Research Projects

Selected Research Projects at the Department of Mathematics

  • Heisenberg Grants - Quantum Fields and Operator Algebras

    (Third Party Funds Single)

    Term: 01-09-2021 - 31-08-2026
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract
    Das Ziel des Heisenberg-Programms ist es, herausragenden Wissenschaftlerinnen und Wissenschaftlern, die alle Voraussetzungen für die Berufung auf eine Langzeit-Professur erfüllen, zu ermöglichen, sich auf eine wissenschaftliche Leitungsfunktion vorzubereiten und in dieser Zeit weiterführende Forschungsthemen zu bearbeiten. In der Verfolgung dieses Ziels müssen nicht immer projektförmige Vorgehensweisen gewählt und realisiert werden. Aus diesem Grunde wird bei der Antragstellung und auch später bei der Abfassung von Abschlussberichten - anders als bei anderen Förderinstrumenten - keine "Zusammenfassung" von Projektbeschreibungen und Projektergebnissen verlangt. Somit werden solche Informationen auch in GEPRIS nicht zur Verfügung gestellt.

  • Fairly allocating vaccines for COVID-19

    (Third Party Funds Single)

    Term: 15-03-2021 - 16-07-2021
    Funding source: andere Förderorganisation

  • Forschungskostenzuschuss zum Forschungsstipendium für erfahrene Wissenschaftler (Herr Dr. Vincenzo Morinelli)

    (Third Party Funds Single)

    Term: 01-03-2021 - 31-08-2022
    Funding source: Alexander von Humboldt-Stiftung

  • Process strategies for the production of thin-walled components during selective laser beam melting of plastics

    (Third Party Funds Group – Sub project)

    Overall project: CRC 814 - Additive Manufacturing
    Term: 01-01-2021 - 31-12-2023
    Funding source: DFG / Sonderforschungsbereich (SFB)
    URL: https://www.crc814.research.fau.eu/projekte/t-transferprojekte/transferproject-t3/
    Abstract

    The aim of theproject is the systematic investigation of the process-geometry-interaction ofthin-walled components for the production of locally adapted properties as wellas the modeling of this effect in finite element simulations and structuraloptimization. In experimental tests, the main influencing factors areidentified and mapped in relation to the building position in the process. Newexposure technologies and strategies are used to manipulate the melting pooland homogenize component properties. The findings are incorporated into a wallthickness dependent material model for structural optimization, which isinvestigated in the project. The participating industrial partners willvalidate the results over the course of the project. The experimental findingsand the wall thickness dependent material model will be used to develop amethodology for the product development of thin-walled structures. In thefuture, the product development process can be accelerated, and the economicefficiency increased. Based on these findings, new application areas for theselective laser beam melting of plastics can be opened up in the future.

  • Parallel mesh loading and partitioning for large-scale simulation

    (Third Party Funds Single)

    Term: since 01-01-2021
    Funding source: Bayerisches Staatsministerium für Wissenschaft und Kunst (StMWK) (seit 2018)
    URL: https://www.konwihr.de/

  • Optimal Decision Making for COVID-19

    (Third Party Funds Single)

    Term: 13-07-2020 - 29-11-2020
    Funding source: andere Förderorganisation

  • Stability for doubly nonlinear parabolic equations (C07 intern)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-05-2020 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    URL: https://trr154.fau.de/

  • EOSCsecretariat.eu: Optimal Spatiotemporal Antiviral Release under Uncertainty

    (Third Party Funds Single)

    Term: 01-05-2020 - 30-04-2022
    Funding source: Research infrastructures, including e-infrastructures

  • Indextheorie angewandt auf quantenmechanische und klassische Systeme

    (Third Party Funds Single)

    Term: 01-04-2020 - 31-03-2023
    Funding source: Deutsche Forschungsgemeinschaft (DFG)

  • Maschinelles Lernen bei korrelativer MR und Hochdurchsatz-NanoCT

    (Third Party Funds Single)

    Term: 01-04-2020 - 31-03-2023
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)

  • Mechanistische, integrative Mehrskalenmodellierung der Umwandlung von Bodenmikroaggregaten

    (Third Party Funds Single)

    Term: 01-04-2020 - 31-08-2024
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

  • Besov regularity of parabolic partial differential equations on Lipschitz domains (continuation)

    (Third Party Funds Single)

