There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given...There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.展开更多
If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a...If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a Poisson curve(after a suitable reparametrization). This fact reveals some interesting self-simi- lar structures in case of regular n-gons in the plane.展开更多
The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （...The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.展开更多
The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. ...The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.展开更多
In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the lin...In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.展开更多
The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. General...The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.展开更多
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite arra...It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.展开更多
In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into...In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation(ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincaré bifurcation theory. Simulation is carried out to verify the theoretical result.展开更多
基金Supported by the National Natural Science Foundation of china
文摘There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.
文摘If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a Poisson curve(after a suitable reparametrization). This fact reveals some interesting self-simi- lar structures in case of regular n-gons in the plane.
基金supported by the National Natural Science Foundation of China (No.50809003)the National Foundation for Excellent Doctorial Dissertation of China (200025).
文摘The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.
文摘The global phase portrait describes the qualitative behaviour of the solution set of a nonlinear ordinary differential equation, for all time. In general, this is as close as we can come to solving nonlinear systems. In this research work we study the dynamics of a bead sliding on a wire with a given specified shape. A long wire is bent into the shape of a curve with equation z = f (x) in a fixed vertical plane. We consider two cases, namely without friction and with friction, specifically for the cubic shape f (x) = x3−x . We derive the corresponding differential equation of motion representing the dynamics of the bead. We then study the resulting second order nonlinear ordinary differential equations, by performing simulations using MathCAD 14. Our main interest is to investigate the existence of periodic solutions for this dynamics in the neighbourhood of the critical points. Our results show clearly that periodic solutions do indeed exist for the frictionless case, as the phase portraits exhibit isolated limit cycles in the phase plane. For the case with friction, the phase portrait depicts a spiral sink, spiraling into the critical point.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61272069,61272114,61073026,61170031,and 61100076)
文摘In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.
基金supported by the National Basic Research Program of China(Grant No.2010CB832800)the National Natural Science Foundation of China(Grant Nos.11175160 and 11275075)the Natural Science Foundation of Key Projects of Hubei Province,China(Grant No.2013CFA045)
文摘The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.
文摘It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.
基金Supported by the National Natural Science Foundation of China(Grant No.12061016)the Applied Mathematics Center of GuangxiFoundation of Guangxi Technological College of Machinery and Electrcity(Grant No.2021YKYZ010).
文摘In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation(PDE).The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation(ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincaré bifurcation theory. Simulation is carried out to verify the theoretical result.
