Synchronization of simplest two-component Hartley’s chaotic circuits: influence of channel

Firstly, the synchronization problem of the simplest two-component Hartley chaotic systems is considered. A simple and effective controller is used to achieve synchronization between the drive and response systems. The proposed controller is built around a linear and a nonlinear parts with each contributing to the achievement of the synchronization process. The stability of the drive–response systems framework is proved through the Lyapunov stability theory. Secondly, the impact of channel on the signal coming from the drive system to synchronize the response system is taken into consideration. In this second part, the conditions to obtain synchronization between both master and slave systems are investigated. For the purpose of illustration, PSpice simulations are given as complement of the numerical analysis.     

Dynamics of the plane and solitary waves in a Noguchi network:Effects of the nonlinear quadratic dispersion

We consider a modified Noguchi network and study the impact of the nonlinear quadratic dispersion on the dynamics of modulated waves. In the semi-discrete limit, we show that the dynamics of these waves are governed by a nonlinear cubic Schrodinger equation. From the graphical analysis of the coefficients of this equation, it appears that the nonlinear quadratic dispersion counterbalances the effects of the linear dispersion in the frequency domain. Moreover, we establish that this nonlinear quadratic dispersion provokes the disappearance of some regions of modulational instability in the dispersion curve compared to the results earlier obtained by Pelap et al.(Phys. Rev. E 91 022925(2015)). We also find that the nonlinear quadratic dispersion limit considerably affects the nature, stability, and characteristics of the waves which propagate through the system. Furthermore, the results of the numerical simulations performed on the exact equations describing the network are found to be in good agreement with the analytical predictions.     

Screening effect on the polaron by plasmons in the field of self-action potential in a planar nanocrystal

We investigate the effect of plasmon screening on the polaron characteristics following the Feynman variational method and find that the screening considerably reduces the polaron characteristics, as plasmon density increases. We establish that the factor contributing to this screening not only depends on the concentration, but also on the anisotropy of the dielectric permittivities, the temperature, and charge as well as on the layer width. The contribution of the surface effects to the total polaron characteristics are exceedingly small and can therefore be safely neglected. The characteristics are found to be strongly dependent on the screen function referred to as the F-function, and when screening parameters vanish this F-function vanishes and the polaron characteristics reduce to the familiar non-screen ones. The decrease of the polaron characteristics with an increase of the screening parameter is not exactly exponential but mimics that of a pseudoatom which has a much more slow decrease.     

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractional-order systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.     

Bipolaron in a quasi-0D quantum dot

Bipolaron states in a quasi-0D quantum dot with a spherical parabolic confinement potential are investigated by applying the Feynman variational principle. The bipolaron coupling energy and self-action potential energy are found to increase with an increase in the Fröhlich electron–phonon-coupling constant. There is also a non-monotonic dependence of the bipolaron coupling energy on the quantum dot radius. With decreasing structure radius the bipolaron coupling energy increases. However, from a critical radius it starts decreasing as the radius decreases, due to the dominance of the coulomb-to-phonon mediated interaction. When electrons in the bipolaron are forcefully neighboured, the polarization of the structure is intensified and consequently there is Coulomb repulsion. The possibility of bipolaron formation depends on the strength of the direct Coulomb repulsion which, in turn, depends on the quantum dot radius. The main contribution to the bipolaron coupling energy comes from the self-action potential. This self-action potential energy influences the energy state of the bipolaron considerably. The ratio of optical-to-static dielectric constants significantly affects the bipolaron coupling energy.     

Material forces in thermoelastic ferromagnets

A systematic construction of the canonical balance of momentum (“pseudomomentum” on the material manifold) and energy is presented for materially inhomogeneous thermoelastic hard ferromagnets in which both exchange forces and magnetic-spin inertia are taken into account. The latter is of the gyroscopic type and endows the sources of quasi-inhomogeneities in the balance of pseudomomentum with special properties. The equations obtained will prove useful in further studies of the fracture of hard ferromagnets and of the propagation of phase-transition fronts in such materials. Received January 23, 1996     

Phase-Transition Fronts in Deformable Ferromagnets

The notions of material inhomogeneity and balance of pseudomomentum are exploited to construct a thermodynamical framework for propagating coherent phase-transition fronts in ferromagnetic thermoelastic materials. This analysis results in the proposal of thermodynamically admissible criteria of progress for the fronts. Magnetoelastic domain walls may be viewed as special cases of such fronts.