Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Locomotor and metabolic activities of Gymnostreptus olivaceus (Diplopoda, Spirostreptida) at different photoperiod conditions

In the present investigation the locomotor and the metabolic activity of Gymnostreptus olivaceus were studied, using 24-hr cycles at different photoperiods and constant temperature and RH. Locomotor activity was studied by the actography method and was reported as coefficients of nocturnalism [CN (N/N + D). 100]. The results showed a nocturnalism coefficient of 98,71% under normal photoperiod conditions and of 29,58% under inverted photoperiod conditions. In constant illumination, the CN of G. olivaceus was 88,22%, and in constant darkness, its rhythm was close to that of the normal photoperiod (CN = 94,92%). The metabolic activity was studied by manometric Warburg respirometry and lit was reported as mu l O-2 . g(-1). h(-1). The respiratory rate of G. olivaceus under normal photoperiod condition was higher at night than during the day (52,52 x 28,76), coinciding with the pattern of nocturnal locomotor activity of the animal. However, under conditions of inverted photoperiod, the millipede maintained its tendency toward a more intense nocturnal respiratory rate (50,35 x 39,14). Similar behaviours were observed under constant illumination and constant darkness, in which G. olivaceus again presented higher nocturnal respiratory rates than diurnal ones(85,84 x 53,48 and 73,18 x 57,0, respectively). The present experimental data suggests the persistence of an endogenous rhythm where the light may not be an important exogenous synchronizer of the activity of G. olivaceus, because it was insufficient to block the start of the biological clock and the natural tendency of higher nocturnal activities of millipedes, principally when the tests were performed in constant illumination or darkness (free-running tests).

Existence and stability of new nanoreactors: Highly swollen hexagonal liquid crystals

We report the preparation of direct hexagonal liquid crystals, constituted of oil-swollen cylinders arranged on a triangular lattice in water. The volume ratio of oil over water, rho, can be as large as 3.8. From the lattice parameter measured by small-angle X-ray scattering, we show that all the oil is indeed incorporated into the cylinders, thus allowing the diameter of the cylinders to be controlled over one decade range, provided that the ionic strength of the aqueous medium and rho are varied concomitantly. These hexagonal swollen liquid crystals (SLCs) have been first reported with sodium dodecyl sulfate as anionic surfactant, cyclohexane as solvent, 1-pentanol as co-surfactant, and sodium chloride as salt (Ramos, L.; Fabre, P. Langmuir 1997, 13, 13). The stability of these liquid crystals is investigated when the pH of the aqueous medium or the chemical nature of the components (salt and surfactant) is changed. We demonstrate that the range of stability is quite extended, rendering swollen hexagonal phases potentially useful for the fabrication of nanomaterials. As illustrations, we finally show that gelation of inorganic particles in the continuous aqueous medium of a SLC and polymerization within the oil-swollen cylinders of a SLC can be conducted without disrupting the hexagonal order of the system.

Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

Torpor in three species of Brazilian hummingbirds under semi-natural conditions

We measured body temperatures in three species of Brazilian hummingbirds, the Versicolored Emerald (Amazilia versicolor; body mass 4.1 g), the Black Jacobin (Me lantrochilus fuscus; body mass 7.7 g) and the Swallow-tailed Hummingbird (Eupetomena macroura; body mass 8.6 g), during overnight exposure to natural conditions of photoperiod and ambient temperatures. All three species entered torpor. In both A. versicolor and E. macroura, individuals entered torpor even if they had access to feeders up to the time of sunset. In contrast, M. fuscus was less prone to enter torpor and did so mainly if it had been fasting for more than two hours before sunset. Furthermore, M. fuscus often spent the whole night in torpor, whereas the two other species entered torpor for a variable, often short, period of the night. We observed more than one torpor bout during a single night in all three species. We suggest that multiple nocturnal torpors result from interruption of the normal torpor pattern by some (unknown) external stimuli. Any interrupted torpor was always followed by a new entry into torpor, supporting the view that there is a body mass threshold below which the hummingbirds must enter torpor Our data also indicate that these hummingbird species might use torpor even if they are not energetically stressed.

Colorimetric assay of ethanol using alcohol dehydrogenase from dry baker's yeast

Alcohol dehydrogenases (ADHs) are oxidoreductases present in animal tissues, plants, and microorganisms. These enzymes attract major scientific interest for the evolutionary perspectives, afforded by their wide occurrence in nature, and for their use in synthesis, thanks to their broad substrate specificity and stereoselectivity. In the present study, the standardization of the activity of the alcohol dehydrogenase from baker's yeast was accomplished, and the pH and temperature stability showed, that the enzyme presented a high stability to pH 6.0-7.0 and the thermal stability were completely maintained up to 50 degrees C during 1 h. The assays of ethanol (detection range 1-5 mM or 4.6 x 10(-2) to 23.0 x 10(-2) g/L) in different samples in alcoholic beverages, presented a maximum deviation of only 7.2%. The standard curve and the analytic curve of this method meet the conditions of precision, sensitivity, simplicity, and low cost, required for a useable analytical method. (c) 2006 Elsevier B.V. All rights reserved.

