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Preprints
- Mair A., Peral E.G., Ptashnyk M., Dupuy L.X.
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Modelling the influence of rhizodeposits on root water uptake,
bioRxiv, 2025
[Link]
- Gomez Peral E., Mair A., Sanchez I.M., de las Heras Martinez G., Ptashnyk M., Dupuy L.X.
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Root exudation facilitate water infiltration and rewetting of dry soil,
bioRxiv, 2025
[Link]
- Verhees S., Venkataraman C., Ptashnyk M.
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Mathematical Modelling of Mechanotransduction via RhoA Signalling Pathways,
arXiv:2501.04407, 2025
[Link]
- Freingruber V., Lorenzi T., Painter K.J., Ptashnyk M.
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Trait-structured chemotaxis: Exploring ligand-receptor dynamics and travelling wave properties in a Keller-Segel model,
arXiv, 2025
[Link]
- Benková K., Pearson J.W., Ptashnyk M.
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Fast numerical solvers for parameter identification problems in mathematical biology,
arXiv, 2024
[Link]
- Mair A., Ptashnyk M.
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Homogenization of a multiscale model for water transport in vegetated soil,
arXiv, 2024
[Link]
- Jans M., Lord G.J., Ptashnyk, M.
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Strong Convergence of a Splitting Method for the Stochastic Complex Ginzburg-Landau Equation,
arXiv, 2024
[Link]
- Popović N., Ptashnyk M., Sattar Z.
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The Burgers-FKPP advection-reaction-diffusion equation with cut-off,
arXiv::2410.08763v1, 2024
[Link]
Peer Reviewed Journal Articles
- Baker K., Banjai L., Ptashnyk M.
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Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping,
Mathematics of Computations, 93, 2711-2743, 2024
[Link] [PDF]
- Freingruber V., Painter K.J., Ptashnyk M., Schumacher L.J.
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A biased random walk approach for modeling the collective chemotaxis of neural crest cells,
J Mathematical Biology, 88, 1-32, 2024
[Link]
[PDF]
- Engel M., Hummel F., Kuehn C., Popović N., Ptashnyk M., Zacharis T.
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Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation,
Nonlinearity, 37, 2024
[Link]
[PDF]
- Boudaoud A., Kiss A., Ptashnyk M.
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Multiscale modelling and analysis of growth of plant tissues,
SIAM J Applied Mathematics, 83, 2354-2389, 2023
[Link]
[PDF]
- Mimault M., Ptashnyk M., Dupuy L.X.
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Particle-based model shows complex rearrangement of tissue mechanical properties are needed for roots to grow in hard soil,
PLOS Computational Biology, 19, e1010916, 2023
[Link] [PDF]
- Mair A., Dupuy L.X., Ptashnyk M.
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Can root systems redistribute soil water to mitigate the effects of drought?
Field Crops Research, 300, 109006, 2023
[Link]
[PDF]
- Engelhardt I.C., Patko D., Liu Y., Mimault M., de Las Heras Martinez G., George T.S., MacDonald M., Ptashnyk M., Sukhodub T., Stanley-Wall N.R., Holden N., Daniell T.J., Dupuy L.X.
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Novel form of collective movement by soil bacteria ,
ISME J., 16, 2337-2347, 2022
[Link]
[PDF]
- Mair A., Dupuy L.X., Ptashnyk M.
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Model for water infiltration in vegetated soil with preferential flow oriented by plant roots,
Plant Soil, 478, 709-729. 2022
[Link]
[PDF]
- Daus E., Ptashnyk M., Raithel C.
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Derivation of a fractional cross-diffusion system as the
limit of a stochastic many-particle system driven by Lévy noise,
J Differential Equations, 309, 386-426, 2022
[Link]
[PDF]
- Painter K.J., Ptashnyk M., Headon D.J.
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Systems for intricate patterning of the vertebrate anatomy,
Phil. Trans. R. Soc. A, 379: 20200270, 2021
[Link]
- King J.R., Köry J., Ptashnyk M.
