Subdiffusion and cage effect in a sheared granular material

We investigate experimentally the diffusion properties of a bidimensional bidisperse dry granular material under quasistatic cyclic shear.The comparison of these properties with results obtained both in computer simulations of hard spheres systems and Lenard-Jones liquids and experiments on colloidal systems near the glass transition demonstrates a strong analogy between the behaviour of granular matter and these systems. More specifically, we study in detail the cage dynamics responsible for the subdiffusion in the slow relaxation regime, and obtain the values of relevant time and length scales.Comment: 4 pages, 6 figures, submitted to PR

The effect of collinearity-influential observations on collinear data set: a Monte Carlo simulation study

In this study, the effect of different patterns of high leverages on the classical multicollinearity diagnostics and collinearity-influential measure is investigated. Specifically the investigation is focus on in which situations do these points become collinearity-enhancing or collinearity-reducing observations. Both the empirical and the Monte Carlo simulation results, in collinear data sets indicate that when high leverages exist in just one explanatory variable or when the values of the high leverages are in different positions of the two explanatory variables, these points will be collinearity-reducing observations. On the other hand, these high leverages are collinearity-enhancing observations when their values and positions are the same for the two collinear explanatory variables

Estimating regression coefficients using weighted bootstrap with probability.

In this paper we propose a new weighted bootstrap with probability (WBP). The basic idea of the proposed bootstrap technique is to do re-sampling with probabilities. These probabilities become the control mechanism for getting good estimates when the original data set contain multiple outliers. Numerical examples and simulation study are carried out to evaluate the performance of the WBP estimates as compared to the bootstrap 1 and diagnostic-before bootstrap estimates. The results of the study signify that the WBP method is more efficient than the other two methods

Model for erosion-deposition patterns

We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling between the fluid flow and the movement of particles due to local drag forces. Our results for this irreversible process show that the model is capable to reproduce typical natural patterns caused by well known erosion processes. Moreover, we observe that, within a certain range of porosity values, the grains form clusters that are tilted with respect to the horizontal with a characteristic angle. We compare our results to recent experiments for granular material in flowing water and show that they present a satisfactory agreement.Comment: 8 pages, 12 figures, submitted to Phys. Rev.

Two-step robust estimator in heteroscedastic regression model in the presence of outliers

Although the ordinary least squares (OLS) estimates are unbiased in the presence of heteroscedasticity, these are no longer efficient. This problem becomes more complicated when the violation of constant error variances comes together with the existence of outliers. The weighted least squares (WLS) procedure is often used to estimate the regression parameters when heteroscedasticity occurs in the data. But there is evidence that the WLS estimators suffer a huge set back in the presence of outliers. Moreover, the use of the WLS requires a known form of the heteroscedastic errors structures. To rectify this problem, we proposed a new method that we call two step robust weighted least squares (TSRWLS) method where prior information on the structure of the heteroscedastic errors is not required. In the proposed procedure, the robust technique is used twice. Firstly, the robust weights are used for solving the heteroscedasic error and secondly, the robust weighting function is used for eliminating the effect of outliers. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations

Estimation of parameters in heteroscedastic multiple regression model using leverage based near-neighbors.

In this study, we propose a Leverage Based Near-Neighbor (LBNN) method where prior information on the structure of the heteroscedastic error is not required. In the proposed LBNN method, weights are determined not from the near-neighbor values of the explanatory variables, but from their corresponding leverage values so that it can be readily applied to a multiple regression model. Both the empirical and Monte Carlo simulation results show that the LBNN method offers substantial improvement over the existing methods. The LBNN has significantly reduced the standard errors of the estimates and also the standard errors of residuals for both simple and multiple linear regression models. Hence, the LBNN can be established as one reliable alternative approach to other existing methods that deal with heteroscedastic errors when the form of heteroscedasticity is unknown

Avalanche statistics and time-resolved grain dynamics for a driven heap

We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-two dimensional heap. To characterize the time-dependent average avalanche flow speed v(t), we image the top free surface. To characterize the grain fluctuation speed dv(t), we use Speckle-Visibility Spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, and that these speeds are largest near the beginning of an event. We also find that the distribution of event durations is peaked, and that event sizes are correlated with the time interval since the end of the previous event. At high rates of grain addition, where successive avalanches merge into smooth continuous flow, the relationship between average and fluctuation speeds changes to dv Sqrt[v]

The S shape of a granular pile in a rotating drum

The shape of a granular pile in a rotating drum is investigated. Using Discrete Elements Method (DEM) simulations we show that the "S shape" obtained for high rotation speed can be accounted for by the friction on the end plates. A theoretical model which accounts for the effect of the end plates is presented and the equation of the shape of the free surface is derived. The model reveals a dimensionless number which quantifies the influence of the end plates on the shape of the pile. Finally, the scaling laws of the system are discussed and numerical results support our conclusions

Dynamics of grain ejection by sphere impact on a granular bed

The dynamics of grain ejection consecutive to a sphere impacting a granular material is investigated experimentally and the variations of the characteristics of grain ejection with the control parameters are quantitatively studied. The time evolution of the corona formed by the ejected grains is reported, mainly in terms of its diameter and height, and favourably compared with a simple ballistic model. A key characteristic of the granular corona is that the angle formed by its edge with the horizontal granular surface remains constant during the ejection process, which again can be reproduced by the ballistic model. The number and the kinetic energy of the ejected grains is evaluated and allows for the calculation of an effective restitution coefficient characterizing the complex collision process between the impacting sphere and the fine granular target. The effective restitution coefficient is found to be constant when varying the control parameters.Comment: 9 page

Robust Wild Bootstrap for Stabilizing the Variance of Parameter Estimates in Heteroscedastic Regression Models in the Presence of Outliers

Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)'s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect