Anisotropic singularities in modified gravity models

We show that the common singularities present in generic modified gravity models governed by actions of the type S = integral d(4)x root-gf(R, phi, X). with X = -1/2 g(ab)partial derivative(a)phi partial derivative(b)phi, are essentially the same anisotropic instabilities associated to the hypersurface F(phi) = 0 in the case of a nonminimal coupling of the type F(phi)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface partial derivative f/partial derivative R = 0 is attained. Some examples are explicitly discussed.

Bayesian updating rules in continuous opinion dynamics models

Here, I investigate the use of Bayesian updating rules applied to modeling how social agents change their minds in the case of continuous opinion models. Given another agent statement about the continuous value of a variable, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a uniform distribution. This represents the idea that the other agent might have no idea about what is being talked about. The effect of updating only the first moments of the distribution will be studied, and we will see that this generates results similar to those of the bounded confidence models. On also updating the second moment, several different opinions always survive in the long run, as agents become more stubborn with time. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.

Scaling of structures subject to impact loads when using a power law constitutive equation

It is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads. (C) 2009 Elsevier Ltd. All rights reserved.

AN ASSESSMENT ON THE USE OF THE DEBYE-HUCKEL EQUATION FOR THE THERMODYNAMIC MODELING OF AQUEOUS SYSTEMS CONTAINING POLYMERS AND SALTS

In this work, a study on the role of the long-range term of excess Gibbs energy models in the modeling of aqueous systems containing polymers and salts is presented. Four different approaches on how to account for the presence of polymer in the long-range term were considered, and simulations were conducted considering aqueous solutions of three different salts. The analysis of water activity curves showed that, in all cases, a liquid-phase separation may be introduced by the sole presence of the polymer in the long-range term, regardless of how it is taken into account. The results lead to the conclusion that there is no single exact solution for this problem, and that any kind of approach may introduce inconsistencies.

Mutually connected phase-locked loop networks: dynamical models and design parameters

Distribution of timing signals is an essential factor for the development of digital systems for telecommunication networks, integrated circuits and manufacturing automation. Originally, this distribution was implemented by using the master-slave architecture with a precise master clock generator sending signals to phase-locked loops (PLL) working as slave oscillators. Nowadays, wireless networks with dynamical connectivity and the increase in size and operation frequency of the integrated circuits suggest that the distribution of clock signals could be more efficient if mutually connected architectures were used. Here, mutually connected PLL networks are studied and conditions for synchronous states existence are analytically derived, depending on individual node parameters and network connectivity, considering that the nodes are nonlinear oscillators with nonlinear coupling conditions. An expression for the network synchronisation frequency is obtained. The lock-in range and the transmission error bounds are analysed providing hints to the design of this kind of clock distribution system.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

Spatial portability of numerical models of leaf wetness duration based on empirical approaches

Leaf wetness duration (LWD) models based on empirical approaches offer practical advantages over physically based models in agricultural applications, but their spatial portability is questionable because they may be biased to the climatic conditions under which they were developed. In our study, spatial portability of three LWD models with empirical characteristics - a RH threshold model, a decision tree model with wind speed correction, and a fuzzy logic model - was evaluated using weather data collected in Brazil, Canada, Costa Rica, Italy and the USA. The fuzzy logic model was more accurate than the other models in estimating LWD measured by painted leaf wetness sensors. The fraction of correct estimates for the fuzzy logic model was greater (0.87) than for the other models (0.85-0.86) across 28 sites where painted sensors were installed, and the degree of agreement k statistic between the model and painted sensors was greater for the fuzzy logic model (0.71) than that for the other models (0.64-0.66). Values of the k statistic for the fuzzy logic model were also less variable across sites than those of the other models. When model estimates were compared with measurements from unpainted leaf wetness sensors, the fuzzy logic model had less mean absolute error (2.5 h day(-1)) than other models (2.6-2.7 h day(-1)) after the model was calibrated for the unpainted sensors. The results suggest that the fuzzy logic model has greater spatial portability than the other models evaluated and merits further validation in comparison with physical models under a wider range of climate conditions. (C) 2010 Elsevier B.V. All rights reserved.

Does using stepwise variable selection to build sequential path analysis models make sense?

Causal inference methods - mainly path analysis and structural equation modeling - offer plant physiologists information about cause-and-effect relationships among plant traits. Recently, an unusual approach to causal inference through stepwise variable selection has been proposed and used in various works on plant physiology. The approach should not be considered correct from a biological point of view. Here, it is explained why stepwise variable selection should not be used for causal inference, and shown what strange conclusions can be drawn based upon the former analysis when one aims to interpret cause-and-effect relationships among plant traits.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Bayesian analysis and constraints on kinematic models from union SNIa

The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter ( constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter ( constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat Lambda CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q(0) and j(0)) and for the transition redshift (z(t)) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the 1 sigma confidence limits imply the following ranges of values: q(0) is an element of [-0.96, -0.46], j(0) is an element of [-3.2,-0.3] and z(t) is an element of [0.36, 0.84], which are compatible with the Lambda CDM predictions, q(0) = -0.57 +/- 0.04, j(0) = -1 and z(t) = 0.71 +/- 0.08. We find that even very simple kinematic models are equally good to describe the data compared to the concordance Lambda CDM model, and that the current observations are not powerful enough to discriminate among all of them.

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.

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.

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.