Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Antimony glasses with large nonlinear refractive indices, small two-photon absorption coefficients and ultrafast response at telecom wavelengths

Nonlinear (NL) optical properties of antimony oxide based glasses (AG) were characterized for excitation wavelengths from 800 to 1600 m. The NL refractive indices, n2, and the two-photon absorption (TPA) coefficient, β, have been evaluated using the Z-scan technique. Values of n2≈ 10-15 - 10-14 cm2/W of electronic origin were measured and negligible TPA coefficients (β < 0.003 cm/GW) were determined. The response time of the nonlinearity is faster than 100 fs as determined using the Kerr shutter technique. The figure-of-merit usually considered for all-optical switching, T = 2βλ/n2 , indicates that AG are very good materials for ultrafast switches at telecom wavelengths. © 2007 IEEE.

Degenerate hope bifurcations in Chua's system

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided. © 2009 World Scientific Publishing Company.

Nonlinear effects generation in suspended core chalcogenide fibre

In this work we report our achievements in the elaboration and optical characterizations of low-losses suspended core optical fibers elaborated from As2S3 glass. For preforms elaboration, alternatively to other processes like the stack and draw or extrusion, we use a process based on mechanical drilling. The drawing of these drilled performs into fibers allows reaching a suspended core geometry, in which a 2 μm diameter core is linked to the fiber clad region by three supporting struts. The different fibers that have been drawn show losses close to 0.9 dB/m at 1.55 μm. The suspended core waveguide geometry has also an efficient influence on the chromatic dispersion and allows its management. Indeed, the zero dispersion wavelength, which is around 5 μm in the bulk glass, is calculated to be shifted towards around 2μm in our suspended core fibers. In order to qualify their nonlinearity we have pumped them at 1.995 μm with the help of a fibered ns source. We have observed a strong non linear response with evidence of spontaneous Raman scattering and strong spectral broadening. © 2011 SPIE.

Estimativa de alguns parâmetros de transporte de contaminantes para solos Brasileiros

This paper introduces an indirect estimate for the coefficients of distribution, hydrodynamic dispersion and retardation for contaminants commonly encountered in sanitary landfills and their liners, such as Cu2+ and K+; this estimate is based on the relationship between concentration and certain physical characteristics of typical Brazilian soils. The results of previous studies investigating the migration of contaminants were used to develop mathematical expressions from multiple non-linear regressions. Using minimal squares regression, this transport was linked to various combinations of contaminant concentration and both structural and textural characteristics of the porous medium. Various combinations of characteristics and concentrations were investigated, with a mathematical expression obtained for each. The relationship between percentage of clay and the contaminant content proved to be the most closely correlated with actual transport parameters, with coefficients close to one.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

An investigation of a two-stage nonlinear vibration isolation system

This paper investigates the most desirable configuration of a two-stage nonlinear vibration isolation system, in which the isolators contain hardening geometric stiffness nonlinearity and linear viscous damping. The force transmissibility of the system is used as the measure of the effectiveness of the isolation system. The hardening nonlinearity is achieved by placing horizontal springs onto the suspended and intermediate masses, which are supported by vertical springs. It is found that nonlinearity in the upper stage has very little effect and thus serves little purpose. The nonlinearity in the lower stage, however, has a profound effect, and can significantly improve the effectiveness of the isolation system. Further, it is found that it is desirable to have high damping in the upper stage and very low damping in the lower stage. © 2012 Elsevier Ltd.

Controle robusto com realimentação derivativa de sistemas não lineares via LMI

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelagem dinâmica de transformadores de corrente para uso em estudos de qualidade da energia e proteção do sistema elétrico

Pós-graduação em Engenharia Elétrica - FEB

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uso de absorvedores de vibrações eletromecânicos lineares e não-lineares em sistemas não-lineares e não-ideais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Caracterização elétrica e microestrutural de cerâmicas varistoras de baixa tensão à base de ('SN IND.1-x''TI IND.x')'O IND.2' e 'SN''O IND.2' dopados com 'CO''O' e 'NB IND.2''O IND.5'

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Síntese e caracterização elétrica de filmes varistores à base de 'SN''O IND.2' modificados superficialmente por difusão 'CR POT.3+' na região do contorno de grão

Pós-graduação em Química - IQ

A teoria da complexidade na aprendizagem de espanhol em Teletandem

Pós-graduação em Estudos Linguísticos - IBILCE

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.