Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

On exact time averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterized by a rate of events, lambda(t), and a magnitude, Phi, following an exponential distribution. We tackle the problem by performing exact time averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.

Medida da visão em candelas: description of a psychophysical technique to quantify luminous intensity

OBJETIVO: Desenvolver um método e um dispositivo para quantificar a visão em candela (cd). Os estudos de medida da visão são importantes para todas as ciências visuais. MÉTODOS: É um estudo teórico e experimental. Foram descritos os detalhes do método psicofísico e da calibração do dispositivo. Foram realizados testes preliminares em voluntários. RESULTADOS: É um teste psicofísico simples e com resultado expresso em unidades do sistema internacional de medidas. Com a descrição técnica será possível reproduzir o experimento em outros centros de pesquisa. CONCLUSÃO: Os resultados aferidos em intensidade luminosa (cd) são uma opção para estudo visual. Esses resultados possibilitarão extrapolar medidas para modelos matemáticos e para simular efeitos individuais com dados aberrométricos.

Ventilation behavior in trained and untrained men during incremental test: evidence of one metabolic transition point

This study aimed to describe and compare the ventilation behavior during an incremental test utilizing three mathematical models and to compare the feature of ventilation curve fitted by the best mathematical model between aerobically trained (TR) and untrained ( UT) men. Thirty five subjects underwent a treadmill test with 1 km.h(-1) increases every minute until exhaustion. Ventilation averages of 20 seconds were plotted against time and fitted by: bi-segmental regression model (2SRM); three-segmental regression model (3SRM); and growth exponential model (GEM). Residual sum of squares (RSS) and mean square error (MSE) were calculated for each model. The correlations between peak VO2 (VO2PEAK), peak speed (Speed(PEAK)), ventilatory threshold identified by the best model (VT2SRM) and the first derivative calculated for workloads below (moderate intensity) and above (heavy intensity) VT2SRM were calculated. The RSS and MSE for GEM were significantly higher (p < 0.01) than for 2SRM and 3SRM in pooled data and in UT, but no significant difference was observed among the mathematical models in TR. In the pooled data, the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.58; p < 0.01) and Speed(PEAK) (r = -0.46; p < 0.05) while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r = -0.43; p < 0.05). In UT group the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.65; p < 0.05) and Speed(PEAK) (r = -0.61; p < 0.05), while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r= -0.73; p < 0.01), Speed(PEAK) (r = -0.73; p < 0.01) and VO2PEAK (r = -0.61; p < 0.05) in TR group. The ventilation behavior during incremental treadmill test tends to show only one threshold. UT subjects showed a slower ventilation increase during moderate intensities while TR subjects showed a slower ventilation increase during heavy intensities.

Exceptional times for the dynamical discrete web

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed tau. In this paper, we study the existence of exceptional (random) values of tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by Haggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, Haggstrom, Peres and Steif. For example, we prove that the walk from the origin S(0)(tau) violates the law of the iterated logarithm (LIL) on a set of tau of Hausdorff dimension one. We also discuss how these and other results should extend to the dynamical Brownian web, the natural scaling limit of the DyDW. (C) 2009 Elsevier B.V. All rights reserved.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Ventilation behavior during upper-body incremental exercise

