Kaiserslautern - Fachbereich Mathematik
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We compute three-dimensional displacement vector fields to estimate the deformation of microstructural data sets in mechanical tests. For this, we extend the well-known optical flow by Brox et al. to three dimensions, with special focus on the discretization of nonlinear terms. We evaluate our method first by synthetically deforming foams and comparing against this ground truth and second with data sets of samples that underwent real mechanical tests. Our results are compared to those from state-of-the-art algorithms in materials science and medical image registration. By a thorough evaluation, we show that our proposed method is able to resolve the displacement best among all chosen comparison methods.
We propose a model for glioma patterns in a microlocal tumor environment under
the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction
eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell
population densities, of which the former infers flux limitation both in the self-diffusion and taxis
terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of
glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor
vascularization on the establishment and maintenance of these histological patterns which are typical
for high-grade brain cancer. Numerical simulations of the population level dynamics are performed
to investigate several model scenarios containing this and further effects.
Various regulatory initiatives (such as the pan-European PRIIP-regulation or the German chance-risk classification for state subsidized pension products) have been introduced that require product providers to assess and disclose the risk-return profile of their issued products by means of a key information document. We will in this context outline a concept for a (forward-looking) simulation-based approach and highlight its application and advantages. For reasons of comparison, we further illustrate the performance of approximation methods based on a projection of observed returns into the future such as the Cornish–Fisher expansion or bootstrap methods.
The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an Ultra Napkin is proposed. Its mean feature is a nonlinear diffusion equation strongly coupled with an ODE describing a reversible absorbtion process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.
Cloudy inhomogenities in artificial fabrics are graded by a fast method which is based on a Laplacian pyramid decomposition of the fabric image. This band-pass representation takes into account the scale character of the cloudiness. A quality measure of the entire cloudiness is obtained as a weighted mean over the variances of all scales.
In this note, we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan–Schwinger map which has been known and used for a long time by physicists. The difference, compared to Jordan–Schwinger map, is that we use generators of Cuntz algebra O∞ (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a “building blocks” instead of creation–annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization, i.e. exact conservation of Lie brackets and linearity.
In the scalar case one knows that a complex normalized function of boundedvariation \(\phi\) on \([0,1]\) defines a unique complex regular Borel measure\(\mu\) on \([0,1]\). In this note we show that this is no longer true in generalin the vector valued case, even if \(\phi\) is assumed to be continuous. Moreover, the functions \(\phi\) which determine a countably additive vectormeasure \(\mu\) are characterized.
This survey provides the reader with an overview of numerous results on p-permu- tation modules and the closely related classes of endo-trivial, endo-permutation and endo-p- permutation modules. These classes of modules play an important role in the representation theory of finite groups. For example, they are important building blocks used to understand and parametrise several kinds of categorical equivalences between blocks of finite group alge- bras. For this reason, there has been, since the late 1990’s, much interest in classifying such modules. The aim of this manuscript is to review classical results as well as all the major recent advances in the area. The first part of this survey serves as an introduction to the topic for non-experts in modular representation theory of finite groups, outlining proof ideas of the most important results at the foundations of the theory. Simultaneously, the connections between the aforementioned classes of modules are emphasised. In this respect, results, which are dispersed in the literature, are brought together, and emphasis is put on common properties and the role played by the p-permutation modules throughout the theory. Finally, in the last part of the manuscript, lifting results from positive characteristic to characteristic zero are collected and their proofs sketched.
In this paper we construct a numerical solver for the Saint Venant equations. Special attention
is given to the balancing of the source terms, including the bottom slope and variable cross-
sectional profiles. Therefore a special discretization of the pressure law is used, in order to
transfer analytical properties to the numerical method. Based on this approximation a well-
balanced solver is developed, assuring the C-property and depth positivity. The performance
of this method is studied in several test cases focusing on accurate capturing of steady states.
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an optimal solution for each non-parametric problem obtained by fixing a parameter vector. For many multi-parametric optimization problems, however, an optimal solution set of minimum cardinality can contain super-polynomially many solutions. Consequently, no polynomial-time exact algorithms can exist for these problems even if P=NP. We propose an approximation method that is applicable to a general class of multi-parametric optimization problems and outputs a set of solutions with cardinality polynomial in the instance size and the inverse of the approximation guarantee. This method lifts approximation algorithms for non-parametric optimization problems to their parametric version and provides an approximation guarantee that is arbitrarily close to the approximation guarantee of the approximation algorithm for the non-parametric problem. If the non-parametric problem can be solved exactly in polynomial time or if an FPTAS is available, our algorithm is an FPTAS. Further, we show that, for any given approximation guarantee, the minimum cardinality of an approximation set is, in general, not ℓ-approximable for any natural number ℓ less or equal to the number of parameters, and we discuss applications of our results to classical multi-parametric combinatorial optimizations problems. In particular, we obtain an FPTAS for the multi-parametric minimum s-t-cut problem, an FPTAS for the multi-parametric knapsack problem, as well as an approximation algorithm for the multi-parametric maximization of independence systems problem.