• 418 Citations
  • 13 h-Index
20062020
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Research Output 2006 2020

  • 418 Citations
  • 13 h-Index
  • 38 Article
  • 1 Chapter
  • 1 Special issue
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Article
2020
4 Downloads (Pure)

Mathematical Modelling of Auxin Transport in Plant Tissues: Flux Meets Signalling and Growth

Allen, H. R. & Ptashnyk, M., Feb 2020, In : Bulletin of Mathematical Biology. 82, 2, p. 1-32 32 p., 17.

Research output: Contribution to journalArticle

Open Access
File
Indoleacetic Acids
Auxin
Mathematical Modeling
plant tissues
auxins
2019

Homogenization of some degenerate pseudoparabolic variational inequalities

Ptashnyk, M., 1 Jan 2019, In : Journal of Mathematical Analysis and Applications. 469, 1, p. 44-75 32 p.

Research output: Contribution to journalArticle

Capillarity
Homogenization
Two phase flow
Variational Inequalities
A Priori Estimates
2018
3 Citations (Scopus)
109 Downloads (Pure)

Micromechanics of root development in soil

Dupuy, L. X., Mimault, M., Patko, D., Ladmiral, V., Ameduri, B., MacDonald, M. P. & Ptashnyk, M., 1 Aug 2018, In : Current Opinion in Genetics & Development. 51, p. 18-25 8 p.

Research output: Contribution to journalArticle

Open Access
File
Soil
Biophysics
Rhizosphere
Physics
Technology
2 Citations (Scopus)
102 Downloads (Pure)

Morphological and genetic characterisation of the root system architecture of selected barley recombinant chromosome substitution lines using an integrated phenotyping approach

Canto, C. D. L. F., Kalogiros, D. I., Ptashnyk, M., George, T. S., Waugh, R., Bengough, A. G., Russell, J. & Dupuy, L. X., 14 Jun 2018, In : Journal of Theoretical Biology. 447, p. 84-97 14 p.

Research output: Contribution to journalArticle

Open Access
File
Root Growth
substitution lines
Barley
Root System
Hordeum
2017
124 Downloads (Pure)

Homogenization of a viscoelastic model for plant cell wall biomechanics

Ptashnyk, M. & Seguin, B., Oct 2017, In : ESAIM: Control, Optimisation and Calculus of Variations. 23, 4, p. 1447-1471 26 p.

Research output: Contribution to journalArticle

Open Access
File
Viscoelastic Model
Biomechanics
Cell Wall
Homogenization
Cells
5 Citations (Scopus)
87 Downloads (Pure)

Homogenization of Biomechanical Models for Plant Tissues

Piatnitski, A. & Ptashnyk, M., 2017, In : Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal. 15, 1, p. 339-387 49 p.

Research output: Contribution to journalArticle

Open Access
File
Biomechanics
homogenizing
Homogenization
biodynamics
Chemical reactions
4 Citations (Scopus)
39 Downloads (Pure)

Mathematical Modelling and Analysis of the Brassinosteroid and Gibberellin Signalling Pathways and their Interactions

Allen, H. R. & Ptashnyk, M., 7 Nov 2017, In : Journal of Theoretical Biology. 432, p. 109-131 23 p.

Research output: Contribution to journalArticle

Open Access
File
Brassinosteroids
Gibberellins
Gibberellin
brassinosteroids
Signaling Pathways
2 Citations (Scopus)
129 Downloads (Pure)
Open Access
File
Multiscale Modeling
Multiscale Analysis
Microstructure
Unfolding
Cell
2016
16 Citations (Scopus)
103 Downloads (Pure)

Analysis of root growth from a phenotyping data set using a density-based model

Kalogiros, D. I., Adu, M. O., White, P. J., Broadley, M. R., Draye, X., Ptashnyk, M., Bengough, A. G. & Dupuy, L. X., Feb 2016, In : Journal of Experimental Botany. 67, 4, p. 1045-1058 14 p.

Research output: Contribution to journalArticle

Open Access
File
root systems
root growth
phenotype
Growth
Genotype
125 Downloads (Pure)

Generalized Darcy–Oseen resolvent problem

Medková, D., Ptashnyk, M. & Varnhorn, W., 29 Mar 2016, In : Mathematical Models and Methods in Applied Sciences. 39, 6, p. 1621-1630 10 p.

Research output: Contribution to journalArticle

Open Access
File
Resolvent
Porous materials
Membranes
Porous Media
Fluids
9 Citations (Scopus)
136 Downloads (Pure)
Open Access
File
Biomechanics
Cell Wall
Reaction-diffusion Equations
Homogenization
Cells
4 Citations (Scopus)
85 Downloads (Pure)

Homogenization of oxygen transport in biological tissues

Matzavinos, A. & Ptashnyk, M., 2016, In : Applicable Analysis. 95, 5, p. 1013-1049 37 p.

