How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the p...How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.展开更多
The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surf...The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surface,which presents a challenge for updating plastic stress.Current research primarily focuses on modified smooth GZZ criteria or approximate solutions,which inevitably lead to increased computational costs or inaccuracies.In this paper,an accurate stress updating algorithm is proposed based on the original GZZ criterion.The algorithm operates entirely in the principal stress space,where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating.This approach simplifies the GZZ criterion compared to its formulation in general stress space.The return mapping is employed to compute the updated stress and consistent stiffness matrix,facilitating calculations using both finite element implicit and explicit algorithms.Finally,the accuracy of the proposed method is validated using rock true triaxial test data and semianalytical solutions for stresses and displacement around a circular opening under the GZZ criterion.展开更多
基于Lemaitre and Chaboche非线性随动强化理论、等向强化和Mises屈服准则,建立了复杂加载模式下非线性混合强化材料模型的弹塑性应力应变本构关系,并采用Backward Euler切向预测径向返回算法计算应力应变增量.基于ABAQUS开发式程序接口...基于Lemaitre and Chaboche非线性随动强化理论、等向强化和Mises屈服准则,建立了复杂加载模式下非线性混合强化材料模型的弹塑性应力应变本构关系,并采用Backward Euler切向预测径向返回算法计算应力应变增量.基于ABAQUS开发式程序接口,编写了非线性混合强化材料模型用户子程序.以Numisheet’93板料U型弯曲考题为例,分析了不同材料强化模型对板料回弹量的影响.结果表明,线性随动强化因模拟板料成形后的应力最小而低估了回弹量,各向同性强化因模拟成形后的应力最大而使预测的回弹量偏大.与Numisheet’93实验值的比较可知,对于复杂加载问题,采用非线性混合强化材料模型预测板料回弹量的精度最高.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.60871085)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y1100119)
文摘How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.
基金the financial support provided by the National Key R&D Program of China(Grant No.2022YFB2302102)the National Natural Science Foundation of China(Grant Nos.42472340 and 42072308).
文摘The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surface,which presents a challenge for updating plastic stress.Current research primarily focuses on modified smooth GZZ criteria or approximate solutions,which inevitably lead to increased computational costs or inaccuracies.In this paper,an accurate stress updating algorithm is proposed based on the original GZZ criterion.The algorithm operates entirely in the principal stress space,where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating.This approach simplifies the GZZ criterion compared to its formulation in general stress space.The return mapping is employed to compute the updated stress and consistent stiffness matrix,facilitating calculations using both finite element implicit and explicit algorithms.Finally,the accuracy of the proposed method is validated using rock true triaxial test data and semianalytical solutions for stresses and displacement around a circular opening under the GZZ criterion.
文摘基于Lemaitre and Chaboche非线性随动强化理论、等向强化和Mises屈服准则,建立了复杂加载模式下非线性混合强化材料模型的弹塑性应力应变本构关系,并采用Backward Euler切向预测径向返回算法计算应力应变增量.基于ABAQUS开发式程序接口,编写了非线性混合强化材料模型用户子程序.以Numisheet’93板料U型弯曲考题为例,分析了不同材料强化模型对板料回弹量的影响.结果表明,线性随动强化因模拟板料成形后的应力最小而低估了回弹量,各向同性强化因模拟成形后的应力最大而使预测的回弹量偏大.与Numisheet’93实验值的比较可知,对于复杂加载问题,采用非线性混合强化材料模型预测板料回弹量的精度最高.
