On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Inflammation-induced modulation of cellular galectin-1 and-3 expression in a model of rat peritonitis

Objective and design: To investigate the effect of galectin-1 (Gal-1) and -3 (Gal-3) on leukocyte migration and analyze the expression of both galectins in inflammatory cells using a model of rat peritonitis.Material or Subjects: Sprague-Dawley rats (n = 4 per group).Treatment: Peritonitis was induced in animals through intraperitoneal injection of carrageenin (1.5 mg/kg) and rat mesenteries were analyzed at different time points (0, 4, 24 and 48h). For pharmacological treatment, rats received intravenous injection of Gal-1 or -3 (3 mu g/kg) followed by carrageenin.Methods: Western blotting and immunoelectron microscopy analysis. Statistical analysis was performed using ANOVA followed by Bonferroni test.Results: Pharmacological treatment with Gal-1, but not Gal-3, inhibited (similar to 50%) leukocyte recruitment into the peritoneal cavity at 4h time-point. In this early phase, immunogold staining of mesenteries showed a diminished Gal-3 expression in degranulated mast cells and Gal-1 in transmigrated neutrophils (similar to 20% reduction compared to intravascular cells). In the later phases (24 and 48 h), leukocyte turnover was associated with augmented Gal-1 expression in neutrophils and macrophages and Gal-3 in mast cells and macrophages.Conclusions: These results point to a balanced expression of cell-associated-Gal-1/Gal-3 and might impact on the development of new therapeutic strategies for inflammatory diseases.

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

Factors contributing to the differences in peritonitis rates between centers and regions

Despite improvements in connectology, peritoneal dialysis (PD) - associated peritonitis contributes significantly to morbidity and modality failure in patients maintained on PD therapy. A broad spectrum of organisms -gram-positive, gram-negative, fungal, anaerobic - are involved in this complication. In addition, a significant percentage of episodes involve polymicrobial and culture-negative infection. Technological advances are being developed to minimize the incidence of access-related complications such as peritonitis. Many traditional factors such as exit-site infection and poor technique have been already identified. In the present review, we discuss the geographic, patient selection, and clinical issues that can affect peritonitis rates in different areas of the world and in different centers in the same area.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Periodic collisions between the moon Prometheus and Saturn's F ring

Saturn's F ring, which lies 3,400 km beyond the edge of the main ring system, was discovered by the Pioneer 11 spacecraft(1) in 1979. It is a narrow, eccentric ring which shows an unusual 'braided' appearance in several Voyager 1 images' obtained in 1980, although it appears more regular in images from Voyager 2 obtained nine months later(3). The discovery of the moons Pandora and Prometheus orbiting on either side of the ring provided a partial explanation for some of the observed features(4). Recent observations of Prometheus(5,6) by the Hubble Space Telescope show, surprisingly, that it is lagging behind its expected position by similar to 20 degrees. By modelling the dynamical evolution of the entire Prometheus-F ring-Pandora system, we show here that Prometheus probably encountered the core of the F ring in 1994 and that it may still be entering parts of the ring once per orbit. Collisions with objects in the F ring provide a plausible explanation for the observed lag and imply that the mass of the F ring is probably less than 25% that of Prometheus.

PARTICIPATION OF MACROPHAGES IN CHLORAMPHENICOL-POTENTIATED CARRAGEENAN-INDUCED PERITONITIS IN RATS

1. We investigated the possible potentiating effect of chloramphenicol succinate (30 mg/kg, every 12 h for 4 days, ip) on the response of polymorphonuclear neutrophils to carrageenin (150 mug, ip) or dextran (100 mug, ip) in the peritoneal cavity of male Wistar rats (180-230 g; N = 12 in each group).2. Chloramphenicol potentiated the cell migration induced by carrageenin (35%) but not that induced by dextran. Previous macrophage depletion in the peritoneal cavity by washing with sterile saline abolished the cell response, whereas a previous thioglycollate-induced increase in macrophage numbers enhanced the potentiating effect (60%).3. These results suggest that the potentiating effect on polymorphonuclear neutrophil migration induced by chloramphenicol may be related to chemotactic factors released by macrophages.

Structural and electronic properties of PbTiO3 slabs: a DFT periodic study

Structural and electronic properties of the bulk and relaxed surfaces (TiO2 and PbO terminated) of cubic PbTiO3 are investigated by means of periodic quantum-mechanical calculations based on density functional theory. It is observed that the difference in surface energies is small and relaxations effects are most prominent for Ti and Ph surface atoms. The electronic structure shows a splitting of the lowest conduction bands for the TiO2 terminated surface and of the highest valence bands for the PbO terminated slab. The calculated indirect band gap is: 3.18, 2.99 and 3.03 eV for bulk, TiO2 and PbO terminations, respectively. The electron density maps show that the Ti-O bond has a partial covalent character, whereas the Pb-O bonds present a very low covalency. (C) 2004 Elsevier B.V. All rights reserved.

Non-periodic bifurcations of one-dimensional maps

We prove that a 'positive probability' subset of the boundary of '{uniformly expanding circle transformations}' consists of Kupka-Smale maps. More precisely, we construct an open class of two-parameter families of circle maps (f(alpha,theta))(alpha,theta) such that, for a positive Lebesgue measure subset of values of alpha, the family (f(alpha,theta))(theta) crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.

Periodic waves and solitons of two-photon propagation

We study the two-photon propagation (TPP) modelling equations. The one-phase periodic solutions are obtained in an effective form. Their modulation is investigated by means of the Whitham method. The theory developed is applied to the problem of creation of TPP solitons on the sharp front of a long pulse.