M. Reißel

Air-Sand Heat Exchanger for High-Temperature Storage

In view of rising energy prices and an increasing share of power generated by renewable energy sources, the importance of energy storage is growing. In the framework of this project, a thermal energy storage concept for solar power towers is being developed, in which quartz sand serves as a storage medium. Sand is suitable due to its properties such as high thermal stability, specific heat capacity, and low-cost availability. Compared with storages based on ceramic bodies, the use of sand promises to reduce costs of energy storage and thus to reduce the costs of electricity generation. In addition, the storage concept could be applicable in the steel industry. The central element of the storage concept is an air-sand heat exchanger, which is presently under development. This paper describes simulation results and measurements of the heat exchanger prototype. It includes sand flow behavior and experience with different porous walls as well as up-scaling options.

The Levenberg–Marquardt method applied to a parameter estimation problem arising from electrical resistivity tomography

Abstract An efficient and robust electrical resistivity tomographic inversion algorithm based on the Levenberg–Marquardt method is considered to obtain quantities like grain size, spatial scale and particle size distribution of mineralized rocks. The corresponding model in two dimensions is based on the Maxwell equations and leads to a partial differential equation with mixed Dirichlet–Neumann boundary conditions. The forward problem is solved numerically with the finite-difference method. However, the inverse problem at hand is a classical nonlinear and ill-posed parameter estimation problem. Linearizing and applying the Tikhonov regularization method yields an iterative scheme, the Levenberg–Marquardt method. Several large systems of equations have to be solved efficiently in each iteration step which is accomplished by the conjugate gradient method without setting up the corresponding matrix. Instead fast matrix–vector multiplications are performed directly. Therefore, the derivative and its adjoint for the parameter-to-solution map are needed. Numerical results demonstrate the performance of our method as well as the possibility to reconstruct some of the desired parameters.

Reconstruction of Electric Currents in a Fuel Cell by Magnetic Field Measurements

In this paper the tomographic problem arising in the diagnostics of a fuel cell is discussed. This is concerned with how well the electric current density j (r) be reconstructed by measuring its external magnetic field. We show that (i) exploiting the fact that the current density has to comply with Maxwells equations it can, in fact, be reconstructed at least up to a certain resolution, (ii) the functional connection between the resolution of the current density and the relative precision of the measurement devices can be obtained, and (iii) a procedure can be applied to determine the optimum measuring positions, essentially decreasing the number of measuring points and thus the time scale of measurable dynamical perturbations-without a loss of fine resolution. We present explicit results for (i)-(iii) by applying our formulas to a realistic case of an experimental direct methanol fuel cell.

Uniqueness of magnetotomography for fuel cells and fuel cell stacks

The criterion for the applicability of any tomographic method is its ability to construct the desired inner structure of a system from external measurements, i.e. to solve the inverse problem. Magnetotomography applied to fuel cells and fuel cell stacks aims at determining the inner current densities from measurements of the external magnetic field. This is an interesting idea since in those systems the inner electric current densities are large, several hundred mA per cm2and therefore relatively high external magnetic fields can be expected. Still the question remains how uniquely the inverse problem can be solved. Here we present a proof that by exploiting Maxwells equations extensively the inverse problem of magnetotomography becomes unique under rather mild assumptions and we show that these assumptions are fulfilled in fuel cells and fuel cell stacks. Moreover, our proof holds true for any other device fulfilling the assumptions listed here. Admittedly, our proof has one caveat: it does not contain an estimate of the precision requirements the measurements need to fulfil for enabling reconstruction of the inner current densities from external magnetic fields.

FSI Schemes: Fast Semi-Iterative Solvers for PDEs and Optimisation Methods

Many tasks in image processing and computer vision are modelled by diffusion processes, variational formulations, or constrained optimisation problems. Basic iterative solvers such as explicit schemes, Richardson iterations, or projected gradient descent methods are simple to implement and well-suited for parallel computing. However, their efficiency suffers from severe step size restrictions. As a remedy we introduce a simple and highly efficient acceleration strategy, leading to so-called Fast Semi-Iterative (FSI) schemes that extrapolate the basic solver iteration with the previous iterate. To derive suitable extrapolation parameters, we establish a recursion relation that connects box filtering with an explicit scheme for 1D homogeneous diffusion. FSI schemes avoid the main drawbacks of recent Fast Explicit Diffusion (FED) and Fast Jacobi techniques, and they have an interesting connection to the heavy ball method in optimisation. Our experiments show their benefits for anisotropic diffusion inpainting, nonsmooth regularisation, and Nesterov’s worst case problems for convex and strongly convex optimisation.

Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation

Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F , we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan-Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time.Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.

Reduktion von Rissartefakten durch nicht-lineare Registrierung in histologischen Schnittbildern

In dieser Arbeit wird ein Verfahren vorgestellt, das Rissartefakte, die in histologischen Rattenhirnschnitten vorkommen konnen, durch nicht-lineare Registrierung reduziert. Um die Optimierung in der Rissregion zu leiten, wird der Curvature Registrierungsansatz um eine Metrik basierend auf der Segmentierung der Bilder erweitert. Dabei erzielten Registrierungen mit der ausschlieslichen Segmentierung des Risses bessere Ergebnisse als Registrierungen mit einer Segmentierung des gesamten Hirnschnitts. Insgesamt zeigt sich eine deutliche Verbesserung in der Rissregion, wobei der verbleibende reduzierte Riss auf die Glatt-heitsbedingungen des Regularisierers zuruckzufuhren ist.