TU Darmstadt | Fachbereich Mathematik | Research Group Numerical Analysis and Scientific Computing

Research Group
Numerical Analysis and Scientific Computing

List of Publications
Dr. Alf Gerisch


List of Publications  |  List of Recent Publications  |  Last update: 23.04.2024 11:41.

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Summary statistics of publications shown below

Refereed Articles (39)

2024
; ; ; ; and : "Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis", Bull Math Biol, vol. 86, pp. (published online 1 Dec 2023), 2024. [doi]
2023
; ; and : "Physics informed neural networks: A case study for gas transport problems", J. Comput. Phys., vol. 481, pp. 112041, 2023. [doi]
2022
; and : "A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis", J Theor Biol, vol. 534, pp. 110963, 2022. [doi] [preprint]
2021
and : "A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems", Engineering Computations, vol. 38, no. 6, pp. 2666-2691, 2021. [doi]
; ; ; and : "Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers", J. Chem. Theory Comput., vol. 17, no. 6, pp. 3760-3771, 2021. [doi]
; ; and : "Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress–Strain Constitutive Equations", Bull Math Biol, vol. 83, pp. Article 80, 2021. [doi] [preprint]
2018
; ; and : "A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis", J. Math. Biol., vol. 76, pp. 429–456, 2018. [doi]
2017
; ; and : "Structured models of cell migration incorporating molecular binding processes", J Math Biol, vol. 75, pp. 1517–1561, 2017. [doi]
and : "The asymptotic homogenization elasticity tensor properties for composites with material discontinuities", Contin. Mech. Thermodyn., vol. 29, pp. 187–206, 2017. [doi]
; and : "Space–time adaptive linearly implicit peer methods for parabolic problems", J. Comput. Appl. Math., vol. 316, pp. 330-344, 2017. [doi]
2016
; ; ; and : "Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues", Bioinspir. & Biomim., vol. 11, pp. 035004, 2016. [doi]
2015
; ; ; ; ; ; and : "To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?", Acta Biomater., vol. 12, pp. 207–215, 2015. [doi]
; ; ; ; and : "Robustness of a new molecular dynamics-finite element coupling approach for soft matter systems analyzed by uncertainty quantification", J. Chem. Phys., vol. 142, pp. 104105, 2015. [doi]
; ; and : "A nonlocal model for contact attraction and repulsion in heterogeneous cell populations", Bull Math Biol, vol. 77, pp. 1132–1165, 2015. [doi]
and : "Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study", Comput. Visual Sci., vol. 17, pp. 185–201, 2015. [doi]
; and : "Defect corrected averaging for highly oscillatory problems", Appl. Math. Comput., vol. 261, pp. 90–103, 2015. [doi]
2014
; ; and : "Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns", J. Theor. Biol., vol. 361, pp. 41-60, 2014. [doi]
; ; ; ; ; ; and : "On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment", Biomech Model Mechanobiol, vol. 13, no. 15, pp. 1003–1023, 2014. [doi]
2012
; ; ; ; ; ; and : "Spatial distribution of tissue level properties in a human femoral cortical bone", J Biomech, vol. 45, pp. 2264 - 2270, 2012. [doi]
2011
; ; ; and : "Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation", J. Math. Biol., vol. 63, pp. 141-171, 2011. [doi]
; ; and : "A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties", Biomech Model Mechanobiol, vol. 10, pp. 925-937, 2011. [doi]
; ; ; and : "A hybrid bioregulatory model of angiogenesis during bone fracture healing", Biomech Model Mechanobiol, vol. 10, pp. 383-395, 2011. [doi]
2010
; ; and : "Numerical simulation of two-dimensional and three-dimensional axisymmetric advection-diffusion systems with complex geometries using finite-volume methods", Proc. R. Soc. A, vol. 466, pp. 1621–1643, 2010. [doi]
; and : "Mathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering", Acta Biotheor, vol. 58, pp. 355–367, 2010. [doi]
: "On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion", IMA J. Numer. Anal., vol. 30, pp. 173–194, 2010. [doi]
; ; and : "Multiscale structure–functional modeling of lamellar bone", Proc. Mtgs. Acoust., vol. 9, pp. 020005, 2010. [doi]
2009
; ; and : "High-order linearly implicit two-step peer–finite element methods for time-dependent PDEs", Appl. Numer. Math., vol. 59, pp. 624–638, 2009. [doi]
2008
; ; ; and : "Angiogenesis in bone fracture healing: A bioregulatory model", J. Theor. Biol., vol. 251, no. 1, pp. 137-158, 2008. [doi]
and : "Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion", J. Theor. Biol., vol. 250, no. 4, pp. 684-704, 2008. [doi]
; ; and : "Derivation of the mesoscopic elasticity tensor of cortical bone from quantitative impedance images at the micron scale", Comput Methods Biomech Biomed Engin, Taylor & Francis, vol. 11, no. 2, pp. 147-157, 2008. [doi]
; and : "Optimised coupling of hierarchies in image registration", Image Vis Comput, vol. 26, no. 7, pp. 1000-1011, 2008. [doi]
2007
and : "Zero-preserving iso-spectral flows based on parallel sums", Linear Algebra Appl, vol. 421, no. 1, pp. 69-84, 2007. [doi]
; and : "Well-posedness of a quasilinear hyperbolic–parabolic system arising in mathematical biology", Nonlinear differ. equ. appl., vol. 14, no. 5, pp. 593-624, 2007. [doi]
2006
; ; ; ; ; and : "Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results", Med Bio Eng Comput, vol. 44, no. 4, pp. 280-289, 2006. [doi]
and : "Robust numerical methods for taxis–diffusion–reaction systems: Applications to biomedical problems", Math. Comput. Modelling, vol. 43, no. 1, pp. 49-75, 2006. [doi]
2005
and : "Linearly implicit Runge–Kutta methods and approximate matrix factorization", Appl. Numer. Math., vol. 53, no. 2, pp. 183-200, 2005. [doi]
2003
and : "The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods", Comput. Math. with Appl., vol. 45, no. 1, pp. 53-67, 2003. [doi]
2002
and : "Operator splitting and approximate factorization for taxis–diffusion–reaction models", Appl. Numer. Math., vol. 42, no. 1, pp. 159-176, 2002. [doi]
2001
; ; and : "A positive splitting method for mixed hyperbolic-parabolic systems", Numerical Methods for Partial Differential Equations, vol. 17, no. 2, pp. 152-168, 2001. [doi]

