In 1979, Moffatt pointed out that the conventional treatment of the simplest self-exciting homopolar disc dynamo has inconsistencies because of the neglect of induced azimuthal eddy currents, which can be resolved by introducing a segmented disc dynamo. Here we return to the simple dynamo system proposed by Moffatt, and demonstrate previously unknown hidden chaotic attractors. Then we study multistability and coexistence of three types of attractors in the autonomous dynamo system in three dimensions: equilibrium points, limit cycles and hidden chaotic attractors. In addition, the existence of two homoclinic orbits is proved rigorously by the generalized Melnikov method. Finally, by using Poincaré compactification of polynomial vector fields in three dimensions, the dynamics near infinity of singularities is obtained.
In this paper, an extended Rikitake system is studied. Several issues, such as Hopf bifurcation, coexistence of stable equilibria and hidden attractor, and dynamics analysis at infinity are investigated either analytically or numerically. Especially, by a simple linear transformation, the wide range of hidden attractors is noticed, and the Lyapunov exponents diagram is given. The obtained results show that the unstable periodic solution generated by Hopf bifurcation leads to the hidden attractor. The existence of hidden attractors that may render the system's behavior unpredictable not only depends on the value of system parameters but also on the value of initial conditions. The phenomena are important and potentially problematic in engineering applications.
Optical resonator arrays are highly important fundamental units for integrated photoelectric devices, such as on‐chip logical circuits, high‐precision sensors, and laser displays. Whispering gallery mode (WGM) microrings (MRs) could reduce the optical losses and provide a small mode volume, which is helpful for the integration of miniaturized devices. However, there still is a great challenge to produce and pattern the circular resonator. Here, a facile poly(dimethylsiloxane) (PDMS) ring‐hole‐stamp confined solution‐growth method is used to fabricate organic (E)‐3‐(4‐(di‐p‐tolylamino)phenyl)‐1‐(1‐hydroxynaphthalen‐2‐yl)prop‐2‐en‐1‐one (DPHP) MR arrays. Low‐threshold multi‐mode near‐infrared lasing is successfully achieved in the single MRs and DPHP MR arrays at room temperature. At the same time, their lasing behaviors change obviously in the lasing intensity, emission position, lasing mode, and lasing threshold after contacting with water and NaOH solution. The present work is a major step for realizing compact near‐infrared optoelectronic devices.
The objective of this study is to evaluate local response to a bioactive glass based composite putty (NovaBone Putty) in a vertebral body defect model in sheep, as compared to NovaBone, a bioactive glass particulate. Two time periods were used for the study, 6 and 12 weeks. Empty defects were also used as a control. In comparing the three test groups, the relative amount of new bone for both grafted defects was substantially greater than for the empty controls (P < 0.05). At 6 weeks, the bone formation was 42% for NovaBone Putty, 27% for NovaBone and 1.2% for the ungrafted empty defect. At 12 weeks, the bone formation was 51.4% for NovaBone Putty, 47.3% for NovaBone and 5.1% for the empty defect. NovaBone Putty, the test material, had greater bone content than the NovaBone, both of which were significantly greater than the empty control.
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