Control and chaos for vibro-impact and non-ideal oscillators

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implementations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic motion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we investigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Structural parameters of polyacrylamide hydrogels obtained by the Equilibrium Swelling Theory

In this paper, the synthesis and structural characterization of a series of polyacrylamide hydrogels with different degrees of reticulation are reported. Although the Equilibrium Swelling Theory was recognized as a simple and reliable tool for the determination of structural hydrogels network parameters like equilibrium degree of swelling, cross-link ratio and mesh size, this is the first application of this methodology for polyacrylamide hydrogels. By changing the total monomer content in the synthesis solution (%T) from 5 to 30%, at a fixed value of cross-linker content in the total monomer amount (%C) of 5%, the final parameter obtained, the mesh size, can be tuned from 2 to 0.3 nm. It was also possible to change the mesh size (0.19-0.35) by varying %C from 5 to 12% (at %T = 20%). Scanning Electron Microscopy images for the most different formulations are shown and corroborate data obtained from the theory. (c) 2008 Elsevier Ltd. All rights reserved.

Mode of cembranoid action on embryonic muscle acetylcholine receptor

The mechanism of eupalmerin acetate (EUAC) actions on the embryonic muscle nicotinic acetylcholine receptor (nAChR) in BC3H-1 cells was studied by using whole-cell and single-channel patch-clamp current measurements. With whole-cell currents, EUAC did not act as an agonist on this receptor. Coapplication of 30 mu M EUAC with 50 mu M, 100 N, or 500 mu M carbamoylcholine (CCh) reversibly inhibited the current amplitude, whereas, with 20 mu M CCh, current was increased above control values in the presence of EUAC. EUAC concentration curves (0.01-40 N) obtained with 100 mu M and 500 mu M CCh displayed slope coefficients, n(H), significantly smaller than one, suggesting that EUAC bound to several sites with widely differing affinities on the receptor molecule. The apparent rate of receptor desensitization in the presence of EUAC and CCh was either slower than or equal to that obtained with CCh alone. The major finding from single-channel studies was that EUAC did not affect single-channel conductance or the ability of CCh to interact with the receptor. Instead, EUAC acted by increasing the channel closing rate constant. The results are not consistent with the competitive model for EUAC inhibition, with the sequential open-channel block model, or with inhibition by increased desensitization. The data are best accounted for by a model in which EUAC acts by closed-channel block at low concentrations, by positive modulation at intermediate concentrations, and by negative allosteric modulation of the open channel at high concentrations. (c) 2007 Wiley-Liss, Inc.

Development and Application of a Highly Selective Biomimetic Sensor for Detection of Captopril, an Important Ally in Hypertension Control

A biomimetic sensor is proposed as a promising new analytical method for determination of captopril in different classes of samples. The sensor was prepared by modifying a carbon paste electrode with iron (II) phthalocyanine bis(pyridine) [FePe(dipy)] complex. Amperometric measurements in a batch analytical mode were first carried out in order to optimize the sensor response. An applied potential lower than 0.2 V vs Ag vertical bar AgCl in 0.1 mol L(-1) of TRIS buffer at pH 8.0 provided the best response, with a linear range of 2.5 x 10(-5) to 1.7 x 10(-4) mol L(-1). A detailed investigation of the selectivity of the sensor, employing seventeen other drugs, was also performed. Recovery studies were carried out using biological and environment samples in order to evaluate the sensor`s potential for use with these sample classes. Finally, the performance of the biomimetic sensor was optimized in a flow injection (FIA) system using a wall jet electrochemical cell. Under optimized flow conditions, a broad linear response range, from 5.0 x 10(-4) to 2.5 x 10(-2) mol L(-1), was obtained for captopril, with a sensitivity of 210 +/- 1 mu A L mol(-1).