Refereed Conference and Workshop Papers (7)

2012
; ; ; ; ; and : "Contributions of Pore Volume Fraction and Mineralized Matrix Elasticity to Millimeter-Scale Cortical Bone Elastic Coefficients", In: IASTED Biomedical Engineering, 15.-17.02.2012, Innsbruck, Austria (Hellmich, C.; Hamza, M. H.; Simsik, D., eds.), ACTA Press, pp. Contribution 764-133, 2012. [doi]
2010
; and : "Insight into the Structure-Function Relationship of the Bone Lamellar Unit through Finite Element Modelling Based on High-Frequency SAM Data", In: World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany (Dössel, Olaf; Schlegel, Wolfgang C., eds.), Springer Berlin Heidelberg, pp. 2246–2249, 2010. [doi]
2005
; and : "OSI Network‐layer Abstraction: Analysis of Simulation Dynamics and Performance Indicators", In: SCIENCE OF COMPLEX NETWORKS: From Biology to the Internet and WWW: CNET 2004. Volume 776 of AIP Conference Proceedings (Mendes, J.F.F. et al., ed.), pp. 166-200, 2005. [doi]
2004
; ; ; and : "Surface Roughening in Homoepitaxial Growth: A Lattice Gas Cellular Automaton Model", In: Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305 (Sloot, Peter M. A.; Chopard, Bastien; Hoekstra, Alfons G., eds.), Springer-Verlag, Berlin, Heidelberg, pp. 286–295, 2004. [doi]
; and : "From Individual to Collective Behaviour in CA Like Models of Data Communication Networks", In: Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305 (Sloot, Peter M. A.; Chopard, Bastien; Hoekstra, Alfons G., eds.), Springer-Verlag, Berlin, Heidelberg, pp. 325–334, 2004. [doi]
2003
; ; ; and : "Lattice gas cellular automaton modeling of surface roughening in homoepitaxial growth in nanowires", In: CCECE 2003 - Canadian Conference on Electrical and Computer Engineering. Toward a Caring and Humane Technology (Cat. No.03CH37436), pp. 1413-1416 vol.2, 2003. [doi]
2000
and : "Splitting Methods for the Simulation of Tumor Angiogenesis Models", In: Proceedings of the 16th IMACS World Congress, Lausanne, Switzerland (Deville, M.; Owens, R., eds.), published on CD-ROM, Rutgers University, New Brunswick, NJ, 2000.