    Term: 01-04-2020 - 30-09-2021
    Funding source: Deutsche Forschungsgemeinschaft (DFG)

  • Process optimization for hospital logistics

    (Third Party Funds Single)

    Term: since 01-01-2020
    Funding source: Industrie
    URL: https://en.www.math.fau.de/edom/projects-edom/logistics-and-production/process-optimization-for-hospital-logistics/

  • Topology, material and shape optimisation for particle ensembles

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1411: Design of particulate products
    Term: 01-01-2020 - 31-12-2023
    Funding source: DFG / Sonderforschungsbereich (SFB)
    Abstract
    The objective is the development of a mathematical framework which allows to conclude from desired optical properties to a corresponding optimised configuration of single particles as well as particle assemblies. A structural optimisation approach based on discrete dipole approximations is explored to allow for a design space with sufficiently high resolution and enabling the prediction of structure-property relations of individual particles. For particle assemblies a structural optimisation method based on a generalised hybrid finite element approach is established. Finally, dispersity and angle independency are taken into account by a new stochastic optimisation method.

  • Information management and computational science support

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1411: Design of particulate products
    Term: 01-01-2020 - 31-12-2023
    Funding source: DFG / Sonderforschungsbereich (SFB)

  • Mechanistische, integrative Mehrskalenmodellierung der Umwandlung von Bodenmikroaggregaten

    (Third Party Funds Single)

    Term: 01-11-2019 - 31-10-2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

  • Geordnete Dilationsräume und Geometrie von Standard-Unterräumen

    (Third Party Funds Single)

    Term: 01-10-2019 - 30-09-2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

  • Multiscale modeling with evolving microstructure: An approach to
    emergence in the rhizosphere via effective soil functions

    (Third Party Funds Group – Sub project)

    Overall project: DFG Priority Programme 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
    Term: 01-02-2019 - 31-01-2022
    Funding source: DFG / Schwerpunktprogramm (SPP)
    URL: https://www.ufz.de/spp-rhizosphere/index.php?en=46495
    Abstract

    The self-organization of the aggregates in the rhizosphere by various
    attracting forces influenced by geochemistry, and microbiology shall
    be studied by a novel, comprehensive model. This model should
    account for processes on the microscale (single roots, pore scale),
    and then be upscaled to the root system scale (macroscale) by
    mathematical homogenization. This goal exceeds the functional range
    of existing models for aggregation and needs the introduction of an
    explicit phase of mucilage, and attachment properties of root hairs in
    the rhizosheath. The project aims at the development of a mechanistic modeling approach that allows for dynamic structural reorganization of the rhizosphere at the single root scale and couples this evolving microscale model to the root system scale including the inference of soil functions. This means that we do not assume a static rhizosphere but develop a tool that is capable to dynamically track this zone on the basis of the underlying spatiotemporal aggregegate formation and geochemical patterns. The collaboration with experimental groups – analyzing CT images in various moisture and growth conditions - the Central Experiment will allow to derive the properties of the mucilage phase, the pore structure and thus the
    influence of root hairs on aggregation mechanisms.

  • Teilprojekt P11 - Fracture Control by Material Optimization

    (Third Party Funds Group – Sub project)

    Overall project: Skalenübergreifende Bruchvorgänge: Integration von Mechanik, Materialwissenschaften, Mathematik, Chemie und Physik (FRASCAL)
    Term: 02-01-2019 - 30-06-2023
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-11-fracture-control-by-material-optimization/
    Abstract

    In previous works, the dependence of failure mechanisms in composite materials like debonding of the matrix-fibre interface or fibre breakage have been discussed.  The underlying model was based on specific cohesive zone elements, whose macroscopic properties could be derived from DFT. It has been shown that the dissipated energy could be increased by appropriate choices of cohesive parameters of the interface as well as aspects of the fibre. However due to the numerical complexity of applied simulation methods the crack path had to be fixed a priori. Only recently models allow computing the full crack properties at macroscopic scale in a quasi-static scenario by the solution of a single nonlinear variational inequality for a given set of material parameters and thus model based optimization of the fracture properties can be approached.

    The goal of the project is to develop an optimization method, in the framework of which crack properties (e.g. the crack path) can be optimized in a mathematically rigorous way. Thereby material properties of matrix, fibre and interfaces should serve as optimization variables.

