Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

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.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Galerkin Method and Weighting Functions Applied to Nonlinear H(infinity) Control with Output Feedback

This paper considers two aspects of the nonlinear H(infinity) control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs equation that arises in the output-feedback case. Design of nonlinear H(infinity) controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Isolation of Pseudomonas aeruginosa strains from dental office environments and units in Barretos, state of São Paulo, Brazil, and analysis of their susceptibility to antimicrobial drugs

A wide variety of opportunistic pathogens has been detected in the tubing supplying water to odontological equipment, in special in the biofilm lining of these tubes. Among these pathogens, Pseudomonas aeruginosa, one of the leading causes of nosocomial infections, is frequently found in water lines supplying dental units. In the present work, 160 samples of water, and 200 fomite samples from forty dental units were collected in the city of Barretos, State of São Paulo, Brazil and evaluated between January and July, 2005. Seventy-six P. aeruginosa strains, isolated from the dental environment (5 strains) and water system (71 strains), were tested for susceptibility to six antimicrobial drugs most frequently used against P. aeruginosa infections. Susceptibility to ciprofloxacin, followed by meropenem was the predominant profile. The need for effective means of reducing the microbial burden within dental unit water lines is emphasized, and the risk of exposure and cross-infection in dental practice, in special when caused by opportunistic pathogens like P. aeruginosa, are highlighted.

Analysis of TMJ vibration sounds before and after use of two types of occlusal splints

Temporomandibular joint (TMJ) sounds are important and common physical signs of temporomandibular disorders (TMD). The aim of this study was to evaluate the influence of the effect of the use of occlusal bite splints (stabilizing and repositioning) on the sounds produced in the TMJ, by means of the electrovibratography (EVG). Thirty-one patients with TMD from the Dental School of Ribeirão Preto, University of São Paulo, Brazil were selected for this study. Group 1 (n=23) wore stabilizing bite splints and Group 2 (n=8) used anterior repositioning splints. Before and after treatment with occlusal splints both groups were analyzed using the SonoPAK Q/S recording system (BioResearch System, Inc.). The treatments with stabilizing bite splints were satisfactory, since they reduced the total amount of the sound energies (p<0.05), but the use of anterior repositioning splints for no more than 4 weeks produced significantly better results (p<0.01). The total amount of vibration energy involved in the vibrating movements of the TMJ showed significant improvement using anterior repositioning splints.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Vibration-induced extra torque during electrically-evoked contractions of the human calf muscles

Background: High-frequency trains of electrical stimulation applied over the lower limb muscles can generate forces higher than would be expected from a peripheral mechanism (i.e. by direct activation of motor axons). This phenomenon is presumably originated within the central nervous system by synaptic input from Ia afferents to motoneurons and is consistent with the development of plateau potentials. The first objective of this work was to investigate if vibration (sinusoidal or random) applied to the Achilles tendon is also able to generate large magnitude extra torques in the triceps surae muscle group. The second objective was to verify if the extra torques that were found were accompanied by increases in motoneuron excitability. Methods: Subjects (n = 6) were seated on a chair and the right foot was strapped to a pedal attached to a torque meter. The isometric ankle torque was measured in response to different patterns of coupled electrical (20-Hz, rectangular 1-ms pulses) and mechanical stimuli (either 100-Hz sinusoid or gaussian white noise) applied to the triceps surae muscle group. In an additional investigation, M(max) and F-waves were elicited at different times before or after the vibratory stimulation. Results: The vibratory bursts could generate substantial self-sustained extra torques, either with or without the background 20-Hz electrical stimulation applied simultaneously with the vibration. The extra torque generation was accompanied by increased motoneuron excitability, since an increase in the peak-to-peak amplitude of soleus F waves was observed. The delivery of electrical stimulation following the vibration was essential to keep the maintained extra torques and increased F-waves. Conclusions: These results show that vibratory stimuli applied with a background electrical stimulation generate considerable force levels (up to about 50% MVC) due to the spinal recruitment of motoneurons. The association of vibration and electrical stimulation could be beneficial for many therapeutic interventions and vibration-based exercise programs. The command for the vibration-induced extra torques presumably activates spinal motoneurons following the size principle, which is a desirable feature for stimulation paradigms.

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.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.