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- Deklarative Spezifikation von Datentransformationen (2012)
- Deklarative Spezifikation von Datentransformationen.

- Statistical RNA Secondary Structure Sampling Based on a Length-Dependent SCFG Model (2012)
- One of the fundamental problems in computational structural biology is the prediction of RNA secondary structures from a single sequence. To solve this problem, mainly two different approaches have been used over the past decades: the free energy minimization (MFE) approach which is still considered the most popular and successful method and the competing stochastic context-free grammar (SCFG) approach. While the accuracy of the MFE based algorithms is limited by the quality of underlying thermodynamic models, the SCFG method abstracts from free energies and instead tries to learn about the structural behavior of the molecules by training the grammars on known real RNA structures, making it highly dependent on the availability of a rich high quality training set. However, due to the respective problems associated with both methods, new statistics based approaches towards RNA structure prediction have become increasingly appreciated. For instance, over the last years, several statistical sampling methods and clustering techniques have been invented that are based on the computation of partition functions (PFs) and base pair probabilities according to thermodynamic models. A corresponding SCFG based statistical sampling algorithm for RNA secondary structures has been studied just recently. Notably, this probabilistic method is capable of producing accurate (prediction) results, where its worst-case time and space requirements are equal to those of common RNA folding algorithms for single sequences. The aim of this work is to present a comprehensive study on how enriching the underlying SCFG by additional information on the lengths of generated substructures (i.e. by incorporating length-dependencies into the SCFG based sampling algorithm, which is actually possible without significant losses in performance) affects the reliability of the induced RNA model and the accuracy of sampled secondary structures. As we will see, significant differences with respect to the overall quality of generated sample sets and the resulting predictive accuracy are typically implied. In principle, when considering the more specialized length-dependent SCFG model as basis for statistical sampling, a higher accuracy of predicted foldings can be reached at the price of a lower diversity of generated candidate structures (compared to the more general traditional SCFG variant or sampling based on PFs that rely on free energies).

- Constitutive models for static granular systems and focus to the Jiang-Liu hyperelastic law (2012)
- Granular systems in solid-like state exhibit properties like stiffness dependence on stress, dilatancy, yield or incremental non-linearity that can be described within the continuum mechanical framework. Different constitutive models have been proposed in the literature either based on relations between some components of the stress tensor or on a quasi-elastic description. After a brief description of these models, the hyperelastic law recently proposed by Jiang and Liu [1] will be investigated. In this framework, the stress-strain relation is derived from an elastic strain energy density where the stable proper- ties are linked to a Drucker-Prager yield criteria. Further, a numerical method based on the finite element discretization and Newton- Raphson iterations is presented to solve the force balance equation. The 2D numerical examples presented in this work show that the stress distributions can be computed not only for triangular domains, as previoulsy done in the literature, but also for more complex geometries. If the slope of the heap is greater than a critical value, numerical instabilities appear and no elastic solution can be found, as predicted by the theory. As main result, the dependence of the material parameter Xi on the maximum angle of repose is established.

- An overview on the usage of some model reduction approaches for simulations of Li-ion transport in batteries (2012)
- In this work, some model reduction approaches for performing simulations with a pseudo-2D model of Li-ion battery are presented. A full pseudo-2D model of processes in Li-ion batteries is presented following [3], and three methods to reduce the order of the full model are considered. These are: i) directly reduce the model order using proper orthogonal decomposition, ii) using fractional time step discretization in order to solve the equations in decoupled way, and iii) reformulation approaches for the diffusion in the solid phase. Combinations of above methods are also considered. Results from numerical simulations are presented, and the efficiency and the accuracy of the model reduction approaches are discussed.