  • Teilprojekt P10 - Configurational Fracture/Surface Mechanics

    (Third Party Funds Group – Sub project)

    Overall project: Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)
    Term: 02-01-2019 - 30-06-2023
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-10-configurational-fracture-surface-mechanics/
    Abstract

    In a continuum the tendency of pre-existing cracks to propagate through the ambient material is assessed based on the established concept of configurational forces. In practise crack propagation is however prominently affected by the presence and properties of either surfaces and/or interfaces in the material. Here materials exposed to various surface treatments are mentioned, whereby effects of surface tension and crack extension can compete. Likewise, surface tension in inclusion-matrix interfaces can often not be neglected. In a continuum setting the energetics of surfaces/interfaces is captured by separate thermodynamic potentials. Surface potentials in general result in noticeable additions to configurational mechanics. This is particularly true in the realm of fracture mechanics, however its comprehensive theoretical/computational analysis is still lacking.

    The project aims in a systematic account of the pertinent surface/interface thermodynamics within the framework of geometrically nonlinear configurational fracture mechanics. The focus is especially on a finite element treatment, i.e. the Material Force Method [6]. The computational consideration of thermodynamic potentials, such as the free energy, that are distributed within surfaces/interfaces is at the same time scientifically challenging and technologically relevant when cracks and their kinetics are studied.

  • PPP Frankreich 2019 Phase I

    (Third Party Funds Single)

    Term: 01-01-2019 - 31-12-2020
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

  • Theoretische Grenzen und algorithmische Verfahren verteilter komprimierender Abtastung

    (Third Party Funds Single)

    Term: 01-01-2019 - 30-06-2020
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract
    The theoretical limits of distributed compressive sensing are studied bytools from both information theory and statistical physics. The investigationscover both noise-free and noisy distributed compressive sensing. The theoretical insightsare utilized to design approximate message passing algorithms for joint recovery of large distributed compressive sensing networks with feasible computational complexity. These algo-rithms enable us to verify the non-rigorous results obtained by the replica method from statistical mechanics, and also, to propose theoretically optimal approaches for sampling and low complexity. The proposed research will lead to improved performance of reconstruction algorithms for distributed compressive sensing, e.g. higher compression rates and/or higher fidelity of reconstruction.

  • Integriertes und an Raum-Zeit-Messungsskalen angepasstes Global Random Walk - Modell für reaktiven Transport im Grundwasser

    (Third Party Funds Single)

    Term: 01-10-2018 - 30-09-2021
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

  • Nonlocal Methods for Arbitrary Data Sources

    (Third Party Funds Group – Sub project)

    Overall project: Nonlocal Methods for Arbitrary Data Sources
    Term: 01-10-2018 - 28-02-2022
    Funding source: EU - 8. Rahmenprogramm - Horizon 2020

  • Parity Sheaves on Kashiwara's flag manifold

    (Third Party Funds Group – Overall project)

    Term: 01-09-2018 - 31-12-2019
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)
    Abstract

    The  project is located in pure mathematics and deals with a problem in geometric representation theory. Parity sheaves and moment graph techniques have proven to be extremely effective in answering questions in modular representation theory.  In the finite-dimensional case a hypercohomology functor establishes a connection between parity sheaves and sheaves on moment graphs. However the geometry  controlling representation theoretic phenomena in this case is often infinite-dimensional. We plan to study the category of parity sheaves on Kashiwara's infinite-dimensional thick-flag variety Y, to define a hypercohomology functor, to interpret its image as a category of moment graph sheaves and to establish an equivalence between parity sheaves and canonical sheaves on the moment graph. In a second phase, we intend to study base change and torsion phenomena in the category of parity sheaves on the thick flag manifold, in order to establish an equivalence between the category of projective objects in the category O of an affine Kac-Moody algebra at negative level and  parity sheaves on Y. 

  • Implementation of vector operations for SBCL

    (Third Party Funds Single)

    Term: 10-07-2018 - 31-03-2019
    Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)
    Abstract
    Ziel des Projekts ist es, AVX2 Vektoroperationen für die Common LispImplementierung SBCL verfügbar zu machen.  SBCL ist derpopulärste und am weitesten Entwickelte freie Compiler für CommonLisp.  Die Verbesserungen aus diesem Projekt machen es möglichCommon Lisp Programme zu schreiben, deren Ausführungsgeschwindigkeitmit C++ und Fortran Programmen auf Augenhöhe liegt.  Dadurchergeben sich interessante Möglichkeiten der Metaprogrammierung imwissenschaftlichen Rechnen.

