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Schafer M.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Frank M.,RWTH Aachen | Levermore C.D.,University of Maryland University College
Multiscale Modeling and Simulation | Year: 2011

In this paper, we investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in Levermore [Transition Regime Models for Radiative Transport, Presentation at the Institute for Pure & Applied Mathematics: Grand Challenge Problems in Computational Astrophysics, Workshop on Transfer Phenomena, 2005, http://www.ipam.ucla.edu/publications/pcaws4/pcaws4-5724.pdf, and Moment Closures for Radiative Transport, manuscript, 2009], of how to improve the well-known P N approximations. We systematically develop a diffusive correction to the P N equations from the operator formulation-the so-called D N approximation. We validate the new approach with numerical examples in one and two dimensions. © 2011 Society for Industrial and Applied Mathematics.

Balzer M.,University of Hamburg | Balzer M.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Gdaniec N.,University of Hamburg | Gdaniec N.,University of Lübeck | And 2 more authors.
Journal of Physics Condensed Matter | Year: 2012

The zero-temperature single-particle Greens function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to obtain the nonequilibrium single-particle Greens function defined on the KeldyshMatsubara contour in the complex time plane which describes the systems nonperturbative response to a sudden parameter switch in the Hamiltonian. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss its efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.

Erlwein C.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Mamon R.,University of Western Ontario | Davison M.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Davison M.,University of Western Ontario
Applied Stochastic Models in Business and Industry | Year: 2011

We develop and analyse investment strategies relying on hidden Markov model approaches. In particular, we use filtering techniques to aid an investor in his decision to allocate all of his investment fund to either growth or value stocks at a given time. As this allows the investor to switch between growth and value stocks, we call this first strategy a switching investment strategy. This switching strategy is compared with the strategies of purely investing in growth or value stocks by tracking the quarterly terminal wealth of a hypothetical portfolio for each strategy. Using the data sets on Russell 3000 growth index and Russell 3000 value index compiled by Russell Investment Services for the period 1995-2008, we find that the overall risk-adjusted performance of the switching strategy is better than that of solely investing in either one of the indices. We also consider a second strategy referred to as a mixed investment strategy which enables the investor to allocate an optimal proportion of his investment between growth and value stocks given a level of risk aversion. Numerical demonstrations are provided using the same data sets on Russell 3000 growth and value indices. The switching investment strategy yields the best or second best Sharpe ratio as compared with those obtained from the pure index strategies and mixed strategy in 14 intervals. The performance of the mixed investment strategy under the HMM setting is also compared with that of the classical mean-variance approach. To make the comparison valid, we choose the same level of risk aversion for each set-up. Our findings show that the mixed investment strategy within the HMM framework gives higher Sharpe ratios in 5 intervals of the time series than that given by the standard mean-variance approach. The calculated weights through time from the strategy incorporating the HMM set-up are more stable. A simulation analysis further shows a higher performance stability of the HMM strategies compared with the pure strategies and the mean-variance strategy. Copyright © 2009 John Wiley & Sons, Ltd.

Iliev O.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Iliev O.,Bulgarian Academy of Science | Lazarov R.,Bulgarian Academy of Science | Lazarov R.,Texas A&M University | Willems J.,Texas A&M University
Multiscale Modeling and Simulation | Year: 2011

We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

Pizarro L.,Saarland University | Pizarro L.,Imperial College London | Mrazek P.,UPEK Inc | Didas S.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | And 2 more authors.
International Journal of Computer Vision | Year: 2010

We propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches. One of such dissimilarity measures is the weighted L 2 distance between patches. In such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain. It can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels, but also the similarity of their corresponding neighbours. This leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure. By slightly modifying the way the similarities are computed we obtain two related filters: The NL-means filter of Buades et al. (SIAM Multiscale Model. Simul. 4(2):490-530, 2005b) and the NDS filter of Mrázek et al. (Geometric Properties for Incomplete Data, Computational Imaging and Vision, vol. 31, pp. 335-352, Springer, Dordrecht, 2006). In fact, the proposed approach can be considered as a generalisation of the latter filter to the space of patches. We also provide novel insights into relations of the NDS filter with diffusion/regularisation methods as well as with some recently proposed graph regularisation techniques. We evaluate our method for the task of denoising greyscale and colour images degraded with Gaussian and salt-and-pepper noise, demonstrating that it compares very well to other more sophisticated approaches. © 2010 Springer Science+Business Media, LLC.

