Feedback Control Methodologies for Nonlinear Systems

A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions.     

Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

Effect of solvent nature on spin exchange in rigid nitroxide biradicals

Intramolecular electron spin exchange as a function of temperature and solvent viscosity and polarity has been studied by X-band electron paramagnetic resonance (EPR) spectroscopy in two rigid nitroxide biradicals existing in one spatial conformation only. Temperature variations of the isotropic hyperfine splitting constanta and exchange integral value |J/a| were measured from EPR spectra and subsequently analyzed. The interaction of polar solvent molecules with >N-O fragments of nitroxide groups led to a slight decrease of the |J/a| value with the increase of temperatureT. In contrast, the interaction of polar solvent molecules with functional groups inside the bridge resulted in a noticeable increase of |J/a| vs.T. In the last case, a coverse relationship between the values of |J/a| and the hyperfine splitting constanta has been observed for solvents with different polarity.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Radiolysis of 1-naphthol in aqueous solutions

The effects of absorbed doses, initial pH and 1-naphthol concentration onto its radiolysis in aqueous sulphuric and hydrochloric acids by gamma rays from ⁶⁰Co were investigated. Under the experimental conditions, 1-naphthol degradation yields increased with increasing the absorbed doses (0.3–3.0 kGy) and with decreasing the initial 1-naphthol concentration (20–1 ppm). It was found out that the hydrated electrons did not play any significant roles in 1-naphthol radiolysis, as the degradation yields were higher at pH₀ ~ 0.46 compared to those at pH₀ ~ 2.0–5.0. The corresponding radiolytic yields G(−1-naphthol) were (6.13 ± 1.00)) × 10⁻² and (5.11 ± 0.22) × 10⁻² μmol/J in sulphuric acids, (15.61 ± 3.85) × 10⁻² and (4.76 ± 0.48) × 10⁻² μmol/J in hydrochloric acids. 1-Naphthol degradation rates could be described by the kinetic equations of pseudo-first-order reactions. An empirical relation between the observed reaction constants k _D and the initial 1-naphthol concentrations was established, enabling to predict the absorbed doses required for a given treatment efficiency. Three products of 1-naphthol degradation were revealed using an HPLC/UV procedure.     

Atomic spectroscopy with surface wave plasmas

The use of microwave induced plasmas, particularly of surface wave plasmas, as detectors in atomic emission spectrometry for elemental analysis is reviewed. Surface wave plasmas have been produced at low HF power and used as gas chromatographic detectors. The analytical performances for the detection of non-metals with a Fourier transform spectrometer and a two-channel filter unit are reported. The excitation behavior of non-metals in helium-based mixed gas-plasmas has also be studied. In particular, the effect of power and of nitrogen concentration on the bromine emission has been systematically investigated. A nine-fold improvement of the detection limits for bromine can be obtained in a high power (900 W) helium-nitrogen (0.1–0.2%) plasma.     

Rat pups and random robots generate similar self‐organized and intentional behavior

Biorobotic research continually demonstrates that behavior and cognition can be the emergent products of (1) embodied agents that are (2) dynamically embedded within an environment and (3) equipped with simple sensorimotor rules. Thigmotaxis is an orientation response to contact manifested in infant rats by wall following, corner burrowing, and group aggregation. Orientation responses have been long thought to be mediated only by sensory or central processes. Here we show that a random control architecture in a morphologically similar robot embedded in a scaled environment can reproduce thigmotaxic behaviors seen in infant rats. We conclude that (1) and (2) may play a larger role than previously thought in the generation of complex behaviors. © 2006 Wiley Periodicals, Inc. Complexity 12: 53–66, 2006     

A stable second‐order mass‐weighted upwind scheme for unstructured meshes

In this paper, an original second‐order upwind scheme for convection terms is described and implemented in the context of a Control‐Volume Finite‐Element Method (CVFEM). The proposed scheme is a second‐order extension of the first‐order MAss‐Weighted upwind (MAW) scheme proposed by Saabas and Baliga (Numer. Heat Transfer 1994; 26B :381–407). The proposed second‐order scheme inherits the well‐known stability characteristics of the MAW scheme, but exhibits less artificial viscosity and ensures much higher accuracy. Consequently, and in contrast with nearly all second‐order upwind schemes available in the literature, the proposed second‐order MAW scheme does not need limiters. Some test cases including two pure convection problems, the driven cavity and steady and unsteady flows over a circular cylinder, have been undertaken successfully to validate the new scheme. The verification tests show that the proposed scheme exhibits a low level of artificial viscosity in the pure convection problems; exhibits second‐order accuracy for the driven cavity; gives accurate reattachment lengths for low‐Reynolds steady flow over a circular cylinder; and gives constant‐amplitude vortex shedding for the case of high‐Reynolds unsteady flow over a circular cylinder. Copyright © 2005 John Wiley & Sons, Ltd.     

Pseudodifferential operators with real analytic symbols and approximation methods for pseudodifferential equations

This paper introduces some methods (including an approximation method) for investigating pseudodifferential equations and related problems (Cauchy problems, boundary value problems,…) based on the technique of pseudodifferential operators with real analytic symbols.