RESUMO

Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.

Assuntos

RESUMO

Lipases and esterases are biocatalysts used at the laboratory and industrial level. To obtain the maximum yield in a bioprocess, it is important to measure key variables, such as enzymatic activity. The conventional method for monitoring hydrolytic activity is to take out a sample from the bioreactor to be analyzed off-line at the laboratory. The disadvantage of this approach is the long time required to recover the information from the process, hindering the possibility to develop control systems. New strategies to monitor lipase/esterase activity are necessary. In this context and in the first approach, we proposed a lab-made sequential injection analysis system to analyze off-line samples from shake flasks. Lipase/esterase activity was determined using p-nitrophenyl butyrate as the substrate. The sequential injection analysis allowed us to measure the hydrolytic activity from a sample without dilution in a linear range from 0.05-1.60 U/mL, with the capability to reach sample dilutions up to 1000 times, a sampling frequency of five samples/h, with a kinetic reaction of 5 min and a relative standard deviation of 8.75%. The results are promising to monitor lipase/esterase activity in real time, in which optimization and control strategies can be designed.

Assuntos

RESUMO

In this paper, we present a class of 3-D unstable dissipative systems, which are stable in two components but unstable in the other one. This class of systems is motivated by whirls, comprised of switching subsystems, which yield strange attractors from the combination of two unstable "one-spiral" trajectories by means of a switching rule. Each one of these trajectories moves around two hyperbolic saddle equilibrium points. Both theoretical and numerical results are provided for verification and demonstration.

RESUMO

The kidney is one of the most complicated organs in terms of structure and physiology, in part because it is highly vascularized. The renal vascular development occurs through two mechanisms that sometimes overlap: vasculogenesis and angiogenesis. Here, we consider angiogenesis to model the renal arterial tree with the two processes of vascular angiogenesis: sprouting and splitting. We recognize the vessels are not tubes with ends that get glued but physiological factors are relevant into the vascular development. Our contribution integrates the graph theory and physiological information to derive a quantitative model for the vascular tree in the sense that the vertices and edges represent, respectively, a branching point and a vessel. From such a premise, development of the arterial vascular tree of the kidney is mathematically expressed, including physiological processes as the effect of the vascular endothelial growth factor (VEGF) on the vessel length. A definition of the graph is used to visualize the topology of vascular tree in kidney providing physiological information into the edges. Thus, renal arterial branching is modeled as a graph where edges are labeled and oriented.

Assuntos

RESUMO

We investigate the pattern formation produced by precipitated species during solvent evaporation through the numerical solution of a set of partial differential equations that account for the mechanisms of evaporation, diffusion, and precipitation. A pattern is formed because solvent evaporation provokes precipitation of species near the border of the system producing ringlike depositions from the edge to the center. Solvent evaporation is modeled as occurs with a liquid drop on a surface. The spacing between rings and its width are constant and roughly constant, respectively. Pattern formation follows the evaporation process inducing trends on pattern formation that are different to those produced by the precipitation of two species in a diffusive front (Liesegang rings). The spatial structure of rings under solvent evaporation is similar to those observed during solvent evaporation on two oppositely charged colloids and is attributable to the competition between precipitation and evaporation processes.

RESUMO

A family of driving forces is discussed in the context of chaos suppression in the Laplace domain. This idea can be attained by increasing the order of the polynomial in the expressions of the driving force to account for the robustness and/or the performance of the closed loop. The motivation arises from the fact that chaotic systems can be controlled by increasing the order of the Laplace controllers even to track arbitrary orbits. However, a larger order in the driving forces can induce an undesirable frequency response, and the control efforts can result in either peaking or large energy accumulation. We overcame these problems by showing that considering the frequency response (interpreted by norms), the closed-loop execution can be improved by designing the feedback suppressor in the Laplace domain. In this manner, the stabilization of the chaotic behavior in jerk-like systems is achieved experimentally. Jerk systems are particularly sensitive to control performance (and robustness issues) because the acceleration time-derivative is involved in their models. Thus, jerky systems are especially helped by a robust control design.

RESUMO

The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. Duffing equation is chosen as slave system whereas Chua oscillator is defined as master system. The synchronization scheme has nonlinear feedback structure. The reduced-order synchronization is attained in a practical sense, i.e., the difference e=x(3)-x(1)(') is close to zero for all time t> or =t(0)> or =0, where t(0) denotes the time of the control activation.

RESUMO

The technique of using Lie derivatives to control chaos introduced by Kocarev et al. [Chaos, Solitons Fractals 9, 1359-1366 (1998)] is extended in this contribution. Here, by using Lie derivatives in an extended space state, it is proved that chaos can be practically suppressed via feedback in spite of the Lie derivative being ill-posed at the reference. The main idea is to construct a dynamically equivalent system. In this way, the chaotic system can be practically stabilized around any point of singularity x(0). The Lorenz equation is used as an illustrative example to show the application in the chaos control context. (c) 2002 American Institute of Physics.