Research

Projects  Reviewer Duties  Publications  Supervised Theses  Conference Talks

See also my Research Profiles at Google Scholar and ResearchGate

Research Interests

Mathematics in the geosciences, in particular structure evolution in soils, modelling and simulation of reactive contaminant transport in porous media, evaluation of natural attenuation, geostatistics, efficient and accurate solution of hydrogeochemical multicomponent models.

Mathematics in biology, in particular spatio-temporal differential equation models of regulatory networks

Left: Temporal evolution of root (brown), mucilage (pink) and soil structures (grey) in 18% clay soil Right: C/N dynamics coupled to microbial turnover after mucilage pulse

Some current research highlights in the framework of the DFG Research Unit 2179 MAD Soil (“Microaggregates: Formation and turnover of the structural building blocks of soils”) and the DFG Priority Program 2089 (Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”:

In the last decade my research focussed on advancing our understanding of structure formation in soils on the microscale, and the coupled carbon turnover. In order to study the self-organization of soil aggregates (particles of diameters less than 250 microns) by various attracting forces influenced by geochemistry, and microbiology, a novel, comprehensive mathematical model  has been developed that explicitly represents the pore structure derived from CT scans. To take into account specific properties of the rhizosphere the functional range of existing models for aggregation or carbon turnover had to be extended and, e.g. an explicit phase of mucilage, root dynamics or C/N specific microbial growth included.
Due to its high complexity, we need to use upscaling techniques to incorporate information from the micro to the macroscale.  We use combinations of Discontinuous Galerkin Methods and Cellular Automata as numerical approximations of the derived mechanistic model and integrate them in an efficient software tool using massively parallel architecture.

Above you see snapshots of a study where we investigate with the help of the fully dynamic spatial and image-based modeling tool how soil aggregation, root growth and exudates mutually interact at the pore scale (Rötzer et al., 2023).  The simulation results support that the deposition of mucilage is an important driver for structure formation in the rhizosphere. Although mucilage is degraded within a few days after exudation, it leads to a persistent stabilization of the aggregated structures for both textures in the vicinity of the root. This stabilization is significantly different from the structures encountered when only particulate organic matter (POM) could trigger the evolution of gluing spots, and is still present after complete degradation of the root. Further aspects incorporated include microbial necromass and C/N specific pathways of microbial transformations. This allows the tracking of different C pools and the identification of hot/cold spots in space and time to better understand carbon turnover in the rhizosphere.

Below you see information gained in Zech et al. (2022)  elucidating the impact of soil texture, POM input and degradation rates on carbon turnover and CO2 production by microbes.

Amount of organic carbon (OC) in different fractions of particulate organic matter (POM) by age (differently colored bars) and gluing agent (number above bar), CO2 production rate (arrows above bars), total CO2 production (rightmost arrows), and remaining share of initial POM in different input scenarios and for both soil textures with high decomposition rate: High/low/no input scenarios for low clay soil (a, c, e) and high clay soil (b, d, f).

 

Subsequently you find information on projects I participated or lead (Volume of third-party funding as PI/Co-PI since 2015 approx. 1.176 M. Euro (2021)), publications, my review activities, supervised bachelor, master and diploma theses, and a list of talks at conferences.

Projects

Term: 01-11-2022 - 31-10-2025
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader: ,

Dr. Alexander Prechtel, Akad. ORat

PD Dr. Nadja Ray

To couple three interwoven areas of rhizosphere research “Processes, Methods and Applications”, we utilize and improve mechanistic, mathematical models in forms of combined cellular automata and PDE/ODE systems on the microscale, offering the opportunity to bridge scales by homogenization techniques. The
systematic study of the interaction of transformation processes in the rhizosphere focussing on mucilage and root hairs, and its couplings to soil structure, geochemistry, microbiology, and…

→ More information

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

Dr. Alexander Prechtel, Akad. ORat

PD Dr. Nadja Ray

→ More information

Term: 01-02-2019 - 31-01-2022
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader: ,

Dr. Alexander Prechtel, Akad. ORat

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…

→ More information

Term: 01-01-2016 - 31-12-2019
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader: ,

Dr. Alexander Prechtel, Akad. ORat

PD Dr. Nadja Ray

→ More information

Term: 01-01-2012 - 31-12-2013
Funding source: Deutscher Akademischer Austauschdienst (DAAD)
Project leader:

Prof. i. R. Dr. Peter Knabner

Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios.   The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical s…

→ More information

Term: 01-10-2009 - 30-09-2011
Funding source: Bundesministerium für Bildung und Forschung (BMBF)
Project leader:

