Note: A balloon-borne accelerometer technique for measuring atmospheric turbulence

A weather balloon and its suspended instrument package behave like a pendulum with a moving pivot. This dynamical system is exploited here for the detection of atmospheric turbulence. By adding an accelerometer to the instrument package, the size of the swings induced by atmospheric turbulence can be measured. In test flights, strong turbulence has induced accelerations greater than 5g, where g = 9.81 m s−2. Calibration of the accelerometer data with a vertically orientated lidar has allowed eddy dissipation rate values of between 10−3 and 10−2 m2 s−3 to be derived from the accelerometer data. The novel use of a whole weather balloon and its adapted instrument package can be used as a new instrument to make standardized in situ measurements of turbulence.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

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.

Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (C) 2008 Elsevier B.V. All rights reserved.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Estudo comparativo do desempenho de controladores robustos aplicados a um sistema de tanques acoplados.

Currently the uncertain system has attracted much academic community from the standpoint of scientific research and also practical applications. A series of mathematical approaches emerge in order to troubleshoot the uncertainties of real physical systems. In this context, the work presented here focuses on the application of control theory in a nonlinear dynamical system with parametric variations in order and robustness. We used as the practical application of this work, a system of tanks Quanser associates, in a configuration, whose mathematical model is represented by a second order system with input and output (SISO). The control system is performed by PID controllers, designed by various techniques, aiming to achieve robust performance and stability when subjected to parameter variations. Other controllers are designed with the intention of comparing the performance and robust stability of such systems. The results are obtained and compared from simulations in Matlab-simulink.

Sistema Híbrido de Inferência Baseado em Análise de Componentes Principais e Redes Neurais Artificiais Aplicado a Plantas de Processamento de Gás Natural

Nowadays, where the market competition requires products with better quality and a constant search for cost savings and a better use of raw materials, the research for more efficient control strategies becomes vital. In Natural Gas Processin Units (NGPUs), as in the most chemical processes, the quality control is accomplished through their products composition. However, the chemical composition analysis has a long measurement time, even when performed by instruments such as gas chromatographs. This fact hinders the development of control strategies to provide a better process yield. The natural gas processing is one of the most important activities in the petroleum industry. The main economic product of a NGPU is the liquefied petroleum gas (LPG). The LPG is ideally composed by propane and butane, however, in practice, its composition has some contaminants, such as ethane and pentane. In this work is proposed an inferential system using neural networks to estimate the ethane and pentane mole fractions in LPG and the propane mole fraction in residual gas. The goal is to provide the values of these estimated variables in every minute using a single multilayer neural network, making it possibly to apply inferential control techniques in order to monitor the LPG quality and to reduce the propane loss in the process. To develop this work a NGPU was simulated in HYSYS R software, composed by two distillation collumns: deethanizer and debutanizer. The inference is performed through the process variables of the PID controllers present in the instrumentation of these columns. To reduce the complexity of the inferential neural network is used the statistical technique of principal component analysis to decrease the number of network inputs, thus forming a hybrid inferential system. It is also proposed in this work a simple strategy to correct the inferential system in real-time, based on measurements of the chromatographs which may exist in process under study

Identificação de uma planta de corrente de um motor de indução utilizando redes de base radial

The present work describes the use of a mathematical tool to solve problems arising from control theory, including the identification, analysis of the phase portrait and stability, as well as the temporal evolution of the plant s current induction motor. The system identification is an area of mathematical modeling that has as its objective the study of techniques which can determine a dynamic model in representing a real system. The tool used in the identification and analysis of nonlinear dynamical system is the Radial Basis Function (RBF). The process or plant that is used has a mathematical model unknown, but belongs to a particular class that contains an internal dynamics that can be modeled.Will be presented as contributions to the analysis of asymptotic stability of the RBF. The identification using radial basis function is demonstrated through computer simulations from a real data set obtained from the plant

Localização de um robô móvel usando odometria e marcos naturais

Several methods of mobile robot navigation request the mensuration of robot position and orientation in its workspace. In the wheeled mobile robot case, techniques based on odometry allow to determine the robot localization by the integration of incremental displacements of its wheels. However, this technique is subject to errors that accumulate with the distance traveled by the robot, making unfeasible its exclusive use. Other methods are based on the detection of natural or artificial landmarks present in the environment and whose location is known. This technique doesnt generate cumulative errors, but it can request a larger processing time than the methods based on odometry. Thus, many methods make use of both techniques, in such a way that the odometry errors are periodically corrected through mensurations obtained from landmarks. Accordding to this approach, this work proposes a hybrid localization system for wheeled mobile robots in indoor environments based on odometry and natural landmarks. The landmarks are straight lines de.ned by the junctions in environments floor, forming a bi-dimensional grid. The landmark detection from digital images is perfomed through the Hough transform. Heuristics are associated with that transform to allow its application in real time. To reduce the search time of landmarks, we propose to map odometry errors in an area of the captured image that possesses high probability of containing the sought mark

Eficiência de uma ETE em escala real composta por reator UASB seguido de lodo ativado

In the state of Rio Grande do Norte (RN), Brazil, there are about 80 sewage treatment systems being the predominant technology waste stabilization ponds. The Baldo s WWTP , due to its location and low availability of area, was designed as a hybrid conventional system (UASB reactor followed by activated sludge with biodiscs) at a tertiary level, being the most advanced WWTP in the State and also with the larger treatment capacity (1620 m3/h) .The paper presents the results of its performance based on samples collections from May to December 2012. Composite samples of the effluent of the grit chamber, UASB reactors, anoxic chambers, aeration tanks and treated effluent were collected weekly, every 4 hours for 24 hours. The results showed that the WWTP effluent presented adequate ranges of temperatures, pH and DO, however removal efficiencies of BOD and TSS were below the predicted by design. The UASB reactors also showed removals of BOD and TSS less than expected, due to the accumulation of sludge in the reactors, which eventually, was washed out in the effluent. The nitrification process was not satisfactory mainly due to problems in the oxygen distribution in the aeration tanks. The removal of ammonia and TKN were high, probably by the assimilation process

Artificial satellites orbits in 2:1 resonance: GPS constellation

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

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2:1 Resonance

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