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Potassium ion batteries (PIBs) have drawn considerable interest because of the resource-abundance and tempting electrochemical potential of potassium. However, developing high-performance anodes for PIBs with superior reversible capacity and ultralong stability is still a huge challenge to meet the requirements of sustainable and cost-effective large area energy storage systems. To address the above-mentioned issues, we report for the first time a simple in situ growth strategy to synthesize pillared graphene nanosheets with expanded interlayer spacing as free-standing flexible electrodes for PIBs. The expanded interlayer spacing is confirmed to accelerate ion transmission by kinetics. The graphene nanosheet/NiO-500 (GS/NiO-500) composite assembled binder-free flexible anode delivers ultrahigh reversible capability (416.1 mA h g−1 at 0.1 A g−1), excellent rate performance (305.6 mA h g−1 at 1 A g−1) and superior capacity retention (82.6% over 3000 cycles at 1 A g−1). This study provides ideas for the development of fast charging potassium electrode materials and promotes the commercialization of large-scale energy storage systems.

Purpose This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework. Design/methodology/approach In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter. Findings Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor. Originality/value The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.

In this paper, for the first time, fractional Taylor–Jumarie series expansion is used to solve a glass of time-fractional delay partial differential equation by piecewise interpolation reproducing kernel method (RKM), this class of equations describe sand motion model in beach formation. The aim of this work is to obtain more accurate numerical solution by fractional Taylor–Jumarie series expansion and piecewise interpolation technique. Three numerical experiments are provided to show the advantage of this method, the results show the characteristics of sand motion. The research in this paper is the theoretical basis for further sand motion study.

With the rapid development of information technology, the data scale expands unceasingly, produce a large amount of image data, a massive image data processing has also is an important technology. Traditional processing techniques, in dealing with such a large scale of image data, have been unable to meet the requirements. One of the important reason is that whether the c ++ or Java, there is memory leak problem, when the data is the relatively small size, these problems may be insignificant, but when the data is very large, will highlight these shortcomings, will lead to serious program crashes, the system outage, ultimately unable to achieve expected goal. In considering the data processing efficiency, stability, is proposed in this paper, based on multithreading, a dynamic self-healing capacity of mass image data processing technology, compared with the traditional technology can improve the efficiency and improve the stability. Finally, after the experimental results verify that the method is effective.

A novel approach for generating real tetrapterous butterfly attractors from Lorenz system is proposed in this paper. The key strategy is to create two additional index-2 equilibrium points by introducing a single pulse function to the third equation of Lorenz system. The evolutions of the strange tetrapterous butterfly attractor are investigated. Furthermore, two coexisting dipterous attractors under different initial conditions are also found. Both the numerical simulations and experimental results demonstrate that the generations of the tetrapterous butterfly attractors by utilizing this control method in Lorenz system are effective.

To seek for a hyperchaotic attractor with complex topological attractor structure, a new four-dimensional continuous autonomous hyperchaotic system is proposed. Within a wider region of the variation of the control parameter, this system can generate novel hperchaotic and chaotic attractors along with quasi-periodic and periodic orbits. By employing Lyapunov exponent spectrum, bifurcation diagram, Poincare mapping and phase portrait, etc., the existence of hyperchaotic behaviors of new system is verified and the dynamical routes from period, quasi-period, chaos and hyperchaos are observed. Furthermore, a practical circuit is designed to realize the system, which the experimental results indicate that new four-dimensional hyperchaotic system is a realizable chaotic system with potential values of engineering applications.

A new hyperchaotic circuit is presented by adding a supplementary circuit block to a chaotic Lu system, from which a novel unsymmetrical hyperchaotic attractor is found. In order to study its dynamical behaviors, this circuit is analyzed in detail by a four-dimensional continuous autonomous dissipative system. The analytical results indicate that the presented circuit can generate hyperchaos, chaos, period and quasi-period in different parameter ranges. In particular, the phase portraits given by the analysis are in good agreement with the experimental observations.

A RLC parallel resonance circuit was built on the basis of the original fourth-order Colpitts oscillator. An improved Colpitts oscillator was given. The Lyapunov exponent spectrum, bifurcation diagram and phase trajectories of chaotic attractors were calculated by control theory and numerical methods. Analysis shows that the change of resistance value R of the RLC parallel resonance circuit to control Colpitts oscillator can obtain better dynamic characteristics than the original fourth-order Colpitts oscillator, and the control circuit implementation is very simple. More interestingly, it is found that the bifurcation behavior of the new system has the Fengenbaum first constant in the logarithm law. The experimental circuit of the new system was designed. The experimental results and theoretical analysis have a good consistency, indicating that this control scheme is of feasibility and better practicability.

Masses of highly uniform silica-shelled carbon nanotube (CNT) coaxial fibers are synthesized in a single step by the catalytic gas-flow reaction method. This method involves the generation of CNTs in the gas flow from the injection catalytic gas flow reactions and the in situ deposition of silica over the gas dispersed CNTs via the decomposition of a polysiloxane downstream of the CNT flow. Silicone grease consisting of polydimethylsiloxane (PDMS) was used as the precursor for silica. The coaxial fibers produced by this process are highly uniform, with each fiber containing a CNT core enclosed in a uniform silica shell. The growth of silica from PDMS over CNTs is efficient, with ∼50 wt% of PDMS converted into silica. The key controlling factor of the growth of the coaxial fibers is the hydrogen flow, which is required for both the growth of CNTs and the formation of silica from the polysiloxanes. The highly localized deposition of silica over the CNTs with the composition of Si/O in silica close to that of PDMS is likely associated to the condensation from Si–O chains decomposed from PDMS. The silica phase of the coaxial fiber resulting from this process is highly oxygen deficient and, as the result, the coaxial fibers emit strong photoluminescence under ultraviolet excitation. Meanwhile, the silica shell phase is highly hydrogenated, which permits the uniform bonding of nanocrystallines on the fibers. The present process provides an effective means to fabricate high quality silica-CNT coaxial fibers for potential functional applications.