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Multiscale analysis of nutrient uptake by plant root hairs
with sparse distribution of hairs: Nonstandard scaling,
SIAM J Applied Mathematics, 81, 1361-1388, 2021, [Link]
arXiv:1911.06293
[Link]
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Piatnitski, A., Ptashnyk, M.
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Homogenization of biomechanical models of plant tissues with
randomly distributed cells,
Nonlinearity, 33, 5510-5542, 2020
[Link]
- Lorenzi, T., Murray, P., Ptashnyk, M.
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From individual-based mechanical models of multicellular systems to free-boundary problems,
Interace and Free Boundary, 22, 205-244, 2020
[Link]
[PDF]
arXiv:1903.06590
[Link]
- Ptashnyk, M., Venkataraman C.
- Multiscale analysis and simulation of a signalling process with surface diffusion,
Multiscale Modelling and Simulation, SIAM Journal, 2020, 18, 851-886
[Link]
[PDF]
- Athanassoulis A., Athanassoulis G., Ptashnyk M., Sapsis T.
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Strong solutions for the Alber equation and stability of unidirectional wave spectra,
Kinetic and Related Models, 13, 703-737, 2020
[Link] [PDF]
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Allen, H.R., Ptashnyk, M.
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Mathematical Modelling of Auxin Transport in Plant Tissues: Flux meets Signalling and Growth,
Bulletin of Mathematical Biology, 82, 17, 2020
[Link]
- Juengel, A., Ptashnyk, M.
- Homogenization of degenerate cross-diffusion systems,
J Differential Equations, 2019
[Link]
[PDF]
- Mimault M., Ptashnyk M., Bassel G.W., Dupuy L.X.
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Smoothed particle hydrodynamics for
root growth mechanics,
Engineering Analysis with Boundary Elements, 105, 20-30, 2019
[Link]
- Ptashnyk M.
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Homogenization of some degenerate pseudoparabolic variational inequalities,
Journal of Mathematical Analysis and Applications, 469, 44-75, 2019
[Link] [PDF]
- Dupuy L.X., Mimault M., Patko D., Ladmiral V., Ameduri B., MacDonald M.P., Ptashnyk M.
- Micromechanics of root development in soil,
Current Opinion in Genetics and Development, 51, 18-25, 2018.
[Link]
- De La Fuente Canto C., Kalogiros D.I., Ptashnyk M., George T.S., Waugh R., Bengough A.G., Russell J., Dupuy L.X.
- Morphological and genetic characterisation of the root system architecture of selected barley Recombinant Chromosome Substitution Lines using an integrated
phenotyping pipeline,
Journal of Theoretical Biology, 447, 84-97, 2018.
[Link]
- Allen, H.R., Ptashnyk, M.
- Mathematical modelling and analysis of the Brassinosteroid and Gibberellin signalling pathways and their interactions,
Journal of Theoretical Biology, 432, 109-131, 2017
[Link]
- Piatnitski, A., Ptashnyk, M.
- Homogenization of biomechanical models for plant tissues,
Multiscale Modelling and Simulations, SIAM Journal, 15, 339-387, 2017
[Link]
- Ptashnyk, M.
- Multiscale modelling and analysis of signalling processes in tissues with non-periodic distribution of cells,
Vietnam Journal of Mathematics, 45, 295-316, 2017 .
[Link]
- Ptashnyk, M., Seguin, B.
- Homogenization of a viscoelastic model for plant cell wall biomechanics,
ESAIM: Control, Optimis., Calculus of Variations, 23, 1447-1471, 2017
[Link]
- Ptashnyk, M., Seguin, B.
- Multiscale analysis of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics, ESAIM M2AN, 50, 593-631, 2016
[Link]
arXiv:1410.6911 [Link]
- Ptashnyk, M., Seguin, B.
- The impact of microfibril orientations on the biomechanics of plant cell walls and tissues: modelling and simulations,
Bulletin of Mathematical Biology, 78, 2135-2164, 2016.
[Link]
- Matzavinos, A., Ptashnyk, M.
