Uma análise da dinâmica do pêndulo eletromecânico utilizando a teoria de pertubações

Pós-graduação em Matemática - IBILCE

Neuroethologic differences in sleep deprivation induced by the single- and multiple-platform methods

It has been proposed that the multiple-platform method (MP) for desynchronized sleep (DS) deprivation eliminates the stress induced by social isolation and by the restriction of locomotion in the single-platform (SP) method. MP, however, induces a higher increase in plasma corticosterone and ACTH levels than SP. Since deprivation is of heuristic value to identify the functional role of this state of sleep, the objective of the present study was to determine the behavioral differences exhibited by rats during sleep deprivation induced by these two methods. All behavioral patterns exhibited by a group of 7 albino male Wistar rats submitted to 4 days of sleep deprivation by the MP method (15 platforms, spaced 150 mm apart) and by 7 other rats submitted to sleep deprivation by the SP method were recorded in order to elaborate an ethogram. The behavioral patterns were quantitated in 10 replications by naive observers using other groups of 7 rats each submitted to the same deprivation schedule. Each quantification session lasted 35 min and the behavioral patterns presented by each rat over a period of 5 min were counted. The results obtained were: a) rats submitted to the MP method changed platforms at a mean rate of 2.62 ± 1.17 platforms h-1 animal-1; b) the number of episodes of noninteractive waking patterns for the MP animals was significantly higher than that for SP animals (1077 vs 768); c) additional episodes of waking patterns (26.9 ± 18.9 episodes/session) were promoted by social interaction in MP animals; d) the cumulative number of sleep episodes observed in the MP test (311) was significantly lower (chi-square test, 1 d.f., P<0.05) than that observed in the SP test (534); e) rats submitted to the MP test did not show the well-known increase in ambulatory activity observed after the end of the SP test; f) comparison of 6 MP and 6 SP rats showed a significantly shorter latency to the onset of DS in MP rats (7.8 ± 4.3 and 29.0 ± 25.0 min, respectively; Student t-test, P<0.05). We conclude that the social interaction occurring in the MP test generates additional stress since it increases the time of forced wakefulness and reduces the time of rest promoted by synchronized sleep.

Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.

Energy method to calculate the density of liquids using ultrasonic reflection techniques

In this work it is introduced a new approach to calculate the density of liquids in terms of the energies of the acoustic signals. This method is compared to other methods in the time domain (peak-to-peak amplitudes) and frequency domain magnitudes at a single frequency. It is used a measurement cell based on a multiple reflection technique, and it is developed an acoustic model for the cell. Simulations and experiments using several liquids are presented, showing that the energy method a less sensitive to noise than the other techniques. The relative errors in the density are smaller than 0.2% when compared to the values measured with a pycnometer.

Optimal and sub-optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright (C) 2001 John Wiley & Sons, Ltd.

Fighting by sleep-deprived rats as a possible manifestation of panic: effects of sodium lactate

Increased fighting is an effect of desynchronized sleep deprivation (DSD) in rats, and recently this behavior has been suggested to be spontaneous panic and equivalent to panic disorder. In the present study we tested this hypothesis by evaluating the effect of sodium lactate on this aggressiveness, because this substance is recognized to induce spontaneous panic attacks in patients. A total of 186 male albino Wistar rats, 250-350 g, 90-120 days of age, were submitted to DSD (multiple platform method) for 0, 4, or 5 days. At the end of the deprivation period the rats were divided into subgroups respectively injected intraperitoneally with 1.86, 2.98 and 3.72 g/kg of 1 M sodium lactate, or 1.86 and 3.72 g/kg of 2 M sodium lactate. The control animals were submitted to the same procedures but received equivalent injections of sodium chloride. Regardless of DSD time, sleep-deprived animals that received sodium lactate presented a significantly higher mean number of fights (0.13 ± 0.02 fights/min) and a longer mean time spent in confrontation (2.43 ± 0.66 s/min) than the controls (0.01 ± 0.006 fights/min and 0.12 ± 0.07 s/min, respectively; P<0.01, Student t-test). For the sodium lactate group, concentration of the solution and time of deprivation increased the number of fights, with the mean number of fights and mean duration of fighting episodes being greater with the 2.98 g/kg dose using 1 M lactate concentration. These results support the hypothesis that fighting induced by DSD is probably a spontaneous panic manifestation. However, additional investigations are necessary in order to accept this as a promising animal model for studies on panic disorder.

Medição de viscosidade de líquidos pelo método de múltiplas reflexões acústicas com conversão de modo

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

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

On the undamped free vibration of a mass interacting with a Hertzian contact stiffness

Three methods are used to determine the natural frequency of undamped free vibration of a mass interacting with a Hertzian contact stiffness. The exact value is determined using the first integral of motion. The harmonic balance method is used on a transformed equation for an approximate solution, and the multiple scales method is used on an approximate equation. The maximum initial displacement avoiding contact loss is also determined, and the corresponding exact natural frequency is also obtained analytically. The methods are evaluated by studying the free vibration of an elastic sphere on a flat rigid surface. © 2011 Elsevier Ltd © 2011 Elsevier Ltd. All rights reserved.

Error estimates for a neumann problem in highly oscillating thin domains

In this work we analyze the convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain with highly oscillatory behavior. We consider the case where the height of the domain, amplitude and period of the oscillations are all of the same order, and given by a small parameter e > 0. Using an appropriate corrector approach, we show strong convergence and give error estimates when we replace the original solutions by the first-order expansion through the Multiple-Scale Method.

Equações diferenciais com retardo em biologia de populações: Renato Mendes Coutinho. -

Pós-graduação em Física - IFT

Um estudo da dinâmica fracamente não-linear de um sistema nanomecânico

Pós-graduação em Matemática - IBILCE

On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface

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

Nonlinear state estimation and control for chaos suppression in MEMS resonator

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