Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Linear and nonlinear transport in a small charge-tunable open quantum ring

We experimentally study the Aharonov-Bohm-conductance oscillations under external gate voltage in a semiconductor quantum ring with a radius of 80 nm. We find that, in the linear regime, the resistance-oscillation plot in the voltage-magnetic-field plane corresponds to the quantum ring energy spectra. The chessboard pattern assembled by resistance diamonds, while loading the ring, is attributed to a short electron lifetime in the open configuration, which agrees with calculations within the single-particle model. Remarkably, the application of a small dc current allows observing strong deviations in the oscillation plot from this pattern accompanied by a magnetic-field symmetry break. We relate such behavior to the higher-order-conductance coefficients determined by electron-electron interactions in the nonlinear regime.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Valve friction and nonlinear process model closed-loop identification

Among several process variability sources, valve friction and inadequate controller tuning are supposed to be two of the most prevalent. Friction quantification methods can be applied to the development of model-based compensators or to diagnose valves that need repair, whereas accurate process models can be used in controller retuning. This paper extends existing methods that jointly estimate the friction and process parameters, so that a nonlinear structure is adopted to represent the process model. The developed estimation algorithm is tested with three different data sources: a simulated first order plus dead time process, a hybrid setup (composed of a real valve and a simulated pH neutralization process) and from three industrial datasets corresponding to real control loops. The results demonstrate that the friction is accurately quantified, as well as ""good"" process models are estimated in several situations. Furthermore, when a nonlinear process model is considered, the proposed extension presents significant advantages: (i) greater accuracy for friction quantification and (ii) reasonable estimates of the nonlinear steady-state characteristics of the process. (C) 2010 Elsevier Ltd. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

Comparative study of laser and LED systems of low intensity applied to tendon healing

The aim of this study was to compare the effects of Low-intensity Laser Therapy (LILT) and Light Emitting Diode Therapy (LEDT) of low intensity on the treatment of lesioned Achilles tendon of rats. The experimental model consisted of a partial mechanical lesion on the right Achilles tendon deep portion of 90 rats. One hour after the lesion, the injured animals received applications of laser/LED (685, 830/630, 880 nm), and the same procedure was repeated at 24-h intervals, for 10 days. The healing process and deposition of collagen were evaluated based on a polarization microscopy analysis of the alignment and organization of collagen bundles, through the birefringence (optical retardation-OR). The results showed a real efficiency of treatments based on LEDT and confirmed that LILT seems to be effective on healing process. Although absence of coherence of LED light, tendon healing treatment with this feature was satisfactory and can certainly replace treatments based on laser light applications. Applications of infrared laser at 830 nm and LED 880 nm were more efficient when the aim is a good organization, aggregation, and alignment of the collagen bundles on tendon healing. However, more research is needed for a safety and more efficient determination of a protocol with LED.

Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua`s circuit behavior

This paper presents an experimental characterization of the behavior of an analogous version of the Chua`s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincar, sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.

Power Transformer Differential Protection Based on Clarke`s Transform and Fuzzy Systems

The power transformer is a piece of electrical equipment that needs continuous monitoring and fast protection since it is very expensive and an essential element for a power system to perform effectively. The most common protection technique used is the percentage differential logic, which provides discrimination between an internal fault and different operating conditions. Unfortunately, there are some operating conditions of power transformers that can affect the protection behavior and the power system stability. This paper proposes the development of a new algorithm to improve the differential protection performance by using fuzzy logic and Clarke`s transform. An electrical power system was modeled using Alternative Transients Program (ATP) software to obtain the operational conditions and fault situations needed to test the algorithm developed. The results were compared to a commercial relay for validation, showing the advantages of the new method.

Photoinduced Degradation of the Herbicide Clomazone Model Reactions for Natural and Technical Systems

The photodegradation of the herbicide clomazone in the presence of S(2)O(8)(2-) or of humic substances of different origin was investigated. A value of (9.4 +/- 0.4) x 10(8) m(-1) s(-1) was measured for the bimolecular rate constant for the reaction of sulfate radicals with clomazone in flash-photolysis experiments. Steady state photolysis of peroxydisulfate, leading to the formation of the sulfate radicals, in the presence of clomazone was shown to be an efficient photodegradation method of the herbicide. This is a relevant result regarding the in situ chemical oxidation procedures involving peroxydisulfate as the oxidant. The main reaction products are 2-chlorobenzylalcohol and 2-chlorobenzaldehyde. The degradation kinetics of clomazone was also studied under steady state conditions induced by photolysis of Aldrich humic acid or a vermicompost extract (VCE). The results indicate that singlet oxygen is the main species responsible for clomazone degradation. The quantum yield of O(2)(a(1)Delta(g)) generation (lambda = 400 nm) for the VCE in D(2)O, Phi(Delta) = (1.3 +/- 0.1) x 10(-3), was determined by measuring the O(2)(a(1)Delta(g)) phosphorescence at 1270 nm. The value of the overall quenching constant of O(2)(a(1)Delta(g)) by clomazone was found to be (5.7 +/- 0.3) x 10(7) m(-1) s(-1) in D(2)O. The bimolecular rate constant for the reaction of clomazone with singlet oxygen was k(r) = (5.4 +/- 0.1) x 10(7) m(-1) s(-1), which means that the quenching process is mainly reactive.

Nitrogen fertilization in common bean crops under no-tillage and conventional systems.

Nitrogen fertilization in common bean crops under no-tillage and conventional systems. Nitrogen fertilizer is necessary for high yields in common bean crops and N responses under conditions of no-tillage and conventional systems are still basic needs. Thus, the objective of this research was to evaluate the effect of N application and common bean yield in no-tillage and conventional systems. The experimental design was a randomized block in a factorial scheme (2x8+1) with four replications. The treatments were constituted by the combination of two N doses (40 and 80 kg ha(-1)) applied at side dressing at eight distinct stadia during vegetative development of the common bean (V(4-3), V(4-4), V(4-5), V(4-6), V(4-7), V(4-8), V(4-9) and V(4-10)), in addition to a control plot without N in side dressing. The experiment was conducted over two years (2002 and 2003) in no-tillage on millet crop residues and conventional plow system. It was concluded that N fertilizer at the V(4) stadium of common bean promotes similar seed yields in no-tillage and conventional systems. Yield differences between no-tillage and conventional systems are inconsistent in the same agricultural area.

Root Canal Area Increase Promoted by the EndoSequence and ProTaper Systems: Comparison by Computed Tomography

Introduction: The aim of this study was to compare the increase of the root canal area after instrumentation with EndoSequence or ProTaper rotary systems. Methods: Twenty-two mesial root canals from mandibular molars were instrumented. Teeth were mounted on a base, numbered, and divided into 2 groups; teeth from 1-11 (PT group) were instrumented by using the ProTaper system, and teeth from 12-22 (ES group) were instrumented by using the EndoSequence system. Cone beam computed tomography was performed on all teeth before and after instrumentation. Measurements at 3,5, and 7 mm as well as differences in instrument performance were statistically compared by the Student t test at 5% significance level. Results: Both systems increased significantly the root canal area (P < .05) at all levels. Comparison between the rotary systems showed significantly greater increase (P < .05) for EndoSequence at 3 mm, with no statistically significant difference (P < .05) at the other levels. Conclusions: Both rotary systems increased significantly the root canal area. (J Endod 2010;36:1179-1182)