- Stochastic homogenization of the Keller–Segel chemotaxis system,
Nonlinear Analysis: Theory, Methods and Applications, 144, 58-76, 2016.
[Link]
[PDF]
- Kalogiros D.I., Adu M.O., White P.J., Broadley M.R., Draye X., Ptashnyk M., Bengough A.G., Dupuy L.X.
- Analysis of root growth from a phenotyping dataset using a density-based model,
J Experimental Botany, 67, 1045-1058, 2016
[Link]
- Ptashnyk, M., Seguin, B.
- Periodic homogenization and material symmetry in linear elasticity,
Journal of Elasticity, 124, 225-241, 2016.
[Link]
arXiv:1504.08165
[Link]
- Medkova, D., Ptashnyk, M., Varnhorn, W.
- Generalized Darcy-Oseen resolvent problem,
Mathematical Methods in Applied Sciences, 39, 1621-1630, 2016
[Link]
[PDF]
- Ptashnyk, M.
- Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures,
Multiscale Modelling and Simulations, SIAM Journal, 13, 1061-1105, 2015.
[Link]
- Matzavinos, A., Ptashnyk, M.
- Homogenization of oxygen transport in biological tissues, Applicable Analysis, 2015.
[Link]
[Link]
- Chaplain, M., Ptashnyk, M., Sturrock, M.
- Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations,
Mathematical Models and Methods in Applied Sciences , 25, 1179-1215, 2015.
[Link] [PDF]
- Medkova, D., Ptashnyk, M., Varnhorn, W.
- Integral representation of a solution to the Stokes-Darcy problem,
Mathematical Methods in Applied Sciences, 38, 3968-3979, 2015.
[PDF]
- Claus, J., Ptashnyk, M., Bohmann, A., Chavarría-Krauser, A.
- Global Hopf Bifurcation in the ZIP regulatory system,
J Mathematical Biology, 71, 795-816, 2015.
[Link]
- Chavarría-Krauser, A., Ptashnyk, M.
- Homogenization approach to water transport in plant tissues with periodic microstructures.
Mathematical Modelling of Natural Phenomena, 8, 80-111, 2013.
[Link]
[PDF]
- Melcher, C., Ptashnyk, M.
- Landau-Lifshitz-Slonczewski equations: Global weak and classical solutions.
SIAM J Mathematical Analysis , 45, 407-429, 2013.
[Link]
[PDF]
- Ptashnyk, M.
- Two-scale convergence for locally-periodic microstructures and
homogenization of plywood structures.
Multiscale Modelling and Simulations, SIAM J, 11, 92-117, 2013.
[Link]
[PDF]
- Mercker, M., Ptashnyk, M., Kühnle, J., Hartmann, D., Weiss, M., Jäger, W.
- A multiscale and multidisciplinary approach to curvature
modulated sorting in biological membranes.
J Theoretical Biology, 301, 67-82, 2012.
[Link] [PDF]
- Golovaty, Y., Marciniak-Czochra, A., Ptashnyk, M.
- Stability of nonconstant stationary solu- tions in a reaction-diffusion equation coupled to the system of ordinary differential equations.
Communications on Pure and Applied Analysis, 11, 229-241, 2012.
[Link]
- Fatima, T., Muntean, A., Ptashnyk, M.
- Error estimate and unfolding method for homogenization of a reaction-diffusion system modeling sulfate corrosion.
Applicable Analysis, 91, 1129-1154, 2012.
[Link]
[PDF]
- Capdeboscq, Y., Ptashnyk, M.
- Root growth: Homogenization in domain with time dependent partial perforation,
ESAIM: Control, Optimisation and Calculus of Variations, online, 18, 856-876, 2012.
[Link] [PDF]
- Ptashnyk, M., Roose, T., Jones, D.L., Kirk, G.J.D.
- Enhanced zinc uptake by rice by phytosiderophore secretion: a modelling study,
Plant, Cell and Environment, 34, 2038-2046, 2011.
[Link][PDF]
- Ptashnyk, M., Roose, T., Kirk, G.
