Mean curvature flow with triple junctions in higher space dimensions

We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120 degree angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hoelder spaces.Comment: 31 pages, 2 figure

Adaptive inferential sensors based on evolving fuzzy models

A new technique to the design and use of inferential sensors in the process industry is proposed in this paper, which is based on the recently introduced concept of evolving fuzzy models (EFMs). They address the challenge that the modern process industry faces today, namely, to develop such adaptive and self-calibrating online inferential sensors that reduce the maintenance costs while keeping the high precision and interpretability/transparency. The proposed new methodology makes possible inferential sensors to recalibrate automatically, which reduces significantly the life-cycle efforts for their maintenance. This is achieved by the adaptive and flexible open-structure EFM used. The novelty of this paper lies in the following: (1) the overall concept of inferential sensors with evolving and self-developing structure from the data streams; (2) the new methodology for online automatic selection of input variables that are most relevant for the prediction; (3) the technique to detect automatically a shift in the data pattern using the age of the clusters (and fuzzy rules); (4) the online standardization technique used by the learning procedure of the evolving model; and (5) the application of this innovative approach to several real-life industrial processes from the chemical industry (evolving inferential sensors, namely, eSensors, were used for predicting the chemical properties of different products in The Dow Chemical Company, Freeport, TX). It should be noted, however, that the methodology and conclusions of this paper are valid for the broader area of chemical and process industries in general. The results demonstrate that well-interpretable and with-simple-structure inferential sensors can automatically be designed from the data stream in real time, which predict various process variables of interest. The proposed approach can be used as a basis for the development of a new generation of adaptive and evolving inferential sensors that can a- ddress the challenges of the modern advanced process industry

Network structural properties for cluster long run dynamics. Evidence from collaborative R&D networks in the European mobile phone industry

In a recent literature, the structural properties of knowledge networks have been pointed out as a critical factor for cluster structural changes and long run dynamics. Mixing evolutionary economic geography and network-based approach of clusters, this contribution aims at capturing and discussing the particular influence of hierarchy (degree distribution) and assortativity (degree correlation) in the innovative capabilities of clusters along the industry life cycle. We test our propositions in the field of the mobile phone industry in Europe from 1988 to 2008. We use EPO PATSTAT and OECD REGPAT to capture cluster trends, and R&D relations from European Framework Programs to capture knowledge networks and their evolving structural properties. Our findings provide new insights to understand the organization of clusters over time in order to perform along the industry life cycl

A stochastic Monte Carlo approach to model real star cluster evolution, II. Self-consistent models and primordial binaries

The new approach outlined in Paper I (Spurzem \& Giersz 1996) to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few percent of the initial number of stars in the cluster). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300.000 equal point-mass stars, plus 30.000 equal mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. In a self-consistent model it is the first time that such a realistically large number of binaries is evolving in a cluster with an even ten times larger number of single stars. Due to the Monte Carlo treatment of the binaries we can at every moment analyze their external and internal parameters in the cluster as in an N-body simulation.Comment: LaTeX MNRAS Style 21 pages, 34 figures, submitted to MNRAS Nov. 1999, for preprint, see ftp://ftp.ari.uni-heidelberg.de/pub/spurzem/warspaper-98.ps.gz for associated mpeg-files (20 MB and 13 MB, respectively), see ftp://ftp.ari.uni-heidelberg.de/pub/spurzem/movie1.mpg and ftp://ftp.ari.uni-heidelberg.de/pub/spurzem/movie2.mp

A multiphysics and multiscale software environment for modeling astrophysical systems

We present MUSE, a software framework for combining existing computational tools for different astrophysical domains into a single multiphysics, multiscale application. MUSE facilitates the coupling of existing codes written in different languages by providing inter-language tools and by specifying an interface between each module and the framework that represents a balance between generality and computational efficiency. This approach allows scientists to use combinations of codes to solve highly-coupled problems without the need to write new codes for other domains or significantly alter their existing codes. MUSE currently incorporates the domains of stellar dynamics, stellar evolution and stellar hydrodynamics for studying generalized stellar systems. We have now reached a "Noah's Ark" milestone, with (at least) two available numerical solvers for each domain. MUSE can treat multi-scale and multi-physics systems in which the time- and size-scales are well separated, like simulating the evolution of planetary systems, small stellar associations, dense stellar clusters, galaxies and galactic nuclei. In this paper we describe three examples calculated using MUSE: the merger of two galaxies, the merger of two evolving stars, and a hybrid N-body simulation. In addition, we demonstrate an implementation of MUSE on a distributed computer which may also include special-purpose hardware, such as GRAPEs or GPUs, to accelerate computations. The current MUSE code base is publicly available as open source at http://muse.liComment: 24 pages, To appear in New Astronomy Source code available at http://muse.l