A method for enhancing the stability and robustness of explicit schemes in astrophysical fluid dynamics

A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or strongly-implicit schemes. From the point of view of matrix-algebra, explicit numerical methods are special cases in which the global matrix of coefficients is reduced to the identity matrix $I$. This extreme simplification leads to severer stability range, hence of their robustness. In this paper it is shown that a condition, which is similar to the Courant-Friedrich-Levy (CFL) condition can be obtained from the stability requirement of inversion of the coefficient matrix. This condition is shown to be relax-able, and that a class of methods that range from explicit to strongly implicit methods can be constructed, whose degree of implicitness depends on the number of coefficients used in constructing the corresponding coefficient-matrices. Special attention is given to a simple and tractable semi-explicit method, which is obtained by modifying the coefficient matrix from the identity matrix $I$ into a diagonal-matrix $D$. This method is shown to be stable, robust and it can be applied to search for stationary solutions using large CFL-numbers, though it converges slower than its implicit counterpart. Moreover, the method can be applied to follow the evolution of strongly time-dependent flows, though it is not as efficient as normal explicit methods. In addition, we find that the residual smoothing method accelerates convergene toward steady state solutions considerably and improves the efficiency of the solution procedure.Comment: 33 pages, 15 figure

On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

Monte Carlo Methods for Equilibrium and Nonequilibrium Problems in Interfacial Electrochemistry

We present a tutorial discussion of Monte Carlo methods for equilibrium and nonequilibrium problems in interfacial electrochemistry. The discussion is illustrated with results from simulations of three specific systems: bromine adsorption on silver (100), underpotential deposition of copper on gold (111), and electrodeposition of urea on platinum (100).Comment: RevTex, 14 pages, 8 figures. To appear in book _Interfacial Electrochemisty

Chemical vapor deposition modeling for high temperature materials

The formalism for the accurate modeling of chemical vapor deposition (CVD) processes has matured based on the well established principles of transport phenomena and chemical kinetics in the gas phase and on surfaces. The utility and limitations of such models are discussed in practical applications for high temperature structural materials. Attention is drawn to the complexities and uncertainties in chemical kinetics. Traditional approaches based on only equilibrium thermochemistry and/or transport phenomena are defended as useful tools, within their validity, for engineering purposes. The role of modeling is discussed within the context of establishing the link between CVD process parameters and material microstructures/properties. It is argued that CVD modeling is an essential part of designing CVD equipment and controlling/optimizing CVD processes for the production and/or coating of high performance structural materials

Information Filtering on Coupled Social Networks

In this paper, based on the coupled social networks (CSN), we propose a hybrid algorithm to nonlinearly integrate both social and behavior information of online users. Filtering algorithm based on the coupled social networks, which considers the effects of both social influence and personalized preference. Experimental results on two real datasets, \emph{Epinions} and \emph{Friendfeed}, show that hybrid pattern can not only provide more accurate recommendations, but also can enlarge the recommendation coverage while adopting global metric. Further empirical analyses demonstrate that the mutual reinforcement and rich-club phenomenon can also be found in coupled social networks where the identical individuals occupy the core position of the online system. This work may shed some light on the in-depth understanding structure and function of coupled social networks

Spectral Generalized Multi-Dimensional Scaling

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, multidimensional scaling into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by implicitly incorporating smoothness of the mapping into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state-of-the-art approaches

Tag-Aware Recommender Systems: A State-of-the-art Survey

In the past decade, Social Tagging Systems have attracted increasing attention from both physical and computer science communities. Besides the underlying structure and dynamics of tagging systems, many efforts have been addressed to unify tagging information to reveal user behaviors and preferences, extract the latent semantic relations among items, make recommendations, and so on. Specifically, this article summarizes recent progress about tag-aware recommender systems, emphasizing on the contributions from three mainstream perspectives and approaches: network-based methods, tensor-based methods, and the topic-based methods. Finally, we outline some other tag-related works and future challenges of tag-aware recommendation algorithms.Comment: 19 pages, 3 figure