Dynamical Behavior of a New Chaotic System with One Stable Equilibrium

This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.

Digital processing of shadowgraph images taking into account the diffraction of light at a shock front

The aim of the study is to determine the shock wave position in experimental shadowgraph images and to evaluate the accuracy by digital image processing. The experimental images were obtained with the shock tube with a rectangular channel. The shadowgraph optical system formed a parallel light beam. It passed through the plane-parallel quartz glasses of the shock tube test section. The process synchronization system at the facility allows registering the shadowgraph images of unsteady flows with shock waves with a high-speed camera or with a single frame camera. The obtained spatial intensity profiles were used to determine the coordinates of gas-dynamic discontinuities at different stages of the flow evolution. shadowgraph patterns were analysed taking into account diffraction at the shock front in case of a laser light source.

Predicting traffic flow evolution on degraded road networks

In order to investigate the influence of the forecast information provided by ATIS on the traffic flow evolution of the degraded road network, a weighted moving average based travel time forecasting method is designed, and the path update rule is established in the forecast information environment. The proposed route update rule is used to analyze the effects of prediction information dependency parameters, information quality parameters, weight parameters and network degradation degree on traffic flow evolution for a small test network. The results show that: 1) there is a threshold value for the dependence of travelers on the predicted information in the information environment, when the dependence is less than this value, the traffic flow quickly evolves to a stable state, and when the dependence is greater than this value, the network traffic flow will oscillate; 2) there is a situation where the higher the quality of the predicted information provided by the information system, the worse the traffic flow evolution; 3) for a particular degraded network, there is a certain optimal combination of weights that can be used to guide the release of forecast information of the network; 4) the smaller the degradation of the road network, the greater the role played by the forecast information.

Contactless generation and trapping of hydrodynamic knots in sessile droplets by acoustic screw dislocations

Hydrodynamics knots are not only promising elementary structures to study mass and momentum transfer in turbulent flows, but also potent analogs for other topological problems arising in particle physics. However, experimental studies of knots are highly challenging due to the limited control over knot generation and difficult observation of the resulting fast-paced multiscale flow evolution. In this paper, we propose using acoustic streaming to tie hydrodynamic knots in fluids. The method is contactless, almost instantaneous and is relatively insensitive to viscosity. Importantly, it allows starting from quite arbitrary three dimensional flow structures without relying on external boundary conditions. We demonstrate our approach by using an acoustic screw dislocation to tie a knot in a sessile droplet. We observe an inversion of the knot chirality (measured by the hydrodynamic helicity) as the topological charge of the screw dislocation is increased. Combined with recent progress in acoustic field synthesis, this work opens a window to study more complex hydrodynamic knot topologies at a broader range of space and timescales.