An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Structure and energetics of nanometer size clusters of sulfuric acid with ammonia and dimethylamine

The structures of positively and negatively charged clusters of sulfuric acid with ammonia and/or dimethylamine ((CH(3))(2)NH or DMA) are investigated using a combination of Monte Carlo configuration sampling, semiempirical calculations, and density functional theory (DFT) calculations. Positively charged clusters of the formula [(NH(4)(+))(x)(HSO(4)(-))(y)](+), where x = y + 1, are studied for 1 ≤ y ≤ 10. These clusters exhibit strong cation-anion interactions, with no contribution to the hydrogen-bonding network from the bisulfate ion protons. A similar hydrogen-bonding network is found for the [(DMAH(+))(5)(HSO(4)(-))(4)](-) cluster. Negatively charged clusters derived from the reaction of DMA with [(H(2)SO(4))(3)(NH(4)(+))(HSO(4)(-))(2)](-) are also studied, up to the fully reacted cluster [(DMAH(+))(4)(HSO(4)(-))(5)](-). These clusters exhibit anion-anion and ion-molecule interactions in addition to cation-anion interactions. While the hydrogen-bonding network is extensive for both positively and negatively charged clusters, the binding energies of ions and molecules in these clusters are determined mostly by electrostatic interactions. The thermodynamics of amine substitution is explored and compared to experimental thermodynamic and kinetic data. Ammonia binds more strongly than DMA to sulfuric acid due to its greater participation in hydrogen bonding and its ability to form a more compact structure that increases electrostatic attraction between oppositely charged ions. However, the greater gas-phase basicity of DMA is sufficient to overcome the stronger binding of ammonia, making substitution of DMA for ammonia thermodynamically favorable. For small clusters of both polarities, substitutions of surface ammonium ions are facile. As the cluster size increases, an ammonium ion becomes encapsulated in the center of the cluster, making it inaccessible to substitution.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.