Transcrição e tradução do audiobook "Eric"

Orientação: Professora Maria Helena Anacleto-Matias

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Pre-meal tomato (Lycopersicon esculentum) intake can have anti-obesity effects in young women?

The effect of pre-meal tomato intake in the anthropometric indices and blood levels of triglycerides, cholesterol, glucose, and uric acid of a young women population (n=35, 19.6 ± 1.3 years) was evaluated. During 4 weeks, daily, participants ingested a raw ripe tomato (~90 g) before lunch. Their anthropometric and biochemical parameters were measured repeatedly during the follow-up time. At the end of the 4 weeks, significant reductions were observed on body weight (-1.09 ± 0.12 kg on average), % fat (-1.54 ± 0.52%), fasting blood glucose (-5.29 ± 0.80 mg/dl), triglycerides (-8.31 ± 1.34 mg/dl), cholesterol (-10.17 ± 1.21 mg/ dl), and uric acid (-0.16 ± 0.04 mg/dl) of the participants. The tomato pre-meal ingestion seemed to interfere positively in body weight, fat percentage, and blood levels of glucose, triglycerides, cholesterol, and uric acid of the young adult women that participated in this study.

The influence of gait cadence on the ground reaction forces and plantar pressures during load carriage of young adults

Biomechanical gait parameters—ground reaction forces (GRFs) and plantar pressures—during load carriage of young adults were compared at a low gait cadence and a high gait cadence. Differences between load carriage and normal walking during both gait cadences were also assessed. A force plate and an in-shoe plantar pressure system were used to assess 60 adults while they were walking either normally (unloaded condition) or wearing a backpack (loaded condition) at low (70 steps per minute) and high gait cadences (120 steps per minute). GRF and plantar pressure peaks were scaled to body weight (or body weight plus backpack weight). With medium to high effect sizes we found greater anterior-posterior and vertical GRFs and greater plantar pressure peaks in the rearfoot, forefoot and hallux when the participants walked carrying a backpack at high gait cadences compared to walking at low gait cadences. Differences between loaded and unloaded conditions in both gait cadences were also observed.