Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The gradually truncated Levy flight for systems with power-law distributions

Power-law distributions have been observed in various economical and physical systems. Levy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the gradually truncated Levy flight in which large steps of a Levy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc. (C) 1999 Elsevier B.V. B.V. All rights reserved.

In Situ and Simultaneous UV-vis/SAXS and UV-vis/XAFS Time-Resolved Monitoring of ZnO Quantum Dots Formation and Growth

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

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

On switched control design of linear time-invariant systems with polytopic uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure. © 2013 Wallysonn A. de Souza et al.

An experimental verification of newton's second law

We describe an experimental procedure to probe the validity of Newton's second law. The experimental arrangement allows us to accelerate a glider on an air track by means of forces that are both steady and known. We also show how to determine acceleration from average speeds calculated for successive time intervals of the motion measured by using several electronic counters connected to a single-crystal oscillator circuit. Within experimental errors, the experiments clearly show the proportionality between acceleration and force for a fixed mass and between acceleration and inverse of mass for a fixed force. © by the Sociedade Brasileira de Física.

Nonlinear formulation based on FEM, Mazars damage criterion and Fick's law applied to failure assessment of reinforced concrete structures subjected to chloride ingress and reinforcements corrosion

Structural durability is an important design criterion, which must be assessed for every type of structure. In this regard, especial attention must be addressed to the durability of reinforced concrete (RC) structures. When RC structures are located in aggressive environments, its durability is strongly reduced by physical/chemical/mechanical processes that trigger the corrosion of reinforcements. Among these processes, the diffusion of chlorides is recognized as one of major responsible of corrosion phenomenon start. To accurate modelling the corrosion of reinforcements and to assess the durability of RC structures, a mechanical model that accounts realistically for both concrete and steel mechanical behaviour must be considered. In this context, this study presents a numerical nonlinear formulation based on the finite element method applied to structural analysis of RC structures subjected to chloride penetration and reinforcements corrosion. The physical nonlinearity of concrete is described by Mazars damage model whereas for reinforcements elastoplastic criteria are adopted. The steel loss along time due to corrosion is modelled using an empirical approach presented in literature and the chloride concentration growth along structural cover is represented by Fick's law. The proposed model is applied to analysis of bended structures. The results obtained by the proposed numerical approach are compared to responses available in literature in order to illustrate the evolution of structural resistant load after corrosion start. (C) 2014 Elsevier Ltd. All rights reserved.

Controllability and stabilizability of linear time-varying distributed hereditary control systems

This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varyinglinear abstract differential equation with distributed delay in the state variables. An approximate controllability propertyis established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operatorsassociated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptoticstability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximatecontrollability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes thesystem. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley &Sons, Ltd.

Discrete-time sliding mode control for uncertain networked system subject to time delay

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Residence Time Distribution Models Derived from Non-Ideal Laminar Velocity Profiles in Tubes

The theoretical E-curve for the laminar flow of non-Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks-in-series models of residence time distribution (RTD). In this work, four RTD models derived from non-ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

The abuse of intellectual property rights and regulations in China: a law and economic analysis

From the institutional point of view, the legal system of IPR (intellectual property right, hereafter, IPR) is one of incentive institutions of innovation and it plays very important role in the development of economy. According to the law, the owner of the IPR enjoy a kind of exclusive right to use his IP(intellectual property, hereafter, IP), in other words, he enjoys a kind of legal monopoly position in the market. How to well protect the IPR and at the same time to regulate the abuse of IPR is very interested topic in this knowledge-orientated market and it is the basic research question in this dissertation. In this paper, by way of comparing study and by way of law and economic analyses, and based on the Austrian Economics School’s theories, the writer claims that there is no any contradiction between the IPR and competition law. However, in this new economy (high-technology industries), there is really probability of the owner of IPR to abuse his dominant position. And with the characteristics of the new economy, such as, the high rates of innovation, “instant scalability”, network externality and lock-in effects, the IPR “will vest the dominant undertakings with the power not just to monopolize the market but to shift such power from one market to another, to create strong barriers to enter and, in so doing, granting the perpetuation of such dominance for quite a long time.”1 Therefore, in order to keep the order of market, to vitalize the competition and innovation, and to benefit the customer, in EU and US, it is common ways to apply the competition law to regulate the IPR abuse. In Austrian Economic School perspective, especially the Schumpeterian theories, the innovation/competition/monopoly and entrepreneurship are inter-correlated, therefore, we should apply the dynamic antitrust model based on the AES theories to analysis the relationship between the IPR and competition law. China is still a developing country with relative not so high ability of innovation. Therefore, at present, to protect the IPR and to make good use of the incentive mechanism of IPR legal system is the first important task for Chinese government to do. However, according to the investigation reports,2 based on their IPR advantage and capital advantage, some multinational companies really obtained the dominant or monopoly market position in some aspects of some industries, and there are some IPR abuses conducted by such multinational companies. And then, the Chinese government should be paying close attention to regulate any IPR abuse. However, how to effectively regulate the IPR abuse by way of competition law in Chinese situation, from the law and economic theories’ perspective, from the legislation perspective, and from the judicial practice perspective, there is a long way for China to go!