Pires, FO, Hammond, J, Lima-Silva, AE, Bertuzzi, RCM, and Kiss, MAPDM. Ventilation behavior during upper-body incremental exercise. J Strength Cond Res 25(1): 225-230, 2011-This study tested the ventilation (V(E)) behavior during upper-body incremental exercise by mathematical models that calculate 1 or 2 thresholds and compared the thresholds identified by mathematical models with V-slope, ventilatory equivalent for oxygen uptake (V(E)/(V) over dotO(2)), and ventilatory equivalent for carbon dioxide uptake (V(E)/(V) over dotCO(2)). Fourteen rock climbers underwent an upper-body incremental test on a cycle ergometer with increases of approximately 20 W.min(-1) until exhaustion at a cranking frequency of approximately 90 rpm. The V(E) data were smoothed to 10-second averages for V(E) time plotting. The bisegmental and the 3-segmental linear regression models were calculated from 1 or 2 intercepts that best shared the V(E) curve in 2 or 3 linear segments. The ventilatory threshold(s) was determined mathematically by the intercept(s) obtained by bisegmental and 3-segmental models, by V-slope model, or visually by V(E)/(V) over dotO(2) and V(E)/(V) over dotCO(2). There was no difference between bisegmental (mean square error [MSE] = 35.3 +/- 32.7 l.min(-1)) and 3-segmental (MSE = 44.9 +/- 47.8 l.min(-1)) models in fitted data. There was no difference between ventilatory threshold identified by the bisegmental (28.2 +/- 6.8 ml.kg(-1).min(-1)) and second ventilatory threshold identified by the 3-segmental (30.0 +/- 5.1 ml.kg(-1).min(-1)), V(E)/(V) over dotO(2) (28.8 +/- 5.5 ml.kg(-1).min(-1)), or V-slope (28.5 +/- 5.6 ml.kg(-1).min(-1)). However, the first ventilatory threshold identified by 3-segmental (23.1 +/- 4.9 ml.kg(-1).min(-1)) or by VE/(V) over dotO(2) (24.9 +/- 4.4 ml.kg(-1).min(-1)) was different from these 4. The V(E) behavior during upper-body exercise tends to show only 1 ventilatory threshold. These findings have practical implications because this point is frequently used for aerobic training prescription in healthy subjects, athletes, and in elderly or diseased populations. The ventilatory threshold identified by V(E) curve should be used for aerobic training prescription in healthy subjects and athletes.

Performance of different immobilized lipases in palm oil biodiesel synthesis

Performance of different immobilized lipases in palm oil biodiesel synthesis. Optimized conditions for palm oil and ethanol enzymatic biodiesel synthesis were determined with different immobilized lipases SiO(2)-PVA-immobilized lipase from Pseudomonas fluorescens and acrylic resin-immobilized lipase, Novozym (R) 435, from Candida antartica, in solvent-free medium. A full factorial design assessed the influence of temperature (42 - 58 degrees C) and ethanol: palm oil (6:1 - 18:1) molar ratio on the transesterification yield. Main effects were adjusted by multiple regression analysis to linear models and the maximum transesterification yield was obtained at 42 degrees C and 18:1 ethanol: palm oil molar ratio. Mathematical models featuring total yield for each immobilized lipase were suitable to describe the experimental results.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Estudo de variabilidade e otimização do circuito de moagem SAG da Usina do Sossego

Sossego was the first Vale SAG mill operation to process copper-gold ore. It is located in the State of Para, southeastern Amazon region of Brazil. In the first three years of continuous operation, Vale investigated different alternatives for improving the circuit`s performance by investigating operating conditions, mainly focusing on the SAG mill. It was decided to further assess the performance of the comminution circuit as a function of ore characteristics. A comprehensive ore characterization program was then conducted, together with the calibration of mathematical models on the basis of surveys carried out at the industrial circuit. The simulator was then used to predict the throughput associated to each ore type, as well as to establish the optimized circuit configuration and tailored operating conditions. This paper describes in detail the main aspects of optimizing the industrial circuit performance, as well as the successful method for predicting the production as a function of ore characteristics and circuit configuration.

Modelling grain boundary migration during geometric dynamic recrystallization

High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2 pi, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2 pi, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.

Investigation of Cationic Polymerization of beta-Pinene Using Calorimetric Measurements

An experimental investigation of the kinetics of cationic polymerization of beta-pinene was performed using two different initiator systems under two different operating conditions (shot additions of initiator, and continuous feeding of monomer). The experiments were done using calorimetric measurements under isoperibolic conditions. The heat of polymerization of beta-pinene was found to be -30.6 kcal . mol(-1). A simple kinetic model was tentatively proposed, and the model fit reasonably well to the different experimental runs. Different values of the fitting parameters were obtained for runs carried out under different conditions, which can probably be ascribed to the presence of adventitious impurities in the commercial-grade monomer used.