COMPARISON OF EXPONENTIAL COVARIANCE FUNCTIONS FOR BIVARIATE GEOSTATISTICAL DATA

In the analysis of multivariate spatial random elds, it is essential to dene a covariance structure that adequately models the relationship between the variables under study. We propose a covariance structure with exponential correlation function for bivariate random elds, the SEC model. We compare the SEC model fits with the bivariate separable exponential model and the bivariate exponential model with constraints, which are particular cases of the full bivariate Matern model, presented in the literature. A simulation study assess characteristics of the proposed model. The model is tted to a weather data set from Brazil, bearing in mind the importance of analyzing climate data to predict adverse environmental conditions. Predictive measures are used to compare the models under study. The satisfactory results compared to the models considered and the simpler structure makes the SEC model an alternative for the analysis of bivariate spatial elds.

Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos

Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem.

Prediction of Springback in the Air Bending Process Using a Kriging Metamodel

This paper addresses the use of the kriging‏ approach to predict the springback in the air bending process. The materials and the geometrical parameters, which significantly affect the springback, were considered as inputs, and the springback angle was considered as the response. A verified nonlinear finite element model was used to generate the training data required to create the kriging‏ metamodel. The training examples were selected based on computer-generated D-optimal designs. A comparison between the kriging approaches and the response surface methodology is conducted and discussed. The results showed that kriging accurately predicts the finite element springback results. Comparing the accuracy of kriging with a response surface methodology shows that kriging with a 2nd degree polynomial and exponential correlation function predicts the springback more accurately than the response surface methodology.

Mobility Limitations due to Dislocations and Interface Roughness in AlGaN/AlN/GaN Heterostructure

The dislocations and surface roughness in an AlGaN/AlN/GaN heterostructure were analyzed by transmission electron microscopy (TEM) and atomic force microscopy (AFM), respectively, and the mobility limitation mechanisms in the two-dimensional electron gas (2DEG) were studied using a theoretical model that took into account the most important scattering mechanisms. An exponential correlation function provides a better description of the statistical properties of surface roughness than the Gaussian form and thus is adopted in the theoretical model. The calculated results are in good agreement with Hall data. The quantitative measurements of dislocations and surface roughness allow the evaluation of the relative importance of each extrinsic scattering mechanism.

Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

We consider a generalized Malthus-Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity.

Consolute Critical Phenomena in Dilute Silica Gel

The effect of even dilute silica networks on the critical phenomena of binary liquid mixtures is profound. The network preferentially adsorbs one component, preventing a portion of the mixture from participating in critical fluctuations. Fluctuations in the remaining mixture are found to decay with a non-exponential correlation function near the consolute point. A correlation function consisting of the sum of an exponential decay and a non-exponential term of either an activated or stretched exponential form fits the data well. In the presence of the silica network, the mixtures are observed to phase separate near the critical temperature of the pure system, but while still in the one-phase region of the pure system.