- Diffusion of strongly sorbed solutes in soil: a dual-porosity model allowing for slow access to sorption sites and time-dependent sorption reactions.
EJSS, 61, 108-119, 2010
[Link][PDF]
- Ptashnyk, M., Roose, T.
- Derivation of a macroscopic model for transport of strongly sorbed solutes in the soil using homogenization theory.
SIAM J Appl Math, 70, 2097-2118, 2010.
[Link] [PDF]
- Leitner, D., Klepsch, S., Ptashnyk, M., Marchant, A., Kirk, G., Schnepf, A., Roose, T.
- A dynamic model of nutrient uptake by root hairs based on homogenisation.
New Phytologist, 185, 792-802, 2010.
[Link][PDF]
- Chavarría-Krauser, A., Ptashnyk, M.
- Homogenization of long-range auxin transport in plant tissues.
Nonlinear Analysis: Real World Applications, 11, 4524-4532, 2010.
[Link] [PDF]
- Ptashnyk, M.
- Derivation of a macroscopic model for nutrient uptake by a single branch of hairy-roots.
Nonlinear Analysis: Real World Applications, 11, 4586-4596, 2010.
[Link][PDF]
- Marciniak-Czochra, A., Ptashnyk, M.
- Boundedness of solutions of a haptotaxis model.
M3AS: Mathematical Models and Methods in Applied Sciences, 20, 449-476, 2010.
[Link] [PDF]
- Bastian, P., Chavarria-Krauser, A., Engwer, C., Jäger, W., Marnach, S., Ptashnyk, M.
- Modeling in vitro growth of dense root network.
J Theoretical Biology, 254 (1), 99-109, 2008.
[Link][PDF]
- Marciniak-Czochra, A., Ptashnyk, M.
- Derivation of a macroscopic receptor-based model using homogenization techniques.
SIAM J. Math Anal, 40 (1), 215-237, 2008.
[Link] [PDF]
- Ptashnyk, M.
- Pseudoparabolic equations with convection.
IMA J. Applied Mathematics, 72 (6), 2007.
[Link][PDF]
- Ptashnyk, M.
- Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities.
Nonlinear Analysis, Theory, Methods, Applications, 66 (12), 2653-2675, 2006.
[Link][PDF]
- Ptashnyk, M.
- Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations.
Applicable Analysis, 85 (10), 1285-1299, 2006.
[Link][PDF]
- Ptashnyk, M.
- Some pseudoparabolic variational inequalities with higher order derivatives.
Ukrainian Mathematical Journal, 54 (1), 112-125, 2002.[PDF]
- Lavrenyuk, S., Ptashnyk, M.
- Problem without initial conditions for a nonlinear pseudoparabolic system.
Differential Equations, 36 (5), 739-748, 2000.
- Lavrenyuk, S., Ptashnyk, M.
- On certain nonlinear pseudoparabolic variational inequalities without initial conditions.
Ukrainian Mathematical Journal, 51 (3), 366-376, 1999.[PDF]
- Lavrenyuk, S., Ptashnyk, M.
- Pseudo-parabolic variational inequalities without initial
conditions.
Ukrainian Mathematical Journal, 50 (7), 1045-1057, 1998.[PDF]
Invited chapters in books
- Ptashnyk, M., Allen, H.R.
- Calcium-Pectin Chemistry and Biomechanics: Biological Background and Mathematical Modelling,
Plant Biomechanics, A. Geitmann, J. Gril, Editors, Springer, 273-303, 2018
[Link]
- Bastian, P., Bauer, J., Chavarría-Krauser, A., Engwer, C., Jäger, W., Marnach, S.,
Ptashnyk, M., Wetterauer, B.
- Modeling and Simulation of Hairy Root Growth.
Mathematics--Key Technology for the Future, 101-115, 2008.
[Link]
[PDF]
PhD thesis
- Ptashnyk, M.
Nonlinear Pseudoparabolic Equations and Variational Inequalities.
- SFB-Preprint, University of Heidelberg, 2004. [PDF]
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