.The corresponding first order Melnikov function M_(1) with respect to ε depends on λ so that it has an expansion of the form M_(1)(h,λ)=∑k=0∞M_(1k)(h)λ^(k).Assume that M_(1k')(h) is the first non-zero coefficient in the expansion.Then by estimating the number of zeros of M_(1k')(h),we give a lower bound of the maximal number of limit cycles emerging from the period annulus of the unperturbed system for 0<ε《λ《1,when k'=0 or 1.In addition,for each k∈N,an upper bound of the maximal number of zeros of M_(1k)(h),taking into account their multiplicities,is presented.展开更多
In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed s...In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.展开更多
A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simul...A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.展开更多
文摘This paper presents the development of the blood flow simulation in two dimensions over the real geometry of the femoral artery. The Navier-Stokes equations are solved using the finite element method, to obtain the distributions of the blood pressure and flow velocity in multiple instants of time and different places of the femoral artery and thus determine the current condition of the blood vessels. The velocity field shows a laminar behavior,where, the velocity is higher in the center of the artery and decreases as the blood flow approaches artery walls. In spite of all artery and blood flow properties not being considered, the values of pressure and velocity obtained are within the normal ranges. Finally the model is used to verify if there exist irregularities in the blood flow in both healthy subjects and sick patients.
基金The first author is supported by the National Natural Science Foundation of China(11671013)the second author is supported by the National Natural Science Foundation of China(11771296).
文摘In this paper we consider a class of polynomial planar system with two small parameters,ε and λ,satisfying 0<ε《λ《1.The corresponding first order Melnikov function M_(1) with respect to ε depends on λ so that it has an expansion of the form M_(1)(h,λ)=∑k=0∞M_(1k)(h)λ^(k).Assume that M_(1k')(h) is the first non-zero coefficient in the expansion.Then by estimating the number of zeros of M_(1k')(h),we give a lower bound of the maximal number of limit cycles emerging from the period annulus of the unperturbed system for 0<ε《λ《1,when k'=0 or 1.In addition,for each k∈N,an upper bound of the maximal number of zeros of M_(1k)(h),taking into account their multiplicities,is presented.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271261,11461001)
文摘In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.
基金supported in part by the NSF Grant DMS 0906440 and DMS 1206438Fund of Indiana Universitysupported by the National Science Council of Taiwan under research grants NSC-100-2115-M-009-009-MY2.
文摘A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.
