Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study the analytical property of the Melnikov function near the origin for near-Hamiltonian system having the origin as its elementary center or nilpotent center. Based on the method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Then, we consider the symmetric singular points and present the conditions for one of them to be elementary center or nilpotent center. Under the condition for the singular point to be a center, we obtain the normal form of the Hamiltonian systems near the center. Moreover, perturbing the symmetric cubic Hamiltonian systems by cubic polynomials, we consider limit cycles bifurcating from the center using the algorithm to compute the coefficients of Melnikov function. Finally, perturbing the symmetric hamiltonian system by symmetric cubic polynomials, we consider the number of limit cycles near one of the symmetric centers of the symmetric near-Hamiltonian system, which is same to that of another center

Photoacoustic Identification of Laser-induced Microbubbles as Light Scattering Centers for Optical Limiting in Liquid Suspension of Graphene Nanosheets

Liquid suspensions of carbon nanotubes, graphene and transition metal dichalcogenides have exhibited excellent performance in optical limiting. However, the underlying mechanism has remained elusive and is generally ascribed to their superior nonlinear optical properties such as nonlinear absorption or nonlinear scattering. Using graphene as an example, we show that photo-thermal microbubbles are responsible for the optical limiting as strong light scattering centers: graphene sheets absorb incident light and become heated up above the boiling point of water, resulting in vapor and microbubble generation. This conclusion is based on direct observation of bubbles above the laser beam as well as a strong correlation between laser-induced ultrasound and optical limiting. In-situ Raman scattering of graphene further confirms that the temperature of graphene under laser pulses rises above the boiling point of water but still remains too low to vaporize graphene and create graphene plasma bubbles. Photo-thermal bubble scattering is not a nonlinear optical process and requires very low laser intensity. This understanding helps us to design more efficient optical limiting materials and understand the intrinsic nonlinear optical properties of nanomaterials

Physicochemical and Electrochemical Properties of 1,1,2,2-Tetrafluoroethyl-2,2,3,3-Tetrafluoropropyl Ether as a Co-Solvent for High-Voltage Lithium-Ion Electrolytes

© 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Although high-voltage positive electrode materials for high energy density lithium-ion batteries have gained a great attention, the lack of compatible electrolytes with sufficiently high oxidative stability to deliver an excellent cycling ability restricts their practical application. Fluorinated solvents are considered as promising candidates for high-voltage electrolyte solvents. In this study, we select 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE) with a high boiling point, low cost, and good SEI-filming ability as a co-solvent of fluoroethylene carbonate-based electrolytes and extensively investigate its physicochemical and electrochemical properties for applications in high-voltage lithium-ion batteries. Our experimental results show that the TTE-containing electrolyte exhibits not only a high oxidative stability up to 5.5 V (vs. Li/Li+), but also excellent wettability with the separator. In addition to high discharge capacity and increased coulombic efficiency of the Li/LiNi0.5Mn1.5O4 half-cell assembled with the TTE-containing electrolyte cycled between 3.0 and 4.9 V, the cell also displays a high rate capability. This work shows that partially fluorinated ethers, e. g., TTE, are promising co-solvents for high-voltage electrolytes that can enable commercial development of high energy density lithium-ion batteries

Nano-channel-based physical and chemical synergic regulation for dendrite-free lithium plating

Uncontrollable dendrite growth resulting from the non-uniform lithium ion (Li+) flux and volume expansion in lithium metal (Li) negative electrode leads to rapid performance degradation and serious safety problems of lithium metal batteries. Although N-containing functional groups in carbon materials are reported to be effective to homogenize the Li+ flux, the effective interaction distance between lithium ions and N-containing groups should be relatively small (down to nanometer scale) according to the Debye length law. Thus, it is necessary to carefully design the microstructure of N-containing carbon materials to make the most of their roles in regulating the Li+ flux. In this work, porous carbon nitride microspheres (PCNMs) with abundant nanopores have been synthesized and utilized to fabricate a uniform lithiophilic coating layer having hybrid pores of both the nano- and micrometer scales on the Cu/Li foil. Physically, the three-dimensional (3D) porous framework is favorable for absorbing volume changes and guiding Li growth. Chemically, this coating layer can render a suitable interaction distance to effectively homogenize the Li+ flux and contribute to establishing a robust and stable solid electrolyte interphase (SEI) layer with Li-F, Li-N, and Li-O-rich contents based on the Debye length law. Such a physical-chemical synergic regulation strategy using PCNMs can lead to dendrite-free Li plating, resulting in a low nucleation overpotential and stable Li plating/stripping cycling performance in both the Li‖Cu and the Li‖Li symmetric cells. Meanwhile, a full cell using the PCNM coated Li foil negative electrode and a LiFePO4 positive electrode has delivered a high capacity retention of ∼ 80% after more than 200 cycles at 1 C and achieved a remarkable rate capability. The pouch cell fabricated by pairing the PCNM coated Li foil negative electrode with a NCM 811 positive electrode has retained ∼ 73% of the initial capacity after 150 cycles at 0.2 C

Linearizability conditions for 1:-5 Lotka-Volterra two-dimensional complex quartic systems

In this paper we investigate the linearizability problem for the planar Lotka-Volterra complex quartic systems which are 1:-5 linear systems perturbed by homogeneous polynomials of degree 4, that is to say, we consider systems of the form ẋ = x(1-a30x3-a21x2y-a12xy2-a03y3), ẏ =-y(5-b30x3-b21x2y-b12xy2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found

Bifurcations of planar Hamiltonian systems with impulsive perturbation

In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists