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Abstract: The simulation of granular materials requires an initial overlap-free packing of spherical particles at high volume packing fractions. In previous work, a dynamics-based collective approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed spheres in an enclosed container. However, the stability and efficiency of the QDM were not fully addressed. In this paper, the algorithm is reformulated with two control parameters and the impact of these parameters on the algorithm performance is investigated. First, theoretical analyses and numerical verifications for extreme 1-D/2-D packing systems are conducted and the range of the control parameters in which the algorithm is convergent is analytically determined. Then, the analysis is extended to 3-D packing systems and the estimation of the parameter range is verified numerically. Finally, the algorithm is applied to modeling a cylindrical 3-D packing system and the convergence performance at different volume packing fractions is studied. Results show that the QDM is highly efficient in packing spheres at volume packing fractions that are close to the random close packing limit. [Copyright &y& Elsevier]

Abstract: Bayesian inference methods are used extensively in the analysis of Generalized Linear Mixed Models (GLMMs), but it may be difficult to handle the posterior distributions analytically. In this paper, we establish the asymptotic normality of the joint posterior distribution of the parameters and the random effects in a GLMM by using Stein’s Identity. We also show that while incorrect assumptions on the random effects can lead to substantial bias in the estimates of the parameters, the assumed model for the random effects, under some regularity conditions, does not affect the asymptotic normality of the joint posterior distribution. This motivates the use of the approximate normal distributions for sensitivity analysis of the random effects distribution. We additionally illustrate that the approximate normal distribution performs reasonably using both real and simulated data. This creates a primary alternative to Markov Chain Monte Carlo (MCMC) sampling and avoids a wide range of problems for MCMC algorithms in terms of convergence and computational time. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new method for finding the optimal smoothing parameter for the abstract smoothing spline . The latter is defined as the solution of the minimization problem and, given an estimate for the noise, the standard choice for is that should satisfy the residual equation Whereas the classical algorithm for solving this equation based on Newton’s method converges quadratically, our new method can have any given order of convergence. [Copyright &y& Elsevier]