Panzer H.,TU Munich | Mohring J.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Eid R.,TU Munich | Lohmann B.,TU Munich
At-Automatisierungstechnik | Year: 2010

In this paper, a new framework for model order reduction of LTI parametric systems is introduced. After generating and reducing several local original models in the parameter space, a parametric reduced-order model is calculated by interpolating the system matrices of the local reduced models. The main task is to find compatible system representations with optimal interpolation properties. Two approaches for this purpose are presented together with several numerical simulations. © Oldenbourg Wissenschaftsverlag.

Latz A.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Zausch J.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik
Journal of Power Sources | Year: 2011

Abstract: Most Li ion insertion batteries consist of a porous cathode, a separator filled with electrolyte and an anode, which very often also has some porous structure. The solid part especially in the cathode is usually produced by mixing a powder of the actual active particles, in which Li ions will be intercalated, binder and carbon black to enhance the electronic conductivity of the electrode. As a result the porous structure of the electrodes is very complex, leading to complex potential, ion and temperature distributions within the electrodes. The intercalation and deintercalation of ions cannot be expected to be homogeneously distributed over the electrode due to the different transport properties of electrolyte and active particles in the electrode and the complex three-dimensional pore structure of the electrode. The influence of the final microstructure on the distribution of temperature, electric potential and ions within the electrodes is not known in detail, but may influence strongly the onset of degradation mechanisms. For being able to numerically simulate the transport phenomena, the equations and interface conditions for ion, charge and heat transport within the complex structure of the electrodes and through the electrolyte filled separator are needed. We will present a rigorous derivation of these equations based exclusively on general principles of nonequilibrium thermodynamics. The theory is thermodynamically consistent i.e. it guarantees strictly positive entropy production. The irreversible and reversible sources of heat are derived within the theory. Especially the various contribution to the Peltier heat due to the intercalation of ions are obtained as a result of the theory. Research highlights: Thermodynamic consistent transport theory for Li ion batteries Derivation of all irreversible and reversible heat sources in Li ion batteries Closed set of equations for ion, charge and heat transport in Li ion batteries Theory of Peltier heat for Li ion intercalation Microstructure resolved transport in porous electrodes © 2010 Elsevier B.V. All rights reserved.

Latz A.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Zausch J.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Iliev O.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

In order to improve the design of Li ion batteries the complex interplay of various physical phenomena in the active particles of the electrodes and in the electrolyte has to be balanced. The separate transport phenomena in the electrolyte and in the active particle as well as their coupling due to the electrochemical reactions at the interfaces between the electrode particles and the electrolyte will influence the performance and the lifetime of a battery. Any modeling of the complex phenomena during the usage of a battery has therefore to be based on sound physical and chemical principles in order to allow for reliable predictions for the response of the battery to changing load conditions. We will present a modeling approach for the transport processes in the electrolyte and the electrodes based on non-equilibrium thermodynamics and transport theory. The assumption of local charge neutrality, which is known to be valid in concentrated electrolytes, is explicitly used to identify the independent thermodynamic variables and fluxes. The theory guarantees strictly positive entropy production. Differences to other theories will be discussed. © 2011 Springer-Verlag.

Herty M.,University of Kaiserslautern | Mohringb J.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik | Sachersa V.,University of Kaiserslautern
Mathematical Methods in the Applied Sciences | Year: 2010

We introduce a new model for gas dynamics in pipe networks by asymptotic analysis. The model is derived from the isothermal Euler equations. We present the derivation of the model as well as numerical results illustrating the validity and its properties. We compare the new model with existing models from the mathematical and engineering literature. We further give numerical results on a sample network. Copyright © 2009 John Wiley & Sons, Ltd.

Klauer A.,Fraunhofer Institute For Techno Und Wirtschaftsmathematik
Journal of Applied Analysis | Year: 2014

The complex Bloch varieties and the associated Fermi curves of two-dimensional periodic Schrödinger operators with quasi-periodic boundary conditions are defined as complex analytic varieties, the Schrödinger potentials being from the Lorentz-Fourier space ?l∞,1. Then, an asymptotic analysis of the Fermi curves is performed. The decomposition of a Fermi curve into a compact part, an asymptotically free part, and thin handles, is recovered as expected. Furthermore, it is shown that the set of potentials whose associated Fermi curve has finite geometric genus is a dense subset of ?l∞,1. Moreover, the Fourier transforms of the potentials are locally isomorphic to perturbed Fourier transforms induced by the handles. Finally, an asymptotic family of parameters describing the sizes of the handles is introduced. These parameters are good candidates for describing parts of the space of all Fermi curves. © 2014 by Walter de Gruyter Berlin/Bosto.

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