Prof. i. R. Dr. Peter Knabner

The project was a cooperation of a group of applied mathematicians with the Russian company Aeroservice for the development and optimization of new photocatalytic filter systems for air cleaning of nanoparticles and organic substances with the help of mathematical simulation tools. For the simulation of aerosol transport in the filter made of polypropylene fibers, which is used in hospitals or airports, e.g., mathematical models and efficient solution algorithms had to be developed. These allow on…

→ More information

Term: 01-11-2006 - 31-12-2009
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:

Prof. i. R. Dr. Peter Knabner

Soil colloids may influence the interaction between solutes and the immobile solid phase. A coupling to the fluid transport is possible by processes of sedimentation, flocculation, precipitation, filtration and deposition. The objective of this research project is the qualitative and quantitative examination of the crucial aspects of colloidal-influenced solute- and fluid transport by means of systematic, prognostic simulation. In detail,

  1. the attachment and detachment of colloids…

    → More information

Term: 01-04-2004 - 31-12-2008
Funding source: BMBF / Verbundprojekt
Project leader: ,

Prof. i. R. Dr. Peter Knabner

Dr. Alexander Prechtel, Akad. ORat

The evaluation of the potential of contaminated sites concerning natural attenuation needs comprehensive process descriptions and accurate, reliable numerical algorithms. Numerical errors may lead to qualitatively completely wrong conclusions concerning the potential of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the quality and efficiency of the calculations ensured by modern numerical methods…

→ More information

Term: 01-06-2001 - 31-05-2003
Funding source: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
Project leader: ,

Prof. i. R. Dr. Peter Knabner

The project included the mathematical modelling of natural attenuation processes in the subsurface and the extension of a software tool for complex reactive multicomponent processes in the framework of mixed hybrid and conforming finite elements. New  parameter identification methods allow the parametrization of unknown functions or a formfree optimization, and help to overcome the dilemma of missing data in complex models. Work included instationary 3D simulations and scenarios of  contaminated s…

→ More information

Term: 01-01-2001 - 31-12-2004
Funding source: Bundesministerium für Bildung und Forschung (BMBF)
Project leader:

Prof. i. R. Dr. Peter Knabner

Mathematical simulation tools allow the quantitative integration of competing transport and transformation processes which are relevant for a seepage water risk prognosis. Therefore model simulations have to contain a comprehensive process description, while they can serve for parameter identification by inverse modelling of suitable column or batch experiments, and allow to quantify the dependence of a key variable on parameters through a simultaneous sensitivity analysis. The software platform…

→ More information

Publications

Reviews

Reviewer for the Agence Nationale de Recherche in France and the DFG (German Research Foundation),

and the following journals: BioSystems, Computer Methods in Applied Mechanics and Engineering, Environmental Pollution, Environmental Science & Technology, Geoderma, International Journal for Numerical Methods in Fluids, International Journal on Geomathematics, Mathematics and Computers in Simulation, Nonlinear Analysis: Real World Applications, Plant and Soil, PLOS One, and Water Resources Research.

Theses that I have supported / supervised / evaluated:

Diploma theses:

Kastner, Stephan: “Mathematische Modellierung und numerische Simulation von Selbstreinigungsprozessen” February 2002

Oßmann, Stephan: “Mathematische Modellierung und numerische Simulation von präferenziellem Fließen mit Stofftransport in strukturierten porösen Medien“, June 2004

Schumann, Robert: “Operator Splitting und voll gekoppelte Lösungsalgorithmen für Transport-Reaktionssysteme in porösen Medien“, May 2006

Frank, Florian: “Hydrogeochemical multi-component transport – mineral dissolution and precipitation with consideration of porosity changes in variably-saturated porous media“, 2008

Bachelor theses:

Hutter, Jana: “Die Adsorptions-Advektions-Dispersionsgleichung“, 2009 (Technomathematik)

Rupp, Andreas: “Numerische Studien zur Strukturbildung in Böden durch Mineralreaktionen“, 2014 (Mathematics)

Clarner, Jan-Patrick: “Modellierung und Simulation der Bildung und Transformation von Aggregaten in Böden“, 2016 (Mathematics)

Conrad, Marcus: “Integration von Reaktionstermen in das 1D-Flachwassermodell basierend auf dem Discontinuous-Galerkin-Verfahren“, 2016 (Integrated Life Sciences)

Klingberg, Tim: “Charakterisierung des stationären Eingangs-/Ausgangsverhaltens von Doppelphosphorylierungszyklen“, 2017 (Integrated Life Sciences)

Pindl, Kathrin: “Charakterisierung des Eingangs-/Ausgangsverhaltens der MAP Kinase Kaskade“, 2017 (Integrated Life Sciences)

Möckel, Marianna: “Einfluss der Autoregulation auf das dynamische Verhalten von Zwei-Komponenten Systemen“, 2017 (Integrated Life Sciences)

