Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

Risk evaluation of diabetes mellitus by relation of chaotic globals to HRV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Preventing chaotic motion in tapping-mode atomic force microscope

During the last 30 years the Atomic Force Microscopy became the most powerful tool for surface probing in atomic scale. The Tapping-Mode Atomic Force Microscope is used to generate high quality accurate images of the samples surface. However, in this mode of operation the microcantilever frequently presents chaotic motion due to the nonlinear characteristics of the tip-sample forces interactions, degrading the image quality. This kind of irregular motion must be avoided by the control system. In this work, the tip-sample interaction is modelled considering the Lennard-Jones potentials and the two-term Galerkin aproximation. Additionally, the State Dependent Ricatti Equation and Time-Delayed Feedback Control techniques are used in order to force the Tapping-Mode Atomic Force Microscope system motion to a periodic orbit, preventing the microcantilever chaotic motion

On suppression of chaotic motions of a portal frame structure under non-ideal loading using a magneto-rheological damper

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.

Chaotic encryption method based on life-like cellular automata

A chaotic encryption algorithm is proposed based on the "Life-like" cellular automata (CA), which acts as a pseudo-random generator (PRNG). The paper main focus is to use chaos theory to cryptography. Thus, CA was explored to look for this "chaos" property. This way, the manuscript is more concerning on tests like: Lyapunov exponent, Entropy and Hamming distance to measure the chaos in CA, as well as statistic analysis like DIEHARD and ENT suites. Our results achieved higher randomness quality than others ciphers in literature. These results reinforce the supposition of a strong relationship between chaos and the randomness quality. Thus, the "chaos" property of CA is a good reason to be employed in cryptography, furthermore, for its simplicity, low cost of implementation and respectable encryption power. (C) 2012 Elsevier Ltd. All rights reserved.

A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Flux and resident injection in gaseous advection experiments

The occurrence of gaseous pollutants in soils has stimulated many experimental activities, including forced ventilation in the field as well as laboratory transport experiments with gases. The dispersion coefficient in advective-dispersive gas phase transport is often dominated by molecular diffusion, which leads to a large overall dispersivity gamma. Under such conditions it is important to distinguish between flux and resident modes of solute injection and detection. The influence of the inlet type oil the macroscopic injection mode was tested in two series of column experiments with gases at different mean flow velocities nu. First we compared infinite resident and flux injections, and second, semi-infinite resident and flux injections. It is shown that the macroscopically apparent injection condition depends on the geometry of the inlet section. A reduction of the cross-sectional area of the inlet relative to that of the column is very effective in excluding the diffusive solute input, thus allowing us to use the solutions for a flux Injection also at rather low mean flow velocities nu. If the whole cross section of a column is exposed to a large reservoir like that of ambient air, a semi-infinite resident injection is established, which can be distinguished from a flux injection even at relatively high velocities nu, depending on the mechanical dispersivity of the porous medium.

Permeable coral reef sediment dissolution driven by elevated pCO2 and pore water advection

Ocean acidification (OA) is expected to drive the transition of coral reef ecosystems from net calcium carbonate (CaCO3) precipitating to net dissolving within the next century. Although permeable sediments represent the largest reservoir of CaCO3 in coral reefs, the dissolution of shallow CaCO3 sands under future pCO2 levels has not been measured under natural conditions. In situ, advective chamber incubations under elevated pCO2 (~800 µatm) shifted the sediments from net precipitating to net dissolving. Pore water advection more than doubled dissolution rates (1.10 g CaCO3/m**2/day) when compared to diffusive conditions (0.42 g CaCO3/m**2 /day). Sediment dissolution could reduce net ecosystem calcification rates of the Heron Island lagoon by 8% within the next century, which is equivalent to a 25% reduction in the global average calcification rate of coral lagoons. The dissolution of CaCO3 sediments needs to be taken into account in order to address how OA will impact the net accretion of coral reefs under future predicted increases in CO2.

Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

Digital chaotic output from an optically processing element

Digital chaotic behavior in an optically processing element is reported. It is obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate, previously reported as a possible main block for optical computing. Outputs for some specific conditions of the circuit are given. Digital chaos is obtained using a feedback configuration. Period doublings in a Feigenbaum‐like scenario are obtained. A new method to characterize this type of digital chaos is reported.