In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincare maps of the flow observed in Khakhar et al. is resolved. It is shown that in long...

For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M, N ; f) of continuous maps homotopic to f : M → N . We will show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f , denoted Λf,f , equals zero. Since Λf,f is equal to ...

This paper examines the recurrent behaviour of a class of hybrid systems which periodically switch between diierent rst order integrators. The analysis is based on studying the Poincare map of the hybrid system. For switched integrator systems, the Poincare maps are linear mappings thereby allowing easy characterization of the system's stability. Extending these results to more general classes ...

We do a study of the real representations of the Poincare group, motivated by the following: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity...

Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincare map generated by the model is conjugate to the shift map on two symbols. The...

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method...

Abstract: In this paper, the nonlinear dynamical behaviors of an active magnetic bearing-rotor system are investigated using numerical simulation. Firstly, the nonlinear magnetic force is obtained by Taylor series. Secondly, the primary-internal resonance of an AMBRS(active magnetic bearing) -rotor system is studied with the help of LungKutta method. To analyze the motion characters of system, ...

Poincare half-maps can be used to characterize the behavior of recurrent dynamical systems. Their usefulness is demonstrated for a linear three-dimensional single-loop feedback system. In this example everything can be calculated analytically. The resulting half-maps are "benign" endomorphic maps with a complicated topological structure. This is surprising since the combination of two such half...

Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincare maps search for suitable path through the interconnected web of periodic orbits and invariant manifolds found in multi-body gravitational systems. This paper is concerned with extraction interactive visual exploration this structural landsca...

A novel manner of one-legged bipedal locomotion (i.e., ballistic flip) is proposed in this paper. A flip is composed of three sequential stages: stance phase, flight phase and touchdown. During the stance phase, the two objectives of control, constant locomotive speed and taking off at the end of stance phase, are achieved via a control algorithm based on nonlinear feedback linearization. The f...