- Residual Demand Modeling and Application to Electricity Pricing (2012)
- Worldwide the installed capacity of renewable technologies for electricity production is rising tremendously. The German market is particularly progressive and its regulatory rules imply that production from renewables is decoupled from market prices and electricity demand. Conventional generation technologies are to cover the residual demand (defined as total demand minus production from renewables) but set the price at the exchange. Existing electricity price models do not account for the new risks introduced by the volatile production of renewables and their effects on the conventional demand curve. A model for residual demand is proposed, which is used as an extension of supply/demand electricity price models to account for renewable infeed in the market. Infeed from wind and solar (photovoltaics) is modeled explicitly and withdrawn from total demand. The methodology separates the impact of weather and capacity. Efficiency is transformed on the real line using the logit-transformation and modeled as a stochastic process. Installed capacity is assumed a deterministic function of time. In a case study the residual demand model is applied to the German day-ahead market using a supply/demand model with a deterministic supply-side representation. Price trajectories are simulated and the results are compared to market future and option prices. The trajectories show typical features seen in market prices in recent years and the model is able to closely reproduce the structure and magnitude of market prices. Using the simulated prices it is found that renewable infeed increases the volatility of forward prices in times of low demand, but can reduce volatility in peak hours. Prices for different scenarios of installed wind and solar capacity are compared and the meritorder effect of increased wind and solar capacity is calculated. It is found that wind has a stronger overall effect than solar, but both are even in peak hours.

- Multiscale Finite Element Coarse Spaces for the Analysis of Linear Elastic Composites (2012)
- In this work we extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [14] to the PDE system of linear elasticity. The application, motivated from the multiscale analysis of highly heterogeneous composite materials, is twofold. Resolving the heterogeneities on the finest scale, we utilize the linear MsFEM basis for the construction of robust coarse spaces in the context of two-level overlapping Domain Decomposition preconditioners. We motivate and explain the construction and present numerical results validating the approach. Under the assumption that the material jumps are isolated, that is they occur only in the interior of the coarse grid elements, our experiments show uniform convergence rates independent of the contrast in the Young's modulus within the heterogeneous material. Elsewise, if no restrictions on the position of the high coefficient inclusions are imposed, robustness can not be guaranteed any more. These results justify expectations to obtain coefficient-explicit condition number bounds for the PDE system of linear elasticity similar to existing ones for scalar elliptic PDEs as given in the work of Graham, Lechner and Scheichl [12]. Furthermore, we numerically observe the properties of the MsFEM coarse space for linear elasticity in an upscaling framework. Therefore, we present experimental results showing the approximation errors of the multiscale coarse space w.r.t. the fine-scale solution.

- A Two-Dimensional Model of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects (2012)
- The paper production is a problem with significant importance for the society and it is a challenging topic for scientific investigations. This study is concerned with the simulations of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. Richards’ type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure–saturation relation proposed by Hassanizadeh and co-workers (Hassanizadeh et al., 2002; Hassanizadeh, Gray, 1990, 1993a) is adopted for the paper production process. The mathematical model accounts for the co-existence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. The numerical experiments are carried out for parameters which are typical for the production process. The static and dynamic capillary pressure–saturation relations are tested to evaluate the influence of the dynamic capillary effect.

- Multibody dynamics simulation of geometrically exact Cosserat rods (2011)
- In this paper, we present a viscoelastic rod model that is suitable for fast and accurate dynamic simulations. It is based on Cosserat’s geometrically exact theory of rods and is able to represent extension, shearing (‘stiff’ dof), bending and torsion (‘soft’ dof). For inner dissipation, a consistent damping potential proposed by Antman is chosen. We parametrise the rotational dof by unit quaternions and directly use the quaternionic evolution differential equation for the discretisation of the Cosserat rod curvature. The discrete version of our rod model is obtained via a finite difference discretisation on a staggered grid. After an index reduction from three to zero, the right-hand side function f and the Jacobian \(\partial f/\partial(q, v, t)\) of the dynamical system \(\dot{q} = v, \dot{v} = f(q, v, t)\) is free of higher algebraic (e. g. root) or transcendental (e. g. trigonometric or exponential) functions and therefore cheap to evaluate. A comparison with Abaqus finite element results demonstrates the correct mechanical behavior of our discrete rod model. For the time integration of the system, we use well established stiff solvers like RADAU5 or DASPK. As our model yields computational times within milliseconds, it is suitable for interactive applications in ‘virtual reality’ as well as for multibody dynamics simulation.

- On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: one-dimensional case (2011)
- This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then the existence of a discrete solution to proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main Theorem shows that the discrete solution converges to the solution of continuous problem. At the end we present numerical studies for the rate of convergence.

- Structure and pressure drop of real and virtual metal wire meshes (2009)
- An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software.