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Altmann E.G.,Max Planck Institute for the Physics of Complex Systems | Portela J.S.E.,Max Planck Institute for the Physics of Complex Systems | Portela J.S.E.,Fraunhofer Institute for Industrial Mathematics | Tel T.,Eotvos Lorand University
Reviews of Modern Physics | Year: 2013

There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. A unified treatment of leaking systems is provided and applications to different physical problems, in both the classical and quantum pictures, are reviewed. The treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption and/or transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the limaçon family of billiards illustrate the main text. Regarding billiard dynamics, it is emphasized that a correct discrete-time representation can be given only in terms of the so-called true-time maps, while traditional Poincaré maps lead to erroneous results. Perron-Frobenius-type operators are generalized so that they describe true-time maps with partial leaks. © 2013 American Physical Society. Source


Wagner A.,Fraunhofer Institute for Industrial Mathematics
Energy Journal | Year: 2014

A model for residual demand is proposed, which extends structural electricity price models to account for renewable infeed in the market. Infeed from wind and solar is modeled explicitly and withdrawn from total demand. The methodology separates the impact of weather and capacity. Efficiency is modeled as a stochastic process. Installed capacity is a deterministic function of time. The residual demand model is applied to the German day-ahead market. Price trajectories show typical features seen in market prices in recent years. The model is able to closely reproduce the structure and magnitude of market prices. Using simulations it is found that renewable infeed increases the volatility of forward prices in times of low demand, but can reduce volatility in peak hours. The meritorder effect of increased wind and solar capacity is calculated. It is found that under current capacity levels in the German market wind has a stronger overall effect than solar, but both are even in peak hours. ©2014 by the IAEE. All rights reserved. Source


Oden L.,Fraunhofer Institute for Industrial Mathematics
Advances in Parallel Computing | Year: 2014

Due to their high parallelism graphics processing units (GPUs) and GPU-based clusters have gained popularity in high-performance computing. However, data transfer in GPU-based clusters remains a challenging problem, due to the disjoint memory of GPU and host. New technologies, such as GPUDirect RDMA, improve data transfer among multiple GPUs, but they require many manual interventions from programmers to reach optimal performance. We present GPI2 for GPUS, a PGAS-based communication framework, for low latency data transfer in heterogeneous clusters. GPI2 provides a Partitioned Global Address Space (PGAS) to applications, in which each part of the address space is local to one node, while all nodes have full and direct access to the whole global address space. GPI2 for GPUs extends this global address space to GPU memory. This allows every GPU and CPU in the cluster to transparently read and write to every GPUs device memory and all CPUs node memory. New GPUDirect technologies are used to optimize communication among multiple GPUs. This can reduce the latency for a direct GPU-to-GPU data transfer reduced to 3μs, which is more than three times faster than previous technologies. Since GPUDirect RDMA is not fully supported on modern chip sets, for larger messages a hybrid protocol is used for optimal bandwidth. Our performance evaluation shows, that GPI2 for GPUs can supports scalable applications for GPU clusters as it reduces communication and synchronization overhead to a minimum and offers a transparent low latency communication interface. © 2014 The authors and IOS Press. Source


Schladitz K.,Fraunhofer Institute for Industrial Mathematics
Journal of Microscopy | Year: 2011

In this paper, the field of quantitative microcomputed tomography arising from the combination of microcomputed tomography and quantitative 3D image analysis, is summarized with focus on materials science applications. Opportunities and limitations as well as typical application scenarios are discussed. Selected examples provide an insight into commonly used as well as recent methods from mathematical morphology and stochastic geometry. © 2011 The Author, Journal of Microscopy © 2011 Royal Microscopical Society. Source


Redenbach C.,University of Kaiserslautern | Vecchio I.,Fraunhofer Institute for Industrial Mathematics
Composites Science and Technology | Year: 2011

The fibre component of many fibre reinforced composites can be modelled by a system of non-overlapping straight cylinders. In this paper we discuss a model based on a random sequential adsorption (RSA) process. Geometric characteristics of the fibre system such as the fibre volume fraction or the fibre direction distribution are estimated from tomographic images of composite samples. Using this information, we fit RSA models to samples of a glass fibre reinforced polymer and a fibre reinforced ultra high performance concrete. © 2010 Elsevier Ltd. Source

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