Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices

In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255-258). Here we give a larger list of values for more than forty lattices in two to six dimensions. In this list are new results for fcc, bcc, and diamond lattices in 4, 5, and 6 dimensions. The list contains examples of lattices with equal site percolation thresholds, but different bond percolation thresholds. These and other examples show that there are deviations from the proposed invariant of up to 12% in two dimensions, increasing to 69% in higher dimensions.Comment: 12 pages, 3 figures (EPS), LaTe

HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part I. Multilevel Analysis

The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge-Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space-time discontinuous Galerkin discretization of the advection-diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for low and high cell Reynolds numbers and on highly stretched meshes

Hot Molecular Cores and High-Mass Star Formation

This review covers hot cores in the context of high-mass star formation. After giving an overview of chemical processes and diversity during high-mass star formation, it reviews the `warm envelope' phase which probably precedes the formation of hot cores. Some recent determinations of the cosmic-ray ionization rate are discussed, as well as recent evidence for hot cores around low-mass stars. Routes for future hot core research are outlined.Comment: 8 pages, 1 figure; to appear in the Proceeding of IAU Symposium 221, Star Formation at High Angular Resolution, Editors M. Burton, R. Jayawardhana & T. Bourke, Astronomical Society of the Pacifi

HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II. Optimization of the Runge-Kutta smoother

Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit Runge-Kutta smoother, such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints. The Runge-Kutta coefficients for a wide range of cell Reynolds numbers and a detailed analysis of the performance of the hp-MGS algorithm are presented. In addition, the computational complexity of the hp-MGS algorithm is investigated. The hp-MGS algorithm is tested on a fourth order accurate space-time discontinuous Galerkin finite element discretization of the advection-diffusion equation for a number of model problems, which include thin boundary layers and highly stretched meshes, and a non-constant advection velocity. For all test cases excellent multigrid convergence is obtained

Discrete Fourier analysis of multigrid algorithms

The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the hp-Multigrid as Smoother algorithm, which is a new algorithm suitable for higher order accurate discontinuous Galerkin discretizations of advection dominated flows. In order to analyze the performance of the multigrid algorithms the error transformation operator for several linear multigrid algorithms are derived. The operator norm and spectral radius of the multigrid error transformation are then computed using discrete Fourier analysis. First, the main operations in the discrete Fourier analysis are defined, including the aliasing of modes. Next, the Fourier symbol of the multigrid operators is computed and used to obtain the Fourier symbol of the multigrid error transformation operator. In the multilevel analysis, two and three level h-multigrid, both for uniformly and semi-coarsened meshes, are considered, and also the analysis of the hp-Multigrid as Smoother algorithm for three polynomial levels and three uniformly and semi-coarsened meshes. The report concludes with a discussion of the multigrid operator norm and spectral radius. In the appendix some useful auxiliary results are summarized

A micromechanical fracture analysis to investigate the effect of healing particles on the overall mechanical response of a self-healing particulate composite

A computational fracture analysis is conducted on a self‐healing particulate composite employing a finite element model of an actual microstructure. The key objective is to quantify the effects of the actual morphology and the fracture properties of the healing particles on the overall mechanical behaviour of the (MoSi2) particle‐dispersed Yttria Stabilised Zirconia (YSZ) composite. To simulate fracture, a cohesive zone approach is utilised whereby cohesive elements are embedded throughout the finite element mesh allowing for arbitrary crack initiation and propagation in the microstructure. The fracture behaviour in terms of the composite strength and the percentage of fractured particles is reported as a function of the mismatch in fracture properties between the healing particles and the matrix as well as a function of particle/matrix interface strength and fracture energy. The study can be used as a guiding tool for designing an extrinsic self‐healing material and understanding the effect of the healing particles on the overall mechanical properties of the material

Mixing in T-junctions

The transport processes that are involved in the mixing of two gases in a T-junction mixer are investigated. The turbulent flow field is calculated for the T-junction with the k- turbulence model by FLOW3D. In the mathematical model the transport of species is described with a mixture fraction variable for the average mass fraction and the variance of the mixture fraction for the temporal fluctuations. The results obtained by numerical simulations are verified in a well-defined experiment. The velocity as well as the concentration field are measured in several types of T-junctions. Comparison of the predicted and measured average concentration fields show good agreement if the Schmidt number for turbulent diffusion is taken as 0.2. Temporal concentration fluctuations are calculated and found to be of equal magnitude as spatial fluctuations. Good mixing is obtained in a T-junction if the branch inlet flow is designed to penetrate to the opposite tube wall in the mixer

On the Micro-Dynamics of a Cash-in-Advance Economy (revised version of WP 04-12)

The purpose of this paper is to develop a general equilibrium model with money and trade taking place at disequilibrium prices. There are multiple markets being visited sequentially and transactions occur along the adjustment path. This implies quantity rationing to clear the market and we assume that there are cash-in-advance constraints on the transactions. The updating of the prices and cash balances along the way makes it necessary for agents to reconsider their trading plans subject to new information due to substitution and spill-over effects. The dynamics of this disequilibrium re-optimization process are shown to depend crucially on the exchange mechanisms that are imposed. One of the results is that the introduction of a cash-in-advance constraint does not help in stabilizing the fluctuations of cash balances, even though it does prevent debts from occurring outside of equilibrium.

A cohesive-zone crack healing model for self-healing materials

A cohesive zone-based constitutive model, originally developed to model fracture, is extended to include a healing variable to simulate crack healing processes and thus recovery of mechanical properties. The proposed cohesive relation is a composite-type material model that accounts for the properties of both the original and the healing material, which are typically different. The constitutive model is designed to capture multiple healing events, which is relevant for self-healing materials that are capable of generating repeated healing. The model can be implemented in a finite element framework through the use of cohesive elements or the extended finite element method (XFEM). The resulting numerical framework is capable of modeling both extrinsic and intrinsic self-healing materials. Salient features of the model are demonstrated through various homogeneous deformations and healing processes followed by applications of the model to a self-healing material system based on embedded healing particles under non-homogeneous deformations. It is shown that the model is suitable for analyzing and optimizing existing self-healing materials or for designing new self-healing materials with improved lifetime characteristics based on multiple healing events

Higher education course content: paper-based, online or hybrid course delivery?

[Abstract]: The emergence of the Internet has made many institutions involved in the delivery of distance education programs re-evaluate the course delivery framework. A variety of models and techniques co-exist in an often uneasy alliance at many such institutions. These range from the traditional distance learning model, which remains paper-based, to the purely online model. Recently, hybrid models have emerged which apparently attempt to forge elements taken from several models into a unified whole. Many of these hybrid models seek to eliminate paper-based materials from the tuition process. While many arguments are put forward about the efficacy of purely electronic delivery mechanisms, cost containment is often the driving motivation. This study explores student perceptions of the various delivery mechanisms for distance learning materials. In particular, it seeks to determine what value students place on paper-based delivery mechanisms. The study surveys a group of undergraduate students and a group of graduate students enrolled in the Faculty of Business at a large regional Australian university