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Start date: 2022 × Has files: Yes × Type: Report × Version: publishedVersion ×

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Now showing 1 - 10 of 54
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    From Floppy Disks to 5-Star LOD: FAIR Research Infrastructure for NFDI4Culture
    (Köln : ZB MED, 2023) Tietz, Tabea; Bruns, Oleksandra; Söhn, Linnaea; Tolksdorf, Julia; Posthumus, Etienne; Steller, Jonatan Jalle; Fliegl, Heike; Norouzi, Ebrahim; Waitelonis, Jörg; Schrade, Torsten; Sack, Harald
    NFDI4Culture is establishing an infrastructure for research data on material and immaterial cultural heritage in the context of the German National Research Data Infrastructure (NFDI) in compliance with the FAIR principles. The NFDI4Culture Knowledge Graph is developed and integrated with the Culture Information Portal to aggregate diverse and isolated data from the culture research landscape and thereby increase the discoverability, interoperability and reusability of cultural heritage data. This paper presents the research data management strategy in the long-term project NFDI4Culture, which combines a CMS and a Knowledge Graph-based infrastructure to enable an intuitive and meaningful interaction with research resources in the cultural heritage domain.
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    Emergence in biology and social sciences
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Hoffmann, Franca; Merino-Aceituno, Sara
    Mathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.
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    Periodic Lp estimates by R-boundedness: Applications to the Navier--Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Eiter, Thomas; Kyed, Mads; Shibata, Yoshihiro
    General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw's transference principle, time-periodic Lp estimates of maximal regularity type are established from R-bounds of the family of solution operators (R-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier--Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.
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    Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Drieschner, Martin; Gruhlke, Robert; Petryna, Yuri; Eigel, Martin; Hömberg, Dietmar
    Imperfections and inaccuracies in real technical products often influence the mechanical behavior and the overall structural reliability. The prediction of real stress states and possibly resulting failure mechanisms is essential and a real challenge, e.g. in the design process. In this contribution, imperfections in elastic materials such as air voids in adhesive bonds between fiber-reinforced composites are investigated. They are modeled as arbitrarily shaped and positioned. The focus is on local displacement values as well as on associated stress concentrations caused by the imperfections. For this purpose, the resulting complex random one-scale finite element model is numerically solved by a new developed surrogate model using an overlapping domain decomposition scheme based on Schwarz alternating method. Here, the actual response of local subproblems associated with isolated material imperfections is determined by a single appropriate surrogate model, that allows for an accelerated propagation of randomness. The efficiency of the method is demonstrated for imperfections with elliptical and ellipsoidal shape in 2D and 3D and extended to arbitrarily shaped voids. For the latter one, a local surrogate model based on artificial neural networks (ANN) is constructed. Finally, a comparison to experimental results validates the numerical predictions for a real engineering problem.
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    Modeling of ultrashort optical pulses in nonlinear fibers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, Shalva
    This work deals with theoretical aspects of pulse propagation. The core focus is on extreme, few-cycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil- tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra- short pulses in which non-envelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu- lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard split-step approach for numerical solutions of the pulse propagation equations.
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    Incompressible limit for a fluid mixture
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Druet, Pierre-Étienne
    In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.
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    Macroscopic loops in the $3d$ double-dimer model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Quitmann, Alexandra; Taggi, Lorenzo
    The double dimer model is defined as the superposition of two independent uniformly distributed dimer covers of a graph. Its configurations can be viewed as disjoint collections of self-avoiding loops. Our first result is that in ℤ d, d>2, the loops in the double dimer model are macroscopic. These are shown to behave qualitatively differently than in two dimensions. In particular, we show that, given two distant points of a large box, with uniformly positive probability there exists a loop visiting both points. Our second result involves the monomer double-dimer model, namely the double-dimer model in the presence of a density of monomers. These are vertices which are not allowed to be touched by any loop. This model depends on a parameter, the monomer activity, which controls the density of monomers. It is known from [Betz, Taggi] that a finite critical threshold of the monomer activity exists, below which a self-avoiding walk forced through the system is macroscopic. Our paper shows that, when d >2, such a critical threshold is strictly positive. In other words, the self-avoiding walk is macroscopic even in the presence of a positive density of monomers.
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    Symmetries in TEM imaging of crystals with strain
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Koprucki, Thomas; Maltsi, Anieza; Mielke, Alexander
    TEM images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.
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    Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Gruhlke, Robert; Eigel, Martin
    A unsupervised learning approach for the computation of an explicit functional representation of a random vector Y is presented, which only relies on a finite set of samples with unknown distribution. Motivated by recent advances with computational optimal transport for estimating Wasserstein distances, we develop a new Wasserstein multi-element polynomial chaos expansion (WPCE). It relies on the minimization of a regularized empirical Wasserstein metric known as debiased Sinkhorn divergence. As a requirement for an efficient polynomial basis expansion, a suitable (minimal) stochastic coordinate system X has to be determined with the aim to identify ideally independent random variables. This approach generalizes representations through diffeomorphic transport maps to the case of non-continuous and non-injective model classes M with different input and output dimension, yielding the relation Y=M(X) in distribution. Moreover, since the used PCE grows exponentially in the number of random coordinates of X, we introduce an appropriate low-rank format given as stacks of tensor trains, which alleviates the curse of dimensionality, leading to only linear dependence on the input dimension. By the choice of the model class M and the smooth loss function, higher order optimization schemes become possible. It is shown that the relaxation to a discontinuous model class is necessary to explain multimodal distributions. Moreover, the proposed framework is applied to a numerical upscaling task, considering a computationally challenging microscopic random non-periodic composite material. This leads to tractable effective macroscopic random field in adopted stochastic coordinates.
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    Jewellery from tessellations of hyperbolic space
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Gangl, Herbert
    In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional hyperbolic space. Many of the building blocks of these tessellations exhibit beautiful symmetry and have inspired the design of 3D printed jewellery.