Cellular automaton for the fracture of disordered media

We study numerically the growth of a crack in an elastic medium under the influence of a travelling shockwave. We describe the implementation of a fast algorithm which is perfectly suited for a data parallel computer. Using large scale simulations on the Connection Machine we generate cracks with more than 10000 sites on a $\scriptstyle 1024 \times 1024$ lattice. We show that the resulting patterns are fractal with a fractal dimension that depends on the chosen breaking criterion and varies between $\scriptstyle 1.$ and $\scriptstyle 2.$Comment: 9 pages, 6 figures (3 included), plain TeX (using vanilla.sty, epsf.tex), HLRZ-preprint 46/9

Power law tail in the radial growth probability distribution for DLA

Using both analytic and numerical methods, we study the radial growth probability distribution $P(r,M)$ for large scale off lattice diffusion limited aggregation (DLA) clusters. If the form of $P(r,M)$ is a Gaussian, we show analytically that the width $\xi(M)$ of the distribution {\it can not} scale as the radius of gyration $R_G$ of the cluster. We generate about $1750$ clusters of masses $M$ up to $500,000$ particles, and calculate the distribution by sending $10^6$ further random walkers for each cluster. We give strong support that the calculated distribution has a power law tail in the interior ($r\sim 0$) of the cluster, and can be described by a scaling Ansatz $P(r,M) \propto {r^\alpha\over\xi}\cdot g\left( {r-r_0}\over \xi \right)$, where $g(x)$ denotes some scaling function which is centered around zero and has a width of order unity. The exponent $\alpha$ is determined to be $\approx 2$, which is now substantially smaller than values measured earlier. We show, by including the power-law tail, that the width {\it can} scale as $R_G$, if $\alpha > D_f-1$.Comment: 11 pages, LaTeX, 5 figures not included, HLRZ preprint-29/9

Improving Informational Bases of Performance Measurement with Grey Relation Analysis

Performance measurement (PM) needs objective empirical data with causal relevance in order to steer and control financial performance generation. In business practice, there is often a lack of such objective data. A surrogate might be collected subjectively based on data generated by questioning corporate experts. Such an involvement of subjects can rapidly lead to an immense extent of data that (partially) imply incomplete information. To handle this imperfection of data, the Grey systems theory (GST) and especially its element, the Grey relation analysis (GRA), seem to be methodologies able to improve informational bases for PM purposes. Therefore, GRA is able to reveal those performance indicators that considerably influence the corporate financial performance, the key performance indicators. GRA is able to supply valid results with only four data points of a time series. Hence, the GST provides an improvement of the PM framework in situations of incomplete information, which is demonstrated in the following

Performance Management by Causal Mapping: An Application Field of Knowledge Management

As implied by the performance management (PM) concept, modern corporate management has to focus on cause-and-effect relationships underlying a firm´s financial performance generation. To determine the causes of financially desirable effects, subject-bound experiences and knowledge of employees, called tacit knowledge, should be realised. For this, knowledge management (KM) offers various elicitation techniques to reveal corporate-specific success factors (SFs) of financial performance generation from the corporate experts´ implicit knowledge. The identified factors have to be organised within a network of cause-and-effect relationships. In this framework, PM can apply the instrument of mapping to structure the individually revealed knowledge, to aggregate and visualise it for the entire company. For a valid representation of the causal relationships, the subjective bias arising within the mentioned process has to be minimised. In the literature, a variety of mapping methods can be found that differ in their approaches and their level of significance. As such a method, causal mapping will be presented in this paper. For providing intersubjectivity, the decision-making trail and evaluation laboratory (DEMATEL) as a multi-criteria approach will be debated in the context of mapping as a research field