Book Chapters (8)

2021
and : "Multi-Scale Analysis of Contact-Dependent Interaction in Tissue Aggregation and Invasion", Chapter in Systems Medicine: Integrative, Qualitative and Computational Approaches (Wolkenhauer, Olaf, ed.), Academic Press, Oxford, pp. 156-168, 2021. [doi]
2017
; and : "Cross-diffusion in reaction-diffusion models: analysis, numerics and applications", Chapter in Progress in Industrial Mathematics at ECMI 2016 (Quintela, P.; Barrali, Patricia; Gómez, Dolores; others, eds.), Springer International Publishing, Cham, pp. 385–392, 2017. [doi]
and : "An introduction to asymptotic homogenization", Chapter in Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications (Gerisch, A.; Penta, R.; Lang, J., eds.), Springer International Publishing, Cham, pp. 1–26, 2017. [doi]
2016
; ; and : "Multiscale Computational Modelling and Analysis of Cancer Invasion", Chapter in Mathematical Models and Methods for Living Systems: Levico Terme, Italy 2014 (Preziosi, Luigi; Chaplain, Mark; Pugliese, Andrea, eds.), Springer International Publishing, Cham, pp. 275–321, 2016. [doi]
2011
and : "Mathematical Modelling of Cell Adhesion in Tissue Engineering using Continuum Models", Chapter in Cellular and Biomolecular Mechanics and Mechanobiology (Gefen, Amit, ed.), Springer Berlin Heidelberg, pp. 431-450, 2011. [doi]
2010
and : "Mathematical Modeling of Cell Adhesion and Its Applications to Developmental Biology and Cancer Invasion", Chapter in Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling (Chauvière, A.; Preziosi, L.; Verdier, C., eds.), Chapman & Hall/CRC, pp. 319–349, 2010. [doi]
2007
and : "A Finite Volume Spatial Discretisation for Taxis-Diffusion-Reaction Systems with Axi-Symmetry: Application to Fracture Healing", Chapter in Mathematical Modeling of Biological Systems, Volume I: Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis (Deutsch, Andreas; Brusch, Lutz; Byrne, Helen; Vries, Gerda de; Herzel, Hanspeter, eds.), Birkhäuser Boston, Boston, MA, pp. 299–311, 2007. [doi]
2005
; ; ; and : "Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber", Chapter in Micro- and Nanostructures of Biological Systems (Bischof, G., ed.), Shaker Verlag, Aachen, pp. 60-76, 2005.

Books (1)

2017
; and : "Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications", Springer, Cham, 2017. [doi]

Other Publications (4)

2008
and : "Let's stick together: Numerische Simulation von Zelladhäsionsprozessen", 2008.
2002
; ; and : "Modelling flow and congestion in packet switching network", 2002.
2001
: "Numerical Methods for the Simulation of Taxis-Diffusion-Reaction Systems", PhD thesis, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany, , 2001. [doi]
1997
: "Finite Difference Methods for Coupled Nonlinear Hyperbolic and Parabolic Partial Differential Equations in One and Two Dimensions", Master's thesis, University of Dundee, UK, , 1997.
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