Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

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.

Nonlinear spectrum effect on the coherent control of molecular systems

This work demonstrates that the detuning of the fs-laser spectrum from the two-photon absorption band of organic materials can be used to reach further control of the two-photon absorption by pulse spectral phase manipulation. We investigate the coherent control of the two-photon absorption in imidazole-thiophene core compounds presenting distinct two-photon absorption spectra. The coherent control, performed using pulse phase shaping and genetic algorithm, exhibited different growth rates for each sample. Such distinct trends were explained by calculating the two-photon absorption probability considering the intrapulse interference mechanism, taking into account the two-photon absorption spectrum of the samples. Our results indicate that tuning the relative position between the nonlinear absorption and the pulse spectrum can be used as a novel strategy to optimize the two-photon absorption in broadband molecular systems. (C) 2011 Elsevier B.V. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Influence of rhBMP-2 on bone formation and osseointegration in different implant systems after sinus-floor elevation. An in vivo study on sheep

Background Several studies have reported certain bone morphogenic proteins (BMPs) to have positive effects on bone generation Although some investigators have studied the effects of human recombinant BMP (rhBMP-2) in sinus augmentation in sheep, none of these studies looked at the placement of implants at the time of sinus augmentation Furthermore, no literature could be found to report on the impact that different implant systems, as well as the positioning of the implants had on bone formation if rhBMP-2 was utilized in sinus-lift procedures Purpose The aim of this study was to compare sinus augmentation with rhBMP-2 on a poly-D, L-lactic-co-glycolic acid gelatine (PLPG) sponge with sinus augmentation with autologous pelvic cancellous bone in the maxillary sinus during the placement of different dental Implants Materials and methods Nine adult female sheep were submitted to bilateral sinus-floor elevation In one side (test group) the sinus lift was performed with rhBMP-2 on a PLPG-sponge, while the contralateral side served as the control by using cancellous bone from the iliac crest Three different implants (Branemark (R), 31 (R) and Straumann (R)) were inserted either simultaneously with the sinus augmentation or as a two staged procedure 6 weeks later The animals were sacrificed at 6 and 12 weeks for histological and histomorphometrical evaluations during which bone-to-implant contact (BIC) and bone density (BD) were evaluated Results BD and BIC were significantly higher at 12 weeks in the test group if the Implants were placed at the time of the sinus lift (p < 0 05) No difference was observed between the different implant systems or positions Conclusions The use of rhBMP-2 with PLPG-sponge increased BIC as well as BD in the augmented sinuses if compared to autologous bone Different implant systems and positions of the implants had no effect on BIC or BD (C) 2010 European Association for Cranio-Maxillo-Facial Surgery

Deterpenation of Bergamot Essential Oil Using Liquid-Liquid Extraction: Equilibrium Data of Model Systems at 298.2 K

The deterpenation of bergamot essential oil can be performed by liquid liquid extraction using hydrous ethanol as the solvent. A ternary mixture composed of 1-methyl-4-prop-1-en-2-yl-cydohexene (limonene), 3,7-dimethylocta-1,6-dien-3-yl-acetate (linalyl acetate), and 3,7-dimethylocta-1,6-dien-3-ol (linalool), three major compounds commonly found in bergamot oil, was used to simulate this essential oil. Liquid liquid equilibrium data were experimentally determined for systems containing essential oil compounds, ethanol, and water at 298.2 K and are reported in this paper. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were lower than 0.0062 in all systems, indicating the good descriptive quality of the molecular models. To verify the effect of the water mass fraction in the solvent and the linalool mass fraction in the terpene phase on the distribution coefficients of the essential oil compounds, nonlinear regression analyses were performed, obtaining mathematical models with correlation coefficient values higher than 0.99. The results show that as the water content in the solvent phase increased, the kappa value decreased, regardless of the type of compound studied. Conversely, as the linalool content increased, the distribution coefficients of hydrocarbon terpene and ester also increased. However, the linalool distribution coefficient values were negatively affected when the terpene alcohol content increased in the terpene phase.

Electrification of precipitating systems over the Amazon: Physical processes of thunderstorm development

This study investigated the physical processes involved in the development of thunderstorms over southwestern Amazon by hypothesizing causalities for the observed cloud-to-ground lightning variability and the local environmental characteristics. Southwestern Amazon experiences every year a large variety of environmental factors, such as the gradual increase in atmospheric moisture, extremely high pollution due to biomass burning, and intense deforestation, which directly affects cloud development by differential surface energy partition. In the end of the dry period it was observed higher percentages of positive cloud-to-ground (+CG) lightning due to a relative increase in +CG dominated thunderstorms (positive thunderstorms). Positive (negative) thunderstorms initiated preferentially over deforested (forest) areas with higher (lower) cloud base heights, shallower (deeper) warm cloud depths, and higher (lower) convective potential available energy. These features characterized the positive (negative) thunderstorms as deeper (relatively shallower) clouds, stronger (relatively weaker) updrafts with enhanced (decreased) mixed and cold vertically integrated liquid. No significant difference between thunderstorms (negative and positive) and nonthunderstorms were observed in terms of atmospheric pollution, once the atmosphere was overwhelmed by pollution leading to an updraft-limited regime. However, in the wet season both negative and positive thunderstorms occurred during periods of relatively higher aerosol concentration and differentiated size distributions, suggesting an aerosol-limited regime where cloud electrification could be dependent on the aerosol concentration to suppress the warm and enhance the ice phase. The suggested causalities are consistent with the invoked hypotheses, but they are not observed facts; they are just hypotheses based on plausible physical mechanisms.

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.

Prediction of dynamical, nonlinear, and unstable process behavior

Process scheduling techniques consider the current load situation to allocate computing resources. Those techniques make approximations such as the average of communication, processing, and memory access to improve the process scheduling, although processes may present different behaviors during their whole execution. They may start with high communication requirements and later just processing. By discovering how processes behave over time, we believe it is possible to improve the resource allocation. This has motivated this paper which adopts chaos theory concepts and nonlinear prediction techniques in order to model and predict process behavior. Results confirm the radial basis function technique which presents good predictions and also low processing demands show what is essential in a real distributed environment.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.