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Research

In page navigation: Applied Mathematics 1
  • Staff Members A-Z
    • Dr. Rufat Badal
    • Apratim Bhattacharya
    • Astrid Bigott
    • Prof. Dr. Martin Burger
    • Sebastian Czop
    • Prof. Dr. Günther Grün
    • Lea Föcke
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    • Samira Kabri
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    • Dr. Nadja Ray
    • Doris Schneider
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    • Dr. habil. Raphael Schulz
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  • Workshop on Recent Developments in Modelling, Analysis, and Simulation of Processes in Porous Media
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      • Multicomponent reactive transport
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      • Program – Workshop on Modelling, Analysis and Simulation of Processes in Porous Media
      • Program – Workshop Porous Media

Research

Interests

  • Nonlinear (multi-scale) partial differential systems (arising in fluid dynamics and evolving microstructures): Weak solvability, regularity, boundedness, etc.
  • Degenerating parabolic equations: Existence of weak solutions by regularization
  • Mathematical modeling of biological processes (biofilms, chemotaxis, etc.) in evolving microstructures: Homogenization in a level-set framework
  • Numerical analysis of nonlinear (multi-scale) PDE systems: (Upwind, mixed) finite element methods

Publications

2022

  • Ray N., Schulz R.:
    Existence and uniqueness of solutions to a flow and transport problem with degenerating coefficients
    In: European Journal of Applied Mathematics (2022)
    ISSN: 0956-7925
    DOI: 10.1017/S0956792522000018
    BibTeX: Download
  • Schnepf A., Carminati A., Ahmed M., Ami M., Benard P., Bentz J., Bonkowski M., Brax M., Diehl D., Duddek P., Kröner E., Javaux M., Landl M., Lehndorff E., Lippold E., Lieu A., Müller CW., Oburger E., Otten W., Portell-Canal X., Phalempin M., Prechtel A., Schulz R., Vanderborght J., Vetterlein D.:
    Linking rhizosphere processes across scales: Opinion
    In: Plant and Soil (2022)
    ISSN: 0032-079X
    DOI: 10.1007/s11104-022-05306-7
    URL: https://link.springer.com/article/10.1007/s11104-022-05306-7
    BibTeX: Download

2020

  • Schulz R.:
    Degenerate equations for flow and transport in clogging porous media
    In: Journal of Mathematical Analysis and Applications 483 (2020), Article No.: 123613
    ISSN: 0022-247X
    DOI: 10.1016/j.jmaa.2019.123613
    BibTeX: Download
  • Schulz R.:
    Degenerate equations in a diffusion-precipitation model for clogging porous media
    In: European Journal of Applied Mathematics (2020)
    ISSN: 0956-7925
    DOI: 10.1017/S0956792519000391
    BibTeX: Download

2019

  • Knabner P., Reuter B., Schulz R.:
    Mit Mathe richtig anfangen
    Eine Einführung mit integrierter Anwendung der Programmiersprache Python

    Berlin Heidelberg: Springer Spektrum, 2019
    ISBN: 978-3-662-59229-8
    DOI: 10.1007/978-3-662-59230-4
    BibTeX: Download
  • Ray N., Schulz R.:
    Derivation of an effective dispersion model for electro-osmotic flow involving free boundaries in a thin strip
    In: Journal of Engineering Mathematics (2019)
    ISSN: 0022-0833
    DOI: 10.1007/s10665-019-10024-8
    BibTeX: Download
  • Schulz R.:
    Biofilm modeling in evolving porous media with Beavers-Joseph condition
    In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 99 (2019)
    ISSN: 0044-2267
    DOI: 10.1002/zamm.201800123
    BibTeX: Download
  • Schulz R.:
    Crystal precipitation and dissolution in a porous medium: Evolving microstructure and perforated solid matrix
    In: Special Topics and Reviews in Porous Media 10 (2019), p. 305-321
    ISSN: 2151-4798
    DOI: 10.1615/SpecialTopicsRevPorousMedia.2019029274
    BibTeX: Download
  • Schulz R.:
    Mathematical Modeling and Analysis of Processes in Evolving Microstructures (Habilitation, 2019)
    DOI: DOI: 10.1615/SpecialTopicsRevPorousMedia.2019029274
    BibTeX: Download
  • Schulz R., Ray N., Zech S., Rupp A., Knabner P.:
    Beyond Kozeny-Carman: Predicting the Permeability in Porous Media
    In: Transport in Porous Media (2019)
    ISSN: 0169-3913
    DOI: 10.1007/s11242-019-01321-y
    BibTeX: Download

