It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating varie...It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.展开更多
An experimental procedure is conducted to investigate the mechanism of the non-monotonic characteristic between curing temperature and mechanical behaviors of the Kevlar/epoxy composite in macro and micro levels. Diff...An experimental procedure is conducted to investigate the mechanism of the non-monotonic characteristic between curing temperature and mechanical behaviors of the Kevlar/epoxy composite in macro and micro levels. Different specimens are fabricated at four different curing temperatures and tested with ±45° off-axis tensile loading on a universal test machine coupled with digital image correlation(DIC). Moreover, the environmental scanning electron microscope(SEM) was used to obtain the micrographs and reveal their mechanism. The tested results show that the tensile mechanical behaviors are sensitive to the curing temperature and the relationship is non-monotonic. Also, as the temperature increases, the thicknesses of the specimens are significantly enlarged. By analyzing the SEM micrographs of the matrix grooves in the damage zone and DIC strain contours, it is concluded that the non-monotonic relationship is dominated by the properties of the Kevlar/epoxy interfaces and deformation of the distorted fibers.展开更多
文摘It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.
基金supported by the National Natural Science Foundation of China(Grant Nos.11672105,11232004)Natural Science Foundation of Hunan Province(Grant No.2016JJ1009)
文摘An experimental procedure is conducted to investigate the mechanism of the non-monotonic characteristic between curing temperature and mechanical behaviors of the Kevlar/epoxy composite in macro and micro levels. Different specimens are fabricated at four different curing temperatures and tested with ±45° off-axis tensile loading on a universal test machine coupled with digital image correlation(DIC). Moreover, the environmental scanning electron microscope(SEM) was used to obtain the micrographs and reveal their mechanism. The tested results show that the tensile mechanical behaviors are sensitive to the curing temperature and the relationship is non-monotonic. Also, as the temperature increases, the thicknesses of the specimens are significantly enlarged. By analyzing the SEM micrographs of the matrix grooves in the damage zone and DIC strain contours, it is concluded that the non-monotonic relationship is dominated by the properties of the Kevlar/epoxy interfaces and deformation of the distorted fibers.
