On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

Giant non-linear absorption in Er3+-doped fluoroindate glass

Non-linear absorption is observed in Er3+-doped fluoroindate glass (in mol% 37InF2:20ZnF2:20SrF2:16BaF2:2GdF2: 2NaF:1GaF3:2ErF3) when the sample is irradiated with a CW laser emitting at 650 nm. An intensity dependence of the optical transmittance is detected. Saturation and sequential absorption of two photons are responsible for the decrease of 50% in the transmittance. The results are explained by simple models which are solved based on rate-equations for the populations of energy levels.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

A set of linear equations to calculate the steady-state operation of an electrical distribution system

In this paper, the calculation of the steady-state operation of a radial/meshed electrical distribution system (EDS) through solving a system of linear equations (non-iterative load flow) is presented. The constant power type demand of the EDS is modeled through linear approximations in terms of real and imaginary parts of the voltage taking into account the typical operating conditions of the EDS's. To illustrate the use of the proposed set of linear equations, a linear model for the optimal power flow with distributed generator is presented. Results using some test and real systems show the excellent performance of the proposed methodology when is compared with conventional methods. © 2011 IEEE.

Non-destructive equations to estimate the leaf area of Styrax pohlii and Styrax ferrugineus

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

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the performance of a dual-mode non-linear vibration energy harvesting device

The research trend for harvesting energy from the ambient vibration sources has moved from using a linear resonant generator to a non-linear generator in order to improve on the performance of a linear generator; for example, the relatively small bandwidth, intolerance to mistune and the suitability of the device for low-frequency applications. This article presents experimental results to illustrate the dynamic behaviour of a dual-mode non-linear energy-harvesting device operating in hardening and bi-stable modes under harmonic excitation. The device is able to change from one mode to another by altering the negative magnetic stiffness by adjusting the separation gap between the magnets and the iron core. Results for the device operating in both modes are presented. They show that there is a larger bandwidth for the device operating in the hardening mode compared to the equivalent linear device. However, the maximum power transfer theory is less applicable for the hardening mode due to occurrence of the maximum power at different frequencies, which depends on the non-linearity and the damping in the system. The results for the bi-stable mode show that the device is insensitive to a range of excitation frequencies depending upon the input level, damping and non-linearity.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Thermodynamic analysis of a non linear lattice

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