Reexamining the Role of Incarceration and Stigma in Criminal Law

One of the ways by which the legal system has responded to different sets of problems is the blurring of the traditional boundaries of criminal law, both procedural and substantive. This study aims to explore under what conditions does this trend lead to the improvement of society's welfare by focusing on two distinguishing sanctions in criminal law, incarceration and social stigma. In analyzing how incarceration affects the incentive to an individual to violate a legal standard, we considered the crucial role of the time constraint. This aspect has not been fully explored in the literature on law and economics, especially with respect to the analysis of the beneficiality of imposing either a fine or a prison term. We observed that that when individuals are heterogeneous with respect to wealth and wage income, and when the level of activity can be considered a normal good, only the middle wage and middle income groups can be adequately deterred by a fixed fines alone regime. The existing literature only considers the case of the very poor, deemed as judgment proof. However, since imprisonment is a socially costly way to deprive individuals of their time, other alternatives may be sought such as the imposition of discriminatory monetary fine, partial incapacitation and other alternative sanctions. According to traditional legal theory, the reason why criminal law is obeyed is not mainly due to the monetary sanctions but to the stigma arising from the community’s moral condemnation that accompanies conviction or merely suspicion. However, it is not sufficiently clear whether social stigma always accompanies a criminal conviction. We addressed this issue by identifying the circumstances wherein a criminal conviction carries an additional social stigma. Our results show that social stigma is seen to accompany a conviction under the following conditions: first, when the law coincides with the society's social norms; and second, when the prohibited act provides information on an unobservable attribute or trait of an individual -- crucial in establishing or maintaining social relationships beyond mere economic relationships. Thus, even if the social planner does not impose the social sanction directly, the impact of social stigma can still be influenced by the probability of conviction and the level of the monetary fine imposed as well as the varying degree of correlation between the legal standard violated and the social traits or attributes of the individual. In this respect, criminal law serves as an institution that facilitates cognitive efficiency in the process of imposing the social sanction to the extent that the rest of society is boundedly rational and use judgment heuristics. Paradoxically, using criminal law in order to invoke stigma for the violation of a legal standard may also serve to undermine its strength. To sum, the results of our analysis reveal that the scope of criminal law is narrow both for the purposes of deterrence and cognitive efficiency. While there are certain conditions where the enforcement of criminal law may lead to an increase in social welfare, particularly with respect to incarceration and stigma, we have also identified the channels through which they could affect behavior. Since such mechanisms can be replicated in less costly ways, society should first try or seek to employ these legal institutions before turning to criminal law as a last resort.

The Law and Economics of Eco-labels

Eco-labels and certification are one of the many environmental policy tools that have been under scrutiny in recent years. This is because the damages of environmental degradation are becoming more apparent over time. Hence there is a pressure to come up with tools that help solve even small parts of the problem. Eco-labels have been around for over 30 years. However the market, the environment and eco-labels have changed drastically during this period. Moreover, in the last 5 years there has been a sudden increase in eco-labels making them more visible in the market and to the average consumer. All this has made evident that little is known about the effectiveness of eco-labels as environmental policy tools. Hence, there is a call to find answers regarding the actual effects of eco-labels on the market and on the environment. While this work cannot address whether eco-labels have an environmental impact it addresses the effects of eco-labels on the markets. Moreover, this work aimed to find the role of law in eco-labelling. In addition, it aims to find a legal solution that would improve the performance of eco-labelling and certification.