  • MIP techniques for equilibrium models with integer constraints (B07) (2018 - 2022)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-07-2018 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    Abstract
    In this subproject we will develop techniques to solve equilibrium problems with integer constraints using MIP techniques. To this end, we will consider first mixed-integer linear, then mixed-integer nonlinear problems as subproblems. To solve the resulting problems we will study both complete descriptions as also generalized KKT theorems for mixed-integer nonlinear optimization problems.

  • Multilevel mixed-integer nonlinear optimization for gas markets (B08) (2018 - 2022)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-07-2018 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    URL: https://trr154.fau.de/index.php/de/teilprojekte/b08
    Abstract

    The main goal of this project is the development of mathematical methods for the solution of multilevel, mixed-integer, and nonlinear optimization models for gas markets. To this end, the focus is on a genuine four-level model of the entry-exit system that can be reformulated as a Bilevel model. The mathematical and algorithmic insights shall then be used to characterize market solutions in the entry-exit system and to compare them to system optima. Particular attention is paid to booking prices for entry or exit capacity.

  • Robustification of Physics Parameters in Gas Networks (B06) (2018 - 2022)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-07-2018 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    Abstract

    The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branch-and-bound implementations shall be developed.

  • Decomposition methods for mixed-integer optimal control (A05) (2018 - 2022)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-07-2018 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    Abstract

    The focus lies on the development of mathematical decomposition methods for mixed-integer nonlinear optimal control problems on networks. On the top level (master) mixed-integer linear problems are in place, whereas in the sub-problem only continuous variables are considered. The exchange between the levels is performed not only via cutting planes, but also via the modelling of disjunctions to deal with non-convex optimal control problems as well. The overall emphasis is the mathematical analysis of structured mixed nonlinear optimization problems based on hierarchical models.

  • Interfaces, complex structures, and singular limits in continuum mechanics

    (Third Party Funds Group – Overall project)

    Term: 01-04-2018 - 30-09-2022
    Funding source: DFG / Graduiertenkolleg (GRK)

  • Free boundary propagation and noise: analysis and numerics of stochastic degenerate parabolic equations

    (Third Party Funds Single)

    Term: 01-04-2018 - 31-03-2020
    Funding source: Deutsche Forschungsgemeinschaft (DFG), DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    URL: https://www1.am.uni-erlangen.de/~gruen/
    Abstract

    The porous-medium equation and the thin-film equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time.
    As they are supposed to describe the spreading of gas in a porous-medium or the spreading of a viscous droplet on a horizontal surface, respectively, mathematical results on the propagation of free boundaries become relevant in applications. In contrast to, e.g., the heat equation, where solutions to initial value problems with compactly supported nonnegative initial data
    instantaneously become globally positive, finite propagation and waiting time phenomena are characteristic features of degenerate parabolic equations.
    In this project, stochastic partial differential equations shall be studied which arise from the aforementioned degenerate parabolic equations by adding multiplicative noise in form of source terms or of convective terms. The scope is to investigate the impact of noise on the propagation of free boundaries, including in particular necessary and sufficient conditions for the occurrence
    of waiting time phenomena and results on the size of waiting times. Technically, the project relies both on rigorous mathematical analysis and on numerical simulation.

  • Optimierung der Netzeingriffe

    (Third Party Funds Group – Sub project)

    Overall project: Flächenbezogene Modellierung, Simulation und Optimierung von Solar-Einspeisung, Lastfluss und Steuerung für Stromverteilnetze, unter Berücksichtigung von Einspeisungsunsicherheiten
    Term: 01-01-2018 - 31-12-2021
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
    URL: https://en.www.math.fau.de/edom/projects-edom/analytics/optimal-control-of-electrical-distribution-networks-with-uncertain-solar

  • Adaptive Verfahren zur Optimierung gekoppelter pH-Systeme

    (Third Party Funds Group – Sub project)

    Overall project: EiFer: Energieeffizienz durch intelligente Fernwärmenetze
    Term: 01-01-2018 - 31-12-2020
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
Friedrich-Alexander-Universität Erlangen-Nürnberg