Purification and characterization of two beta-glucosidases from the thermophilic fungus Thermoascus aurantiacus

beta-Glucosidase from the fungus Thermoascus aurantiacus grown oil semi-solid fermentation medium (using ground corncob as substrate) was partially purified in 5 steps - ultrafiltration, ethanol precipitation, gel filtration and 2 anion exchange chromatography runs, and characterized. After the first anion exchange chromatography, beta-glucosidase activity was eluted in 3 peaks (Gl-1, Gl-2, Gl-3). Only the Gl-2 and Gl-3 fractions were adsorbed on the gel matrix. Gl-2 and Gl-3 exhibited optimum pH at 4.5 and 4.0, respectively. The temperature optimum of both glucosidases was at 75-80 degreesC. The pH stability of Gl-2 (4.0-9.0) was higher than Gl-3 (5.5-8.5); both enzyme activities showed similar patterns of thermostability. Under conditions of denaturing gel chromatography the molar mass of Gl-2 and Gl-3 was 175 and 157 kDa, respectively. Using 4-nitrophenyl beta-D-glucopyranoside as substrate, K-m, values of 1.17 +/- 0.35 and 1.38 +/- 0.86 mmol/L were determined for Gl-2 and Gl-3, respectively. Both enzymes were inhibited by Ag+ and stimulated by Ca2+.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.

The stability evolution of a family of simply periodic lunar orbits

The present work deals with a family of simply periodic orbits around the Moon in the rotating Earth Moon-particle system. Taking the framework of the planar, circular, restricted three-body problem, we follow the evolution of this family of periodic orbits using the numerical technique of Poincaré surface of section. The maximum amplitude of oscillation about the periodic orbits are determined and can be used as a parameter to measure the degree of stability in the phase space for such orbits. Despite the fact that the whole family of periodic orbits remain stable, there is a dichotomy in the quasi-periodic ones at the Jacobi constant Cj = 2.85. The quasi-periodic orbits with Cj < 2.85 oscillate around the periodic orbits in a different way from those with Cj > 2.85. © 1999 Elsevier Science Ltd. All rights reserved.

Purification and characterization of two β-glucosidases from the thermophilic fungus Thermoascus aurantiacus

β-Glucosidase from the fungus Thermoascus aurantiacus grown on semi-solid fermentation medium (using ground corncob as substrate) was partially purified in 5 steps-ultrafiltration, ethanol precipitation, gel filtration and 2 anion exchange chromatography runs, and characterized. After the first anion exchange chromatography, β-glucosidase activity was eluted in 3 peaks (Gl-1, Gl-2, Gl-3). Only the Gl-2 and Gl-3 fractions were adsorbed on the gel matrix. Gl-2 and Gl-3 exhibited optimum pH at 4.5 and 4.0, respectively. The temperature optimum of both glucosidases was at 75-80°C. The pH stability of Gl-2 (4.0-9.0) was higher than Gl-3 (5.5-8.5); both enzyme activities showed similar patterns of thermostability. Under conditions of denaturing gel chromatography the molar mass of Gl-2 and Gl-3 was 175 and 157 kDa, respectively. Using 4-nitrophenyl β-D-glucopyranoside as substrate, Km values of 1.17 ± 0.35 and 1.38 ± 0.86 mmol/L were determined for Gl-2 and Gl-3, respectively. Both enzymes were inhibited by Ag+ and stimulated by Ca2+.

Lyapounov stability for impulsive dynamical systems

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.

Physiological and cellular responses in two populations of the mussel Perna perna collected at different sites from the Coast of São Paulo, Brazil

The physiological conditions of mussels from Ubatuba and Santos and also of organisms transplanted from Ubatuba to Santos were studied by using different techniques. Assays for lysosomal stability were conducted on the haemolymph. Heart rate activity was monitored for 6h. The embryonic development of larvae obtained from the collected mussels was analysed. For all the compared groups of mussels, no significant differences were observed for the cardiac activity monitoring and the embryonic bioassays. The mean Neutral Red (NR) retention time was similar for the animals from Santos and Ubatuba, whereas the organisms transplanted to Santos showed a reduction in the retention time of the dye, indicating damage in the lysosomal membranes. These differences were possibly due to environmental factors, but further investigations are required to confirm this hypothesis.