Input-to-state stability and stabilization for switched nonlinear positive systems

Input-to-state stability (ISS) analysis and stabilization are concerned in this paper for switched nonlinear positive systems (SNPS), where the deterministic and random switching are both included. For general SNPS, switched affine nonlinear positive systems (SANPS) and switched linear positive systems (SLPS) with deterministic and some kinds of random ”slow” switching, some criterions on ISS are provided. From the criterions for SANPS and SLPS, the ISS properties can be judged just by the differential, algebraic and switching characteristics of the systems. Further, based on the criterions for SANPS and SLPS, some state feedback controllers are designed such that the closed-loop systems be positive, ISS or ISS in some stochastic senses. Four simulation examples verify the validity of our results.     

Nonlinear microwave emission in Ba0.6K0.4BiO3 crystals near Tc

We report a detailed investigation of harmonic generation at microwave frequencies in Ba_0.6K_0.4BiO₃ crystals. Second- and third-harmonic signals are investigated as a function of temperature, external magnetic field and input power level, at temperatures close to T_c. The experimental data are discussed in the framework of a phenomenological theory, based on the two-fluid model, which assumes that the microwave and the static fields, penetrating the sample within the penetration depth, perturb the partial concentrations of the normal and condensate fluids. We show that the enhanced nonlinear effects detected near T_c in Ba_0.6K_0.4BiO₃ and YBa₂Cu₃O₇ crystals may have the same origin. However, in order to account for the experimental data of Ba_0.6K_0.4BiO₃, one needs to involve a distribution of T_c over the crystal.     

Globally coupled systems with prescribed synchronized dynamics

A system of globally coupled maps whose synchronized dynamics differs from the individual (chaotic) evolution is considered. For nonchaotic synchronized dynamics, the synchronized state becomes stable at a critical coupling intensity lower than that of the fully chaotic case. Below such critical point, synchronization is also stable in a set of finite intervals. Moreover, the system is shown to exhibit multistability, so that even when the synchronized state is stable not all the initial conditions lead to synchronization of the ensemble. Received 22 October 1999     

Indentation studies on 〈1 0 0〉, 〈0 0 1〉 and 〈1 0 1〉 face of ammonium dihydrogen phosphate (ADP) single crystals: A novel nonlinear optical material

In the present work, Vickers microhardness measurements were carried out on different faces i.e. (1 0 0), (0 0 1) and (1 0 1) of ammonium dihydrogen phosphate (ADP) single crystals grown by slow evaporation solution technique at room temperature in the load ranging from 0.2 to 2 N. The obtained results show that the load independent hardness values are 0.8, 0.7 and 0.66 GPa, respectively at different faces of ADP crystal. From the crack length measurements, the fracture toughness values (K_c) was estimated using Evans and Anstis model and the present studies suggest that Evans model is more relevant when compared to Anstis model. The load variation of some mechanical properties viz. brittle index number (B_i) and yield strength (σ_y) for ADP have also been calculated for the first time.     

Synthesis,growth and characterization of non-linear optical material: l-Tryptophan p-nitrophenol (LTPNP) single crystal

A new nonlinear optical organic crystal l-tryptophan p-nitrophenol (LTPNP) of dimension 19 mm × 2 mm × 1.5 mm has been grown from an aqueous solution for the first time by slow evaporation technique at ambient temperature. The crystal structure of LTPNP was confirmed by single crystal X-ray diffraction. LTPNP crystallizes in non-centrosymmetric monoclinic system with space group P₂₁. The recorded FTIR spectrum confirms the presence of various functional groups in the grown crystal and confirms the formation of LTPNP. Thermal stability and melting temperature of the LTPNP crystal were identified from TG/DTA analysis. The optical absorption study confirms the suitability of the crystal for device applications. LTPNP exhibits SHG efficiency over 1.7 orders of magnitude higher than that of urea and 4 orders of magnitude higher than that of KDP.     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Study of nonlinear dissipative pulse propagation under the combined effect of two-photon absorption and gain dispersion: A variational approach involving Rayleigh’s dissipation function

We try to derive some explicit equations for predicting the laws which govern the evolution of different parameters of a propagating optical pulse in a nonlinear medium under the combined influence of two-photon absorption and gain dispersion. Using the generalized Euler-Lagrange equation, the dynamics of different pulse parameters are generated. The Rayleigh’s dissipation function is incorporated in order to take recourse to the dissipative part, with an analogy with the non-conservative frictional problem in classical mechanics. It appears from the study that the influence of the dissipative part can well be explained using the proposed model. The analytically predicted results are compared with the numerical data obtained from direct simulation of the Ginzburg-Landau equation and the results are found to be quite satisfactory, supporting the prediction.