2018

  • Farwig R., Schulz R., Taniuchi Y.:
    Spatial asymptotic profiles of solutions to the Navier-Stokes system in a rotating frame with fast decaying data
    In: Journal of the Hokkaido University, Faculty of Science, Series VII: Geophysics 47 (2018), p. 501 - 529
    ISSN: 0441-067X
    DOI: 10.14492/hokmj/1537948828
    BibTeX: Download
  • Ray N., Rupp A., Schulz R., Knabner P.:
    Old and New Approaches Predicting the Diffusion in Porous Media
    In: Transport in Porous Media 124 (2018), p. 803-824
    ISSN: 0169-3913
    DOI: 10.1007/s11242-018-1099-x
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_RayRuppSchulzKn_OldAndNewApproachesPredictingTheDiffInPM
    BibTeX: Download

2017

  • Schulz R.:
    Analysis of chemotactical biofilm growth in evolving microstructures
    88th GAMM Annual Meeting (Weimar, 06-03-2017 - 10-03-2017)
    In: Proceedings in Applied Mathematics and Mechanics PAMM 2017
    DOI: 10.1002/pamm.201710326
    BibTeX: Download
  • Schulz R.:
    Boundedness in a biofilm-chemotaxis model in evolving porous media
    In: Mathematical Modelling and Analysis 22 (2017), p. 852-869
    ISSN: 1392-6292
    DOI: 10.3846/13926292.2017.1389772
    BibTeX: Download
  • Schulz R., Knabner P.:
    An effective model for biofilm growth made by chemotactical bacteria in evolving porous media
    In: SIAM Journal on Applied Mathematics 77 (2017), p. 1653-1677
    ISSN: 0036-1399
    DOI: 10.1137/16M108817X
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_AnEffectiveModelForBiofilmGrowthInEvolvinPM
    BibTeX: Download
  • Schulz R., Knabner P.:
    Derivation and analysis of an effective model for biofilm growth in evolving porous media
    In: Mathematical Methods in the Applied Sciences 40 (2017), p. 2930-2948
    ISSN: 0170-4214
    DOI: 10.1002/mma.4211
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_DerivAnalysOfEffectModelForBiofilmGrowthInEvolvPM
    BibTeX: Download

2016

  • Schulz R., Ray N., Frank F., Mahato H., Knabner P.:
    Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium
    In: European Journal of Applied Mathematics (2016), p. 1-29
    ISSN: 0956-7925
    DOI: 10.1017/S0956792516000164
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SchulzRayFrankMahatoKn_StrongSolvUpToCloggingInAnEvolvingPM
    BibTeX: Download

2014

  • Farwig R., Schulz R., Yamazaki M.:
    Concentration-diffusion phenomena of heat convection in an incompressible fluid
    In: Asymptotic Analysis 88 (2014), p. 17 - 41
    ISSN: 0921-7134
    DOI: 10.3233/ASY-131211
    BibTeX: Download

2012

  • Schulz R.:
    Spatial Asymptotic Profile in Geophysical Fluid Dynamics (Dissertation, 2012)
    BibTeX: Download

Projects

  • 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.

    →More information
  • German-Norwegian collaborative research support scheme

    (Third Party Funds Single)

    Term: 01-01-2016 - 31-12-2017
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)
    Abstract

    Homogenisierung reaktiven Transports in variablen Mikrostrukturen

    →More information
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