David Yemélé

Suppression of the fast and slow modulated waves mixing in the coupled nonlinear discrete LC transmission lines

The conditions for the propagation of fast- and slow-modes of modulated waves on two coupled discrete nonlinear LC transmission lines are examined, each line of the network containing a finite number of cells. We show analytically that the use of an appropriate unit cell, a band-pass filter and a convenient associated choice of the intermediate coupling capacitor between the two lines permits the avoidance of the crucial problem of the mixing of waves of different modes in the network. It is observed that there is good qualitative and quantitative agreement between the analytical results and numerical experiments.

Dynamics of modulated waves in a nonlinear discrete LC transmission line: dissipative effects

We investigate analytically the dynamics of modulated waves in a nonlinear LC transmission line with dissipative elements. The damped nonlinear Schrodinger equation governing slowly modulated wave propagation is derived. Considering modulated plane wave propagating in the line, we establish their criteria of instability and show that, in the case of weak dissipation, there are no significant changes for the bandwidth frequency where the network may exhibit modulational instability (MI). However, dissipative losses constitute a great limiting factor to the experimental observation of the MI phenomenon. We show that the amplitude decreases, the width increases while the velocity remains constant when the soliton propagates along the dissipative network.

Kink compactons in the thermodynamic properties of nonlinear Klein–Gordon systems

Thermodynamic properties of one-dimensional nonlinear Klein–Gordon systems with anharmonic interparticle interaction are studied by means of the transfer integral method. We show that the presence of kink compactons is signalled by a term proportional to exp [−χ(βEkc)3/4] in the free energy where Ekc is the static kink compacton energy and χ a model temperature independent coefficient.

Temperature dependence of first lattice corrections to the free-energy of kink compacton-bearing systems

The free-energy of discrete nonlinear Klein–Gordon (NKG) systems with anharmonic interparticle interactions is derived by means of the transfer integral operator method, with the first lattice corrections and kink–kink interactions taken into account. Two particular substrate potentials are considered: the −four and the sine-Gordon (sG). We show that, in the general case where the system exhibits the kink soliton like excitations, the correction factors, due to the lattice discreteness, appearing in the free-energy and in the lattice corrected static kink soliton energy, depend on the temperature through a coupling of the interparticle anharmonicity strength to the temperature. Similarly, in the purely anharmonic NKG systems, characterized by the absence of the linear dispersion, where thermodynamic properties are sensitive to kink compactons, we find also that the correction factors are temperature dependent. In both cases, they decrease with increasing temperatures, although the correction factors verify different temperature laws.

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions |μ|≥0.1

Structural static stability and dynamic chaos of active electromagnetic bearing systems: Analytical investigations and numerical simulations:

\vert \mu \vert \geq0.1

Compact envelope dark solitary wave in a discrete nonlinear electrical transmission line

is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.

Kink compactons in models with parametrized periodic double-well and asymmetric substrate potentials

The complete nonlinear dynamics of an active magnetic bearing (AMB) with proportional and derivative controller is revisited analytically. Through the stability analysis of the second-order nonlinear differential equation governing the dynamics of the system, a state diagram is obtained in the proportional gain and precontrol current space. This diagram is fundamental and may help in making important design decisions namely in the identification of a controller for the complete range of the rotor mass, in order to ensure structural stability. In particular, we find that there exists a threshold for the proportional gain whose expression depends both on the inner radius of the bearing and on the bias current, and below which no stable dynamics of the system can occur. In the operating range, we show that the system exhibits a rich dynamics characterized by the possibility for the existence of many kinds of nonlinear localized excitations in the transient state, which may lead to an irregular or a chaotic behavior of the shaft. In this regime, the expressions of the critical running speed obtained by means of the Melnikov theory indicate its dependence on the AMB characteristic parameters.