Eckstein, Nadja: “Charakterisierung der dynamischen Regulation von SCF Ligasen durch CAND1“, 2017 (Integrated Life Sciences)

Hermann, Anne: “The influence of a symmetric boundary condition on the effective diffusion tensor of a soil column calculated by homogenisation“, 2022 (Mathematics)

Heimann, Lennard: “Untersuchungen zu Metabolismus und Genregulation in Corynebacterium diphteriae“, 2023 (Integrated Life Sciences)

Master theses:

Hutter, Jana: “Spatio-temporal modelling of cell cycle control“, 2011 (Technomathematik)

Pérez Pardo, Beatriz: “Mathematical modeling and simulation of a microfluidic reactor. From real application towards a 2D computer simulation“, August 2012 (Computational Engineering)

Eckstein, Nadja: “Mathematical Modelling and Simulation of the Influence of Extracellular Polymeric Substances on Microaggregate Formation in Soils“, November 2018 (Integrated Life Sciences)

Tapia Schulze, Lorenzo: “Mathematical Modeling and Simulation of the chemotactic movement of neutrophils in inflammatory environments“, September 2022 (Computational and Applied Mathematics)

Talks:

  • “A Comprehensive Tool for the Simulation of Complex Reactive Transport and Flow in Soils”.
    XXV General Assembly of the European Geophysical Society (EGS), April 25-29, 2000, Nice, France.
  • “Accurate and Efficient Simulation of Coupled Water Flow and Nonlinear Reactive Transport in the Saturated and Vadose Zone – Application to Surfactant Enhanced and Intrinsic Bioremediation”.
    Computational Methods in Water Resources XIV, June 23-28, 2002, Delft, The Netherlands.
  • “Entwicklung einer Simulationssoftware zur Prognose von Schadstoffausbreitung und -abbau in der (un-)gesättigten Bodenzone”.
    Workshop Forschungsverbundvorhaben “Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens”, July 18-19, 2002, Freising, Germany.
  • Talks on “Mikrobiologie”, “Hydrochemie” and “Modellierung”.
    Workshop Forschungsverbundvorhaben “Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens”, February 20-21, 2003, Freising, Germany.
  • “Modelling and numerical simulation of variably saturated flow and coupled reactive, biogeochemical transport”.
     Workshop on Modeling and Simulation in Chemical Engineering, June 30 – July 4, 2003, Coimbra, Portugal.
  • “Abbaukinetiken: Möglichkeiten der Modellierung und Simulation”.
    BMBF-Förderschwerpunkt KORA (Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Grundwässer und Böden), Fachgespräch Mikrobiologie, September 18-19, 2003, Karlsruhe, Germany.
  • “Handlungsempfehlung: Schwerpunkt Modellierung”.
    Symposium Natürliches Reinigungsvermögen – Natural Attenuation, Landesamt für Umweltschutz, November 10-11, 2003, Augsburg, Germany.
  • “Modeling and Simulation of Reactive Multicomponent Transport: Model Equations and Efficient Solution Concepts”.
     Workshop Porous Media, Zentrum für Angewandte Geowissenschaften, December 2-3, 2004, Blaubeuren, Germany.
  • “Efficient Modified Newton’s Method for Solving Reactive Multicomponent Transport Problems in Porous Media”.
    SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 6-10, 2005, Avignon, France.
  • “Grundlagen und Modellierung der Schadstoffausbreitung im Boden”.
     DECHEMA-Arbeitskreis “Auswirkungen von Stoff- und Energiefreisetzungen”, November 3, 2005, Frankfurt am Main, Germany.
  • “Große Mehrkomponentenprobleme berechenbar machen: Reduktion der Komplexität”.
    2. BMBF Statusseminar KORA, November 22-23, 2005, Frankfurt am Main, Germany.
  • “Grundlagen und Stolpersteine der Modellierung in der Altlastenbearbeitung”.
    BEW-Seminar “Numerische Modelle als Instrument in der Altlastenbearbeitung”, 31. Mai 2006, Duisburg, Germany
  • “Efficient process-preserving modified Newton’s method for solving reactive multicomponent transport problems in porous media”.
     Workshop on simulation, modelling and numerical analysis, September 18-20, 2006, Liberec, Czech Republic.
  • “Efficient process-preserving and adaptive modified Newton’s method for solving reactive multicomponent transport problems in porous media”.
    6th International Congress on Industrial and Applied Mathematics, July 16-20, 2007, Zurich, Switzerland.
  • “Modellierung als Werkzeug zur Prozessidentifikation und -quantifizierung von NA-Prozessen sprengstofftypischer Verbindungen”.
    Abschließendes BMBF-Statusseminar des TV5 “Rüstungsaltlasten” – KORA, 17.-18. Juni 2008, Berlin, Germany.
  • “An adaptive, process-preserving modified Newton’s method to solve reactive multicomponent transport problems efficiently”.
    5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), June 30 – July 5, 2008, Venice, Italy.
  • “Efficient and Reliable Simulation of Reactive Multicomponent Problems”.
    Bio-Geo-Kolloquium Friedrich-Schiller-Universität Jena, December 16, 2008.
  • “Adaptive, Selective Coupling of Multicomponent Transport and Kinetic Reactions”.
    SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 15 – 18, 2009, Leipzig, Germany.
  • “Identification of biogeochemical degradation parameters of propylene glycol by complex modelling”.
    Computational Methods in Water Resources XIX, June 17-21, 2012, Urbana-Champaign, Illinois, USA.
  • “Spatio-Temporal Modelling of Cell Cycle Control”.
    SIAM Conference on the Life Sciences, August 7 – 10, 2012, San Diego, California, USA.
  • “Solving Coupled Reactive Multicomponent Problems in Geosciences and Biology”, May 30, 2013, University of Bergen, Norway.
  • “Mechanistic Modeling of the Formation and Consolidation of Soil Microaggregates”, SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 29 – July 2, 2015, Stanford, California, USA.
  • “Process-based Modelling of the Formation and Consolidation of Soil Microaggregates”.
    Computational Methods in Water Resources XXI, June 20-24, 2016, Toronto, Canada.
  • “Hybrid Discrete-Continuum Modeling for Transport, Biofilm Development and Solid Restructuring including Electrostatic Effects”.
    General Assembly of the European Geophysical Union, April 23-28, 2017, Vienna, Austria.
  • “Mechanistic Model for Transport, Biofilm Development and Solid Restructuring in Soil Microaggregates”.
    Workshop on Formation, Properties and Function of Soil Microaggregates, October 10-12, 2017, Munich.
  • “Linking Processes to Structure and Structure to Function: Hybrid Discrete-Continuum Modeling forMicroaggregate Formation”.
    General Assembly of the European Geophysical Union, April 8-13, 2018, Vienna, Austria.
  • “Discrete-Continuum Multiscale Model for Evolving Microaggregates in Porous Media”.
    PICO Presentation, General Assembly of the European Geophysical Union, April 8-13, 2018, Vienna, Austria.
  • “Hybrid cellular automata / PDE modeling  for solid restructuring including EPS“, Computational Methods in Water Resources XXII, June 3-7, 2018, St. Malo, France.
  • „Hybrid Cellular Automata / PDE Modeling for Self-organisation of Soil Microaggregate Structures“, SIAM Conference on Mathematical and Computational Issues in the Geosciences, March 11 – 14, 2019, Houston, Texas, USA.
  • “Microaggregation of goethite and illite: Linking mechanistic modeling and laboratory experiments”,

