Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Singularly perturbed biharmonic problems with superlinear nonlinearities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wide vector solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Third-order nonlinearities and other properties of molybdenum lead-pyrophosphate glass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of structural nonlinearities in stall-induced aeroelastic response of pitching airfoils

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system's instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.

Optical Nonlinearities at the Interface between Glass and Liquid Crystal

In this paper, the optical behavior of a nonlinear interface is studied. The nonlinear medium has been a nematic liquid crystal, namely MBBA, and the nonlinear one, glasses of different types (F-10 and F-2) depending on the experimental needs. The anchoring forces at the boundary have been found to inhibit the action of the evanescent field in the case of total internal reflection. Most of observed nonlinearities are due to thermal effects. As a consequence, liquid crystals do not seem to be good candidates for total internal reflection optical bistability.

Optical Nonlinearities Between Glass And Liquid Crystal

The nonlinear optical properties of the interface between glass and liquid crystal are reported. Switching characteristics and optical hysterfisis have beam studied.

Optical nonlinearities at the interface between liquid crystal and glass: behavior of the transmitted beam.

During the past years a great interest has been devoted to the study of possible applications of non-linear interfaces, mainly in the field of Optical Bistability. Several papers have been published in this field, and some of them dealing with liquid crystals as non-linear material.

Optical nonlinearities and blstability in a glass-liquid crystal interface

As reported previously, an interface between linear and liquid crystal media shows some nonlinear properties that can be employed in the analysis of this type of optical bistable device.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

A new approach to control of MIMO processes with static nonlinearities using an extended IMC framework

In this paper, a new control design method is proposed for stable processes which can be described using Hammerstein-Wiener models. The internal model control (IMC) framework is extended to accommodate multiple IMC controllers, one for each subsystem. The concept of passive systems is used to construct the IMC controllers which approximate the inverses of the subsystems to achieve dynamic control performance. The Passivity Theorem is used to ensure the closed-loop stability. (c) 2005 Elsevier Ltd. All rights reserved.