Extreme Multistability and Antimonotonicity in a Shinriki Oscillator with Two Flux-Controlled Memristors

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.

The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

Modeling of In0.17Ga0.83N/InxGa1–xN/AlyGa1–yN light emitting diode structure on ScAlMgO4 (0001) substrate for high intensity red emission

An In0.17Ga0.83N light emitting diode (LED) structure on ScAlMgO4 (0001) substrate is modeled for high intensity red emission. The high indium composition (In > 15%) inside the c-plane polar quantum well (QW) for longer wavelength emission degrades the structural and optical properties of LEDs because of induced strain energy and quantum confinement Stark effect. To compensate these effects, it has been demonstrated by simulation that an AlyGa1–yN cap layer of 2 nm thick and Al composition of 17% deposited onto QW of 3 nm thick and In composition of 35% will allow to have less defect density and higher intensity red emission at 663 nm than that of In0.17Ga0.83N/InxGa1–xN LEDs grown on ScAlMgO4 (0001) substrate. This LED structure has perfect in-plane equilibrium lattice parameter (αeq = 3.249 Å) and higher logarithmic oscillator strength (Γ = –0.93) values.

A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation

In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.

Inverse problem of breaking line identification by shape optimization

An inverse breaking line identification problem formulated as an optimal control problem with a suitable PDE constraint is studied. The constraint is a boundary value problem describing the anti-plane equilibrium of an elastic body with a stress-free breaking line under the action of a traction force at the boundary. The behavior of the displacement is observed on a subset of the boundary, and the optimal breaking line is identified by minimizing the {L^{2}}-distance between the displacement and the observation. Then the optimal control problem is solved by shape optimization techniques via a Lagrangian approach. Several numerical experiments are carried out to show its performance in diverse situations.