An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Boundary oscillations and nonlinear boundary conditions

We study how oscillations in the boundary of a domain affect the behavior of solutions of elliptic equations with nonlinear boundary conditions of the type partial derivative u/partial derivative n + g(x, u) = 0. We show that there exists a function gamma defined on the boundary, that depends on an the oscillations at the boundary, such that, if gamma is a bounded function, then, for all nonlinearities g, the limiting boundary condition is given by partial derivative u/partial derivative n + gamma(x)g(x, u) = 0 (Theorem 2.1, Case 1). Moreover, if g is dissipative and gamma infinity then we obtain a Dirichlet an boundary condition (Theorem 2.1, Case 2).

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Stability results for impulsive functional differential equations with infinite delay

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

PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

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

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

Group A T-loop for differential moment mechanics: An implant study

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below

The effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below are investigated. It is shown that the (2+1)-dimensional Burgers equation may appear as the equation governing the upper free surface perturbations of a Bénard system, even when the viscosity is assumed to depend on temperature. The critical Rayleigh number for the appearance of waves governed by the Kadomtsev-Petviashvili equation, however, will be smaller than R=30, which is the critical number obtained for a constant viscosity. © 1992.

Hydrothermal surface-wave instability and the Kuramoto-Sivashinsky equation

We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient and a basic nonlinear bulk velocity profile. In the limit of long wavelength and large nondimensional surface tension we show that hydrothermal surface-wave instabilities may give rise to disturbances governed by the Kuramoto-Sivashinsky equation. A possible connection to hot-wire experiments is also discussed. © 1994.