    Online Presentation, General Assembly of the European Geophysical Union, May 4-8, 2020, Vienna, Austria.

  • „Evaluating the Interaction of Biofilms, Organic Matter and Soil Structures at the pore scale“,

    Online Presentation, at 3rd ISMC Conf. on Advances in Modeling Soil Systems, May 18-21; and at InterPore 2021, 13th General Assembly, May 31- June 4, 2021.

  • „Process-based, mechanistic modeling of dynamic structures at the pore scale“, Goldschmidt Conference, July 10-15, 2022, Honolulu, Hawaii, USA.
  • „Soils in silico – process-based modeling of dynamic structures at the pore scale“, 22nd World Congress of Soil Science, July 31- August 5, 2022, Glasgow, UK.
  • “Seven years of research on process-based, mechanistic modeling of aggregation and its drivers“, General Assembly of the European Geophysical Union, April 23-28, 2023, Vienna, Austria.
  • “Pore Scale Modelling of Evolving Soil Structures“, SIAM Conference on Mathematical and Computational Issues in the Geosciences, June 19-22, 2023, Bergen, Norway.
  • “Cellular Automata in Soil Science“, Invited Seminar Talk at Lappeenranta-Lahti University of Technology, August 8, 2023, Lappeenranta, Finland.
  • “Coupling scales in process-based soil organic carbon modeling including dynamic aggregation“, General Assembly of the European Geophysical Union, April 14-19, 2024, Vienna, Austria.
  • “Pore scale modeling of the mutual influence of roots and soil aggregation in the rhizosphere”, 12th International Symposium of the Int. Soc. Root Research, June 2-7, 2024, Leipzig
  • “Modeling of structural development in soil and rhizosphere”, BayInt Workshop on Fluid flow and reactive transport in porous media, Nov. 5, 2024, KU Eichstätt-Ingolstadt.
  • “Coupling scales in soil C (and N) turnover modeling including soil structure dynamics”, MicroSoil, June 9-12, 2025, Saint-Loup Lamaire, France.