Research output: Contribution to journalArticle

Open Access
File
Biological Tissue
Homogenization
Oxygen
Tissue
Two-scale Convergence
1 Citation (Scopus)
93 Downloads (Pure)

Periodic Homogenization and Material Symmetry in Linear Elasticity

Ptashnyk, M. & Seguin, B., Aug 2016, In : Journal of Elasticity. 124, 2, p. 225-241 17 p.

Research output: Contribution to journalArticle

Open Access
File
Elasticity
Tensors
101 Downloads (Pure)

Preface. Bifurcations and Pattern Formation in Biological Applications

Morozov, A., Ptashnyk, M. & Volpert, V., 2016, In : Mathematical Modelling of Natural Phenomena. 11, 5, p. 1-3 3 p.

Research output: Contribution to journalArticle

Open Access
File
Pattern Formation
Mathematical Modeling
Bifurcation
115 Downloads (Pure)

Stochastic homogenization of the Keller-Segel chemotaxis system

Matzavinos, A. & Ptashnyk, M., Oct 2016, In : Nonlinear Analysis. 144, p. 58-76 19 p.

Research output: Contribution to journalArticle

Open Access
File
Stochastic Homogenization
Chemotaxis
A Priori Estimates
Boundedness
3 Citations (Scopus)
72 Downloads (Pure)

The impact of microbril orientations on the biomechanics of plant cell walls and tissues

Ptashnyk, M. & Seguin, B., Nov 2016, In : Bulletin of Mathematical Biology. 78, 11, p. 2135-2164 30 p.

Research output: Contribution to journalArticle

Open Access
File
biomechanics
Biomechanics
Microfibrils
Cell Wall
Plant Cells
2015
1 Citation (Scopus)
189 Downloads (Pure)

Global Hopf bifurcation in the ZIP regulatory system

Claus, J., Ptashnyk, M., Bohmann, A. & Chavarría-Krauser, A., Oct 2015, In : Journal of Mathematical Biology. 71, 4, p. 795-816 22 p.

Research output: Contribution to journalArticle

Open Access
File
Hopf bifurcation
Global Bifurcation
Zinc
Hopf Bifurcation
orbits
14 Citations (Scopus)
100 Downloads (Pure)

Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations

Chaplain, M., Ptashnyk, M. & Sturrock, M., 15 Jun 2015, In : Mathematical Models and Methods in Applied Sciences. 25, 6, p. 1179-1215 37 p.

Research output: Contribution to journalArticle

Open Access
File
Hopf bifurcation
Gene Regulatory Network
Hopf Bifurcation
Network Model
Genes
1 Citation (Scopus)
151 Downloads (Pure)

Integral representation of a solution to the Stokes-Darcy problem

Medková, D., Ptashnyk, M. & Varnhorn, W., 30 Nov 2015, In : Mathematical Methods in the Applied Sciences. 38, 17, p. 3968-3979 12 p.

Research output: Contribution to journalArticle

Open Access
File
Potential Theory
Stokes
Integral Representation
Model
7 Citations (Scopus)
164 Downloads (Pure)
Open Access
File
Two-scale Convergence
Unfolding
Microstructure
microstructure
perforation
2013
12 Citations (Scopus)

Landau-Lifshitz-Slonczewski equations: global weak and classical solutions

Melcher, C. & Ptashnyk, M., 2013, In : SIAM Journal on Mathematical Analysis. 45, 1, p. 407-429 23 p.

Research output: Contribution to journalArticle

Global Classical Solution
Landau-Lifshitz Equation
Global Weak Solutions
Magnetization
Torque
8 Citations (Scopus)
plywood
Two-scale Convergence
Plywood
homogenizing
Homogenization
2012
15 Citations (Scopus)

A multiscale approach to curvature modulated sorting in biological membranes

Mercker, M., Ptashnyk, M., Kuhnle, J., Hartmann, D., Weiss, M. & Jager, W., May 2012, In : Journal of Theoretical Biology. 301, 5, p. 67-82 16 p.

Research output: Contribution to journalArticle

Biological membranes
Sorting
sorting
Membrane
Curvature
2 Citations (Scopus)

Root growth: homogenization in domains with time dependent partial perforations

Capdeboscq, Y. & Ptashnyk, M., 2012, In : ESAIM: Control, Optimisation and Calculus of Variations. 18, 3, p. 856-876 21 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)

Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations

Golovaty, Y., Marciniak-Czochra, A. & Ptashnyk, M., Jan 2012, In : Communications on Pure and Applied Analysis. 11, 1, p. 229-241 13 p.

Research output: Contribution to journalArticle

19 Citations (Scopus)

Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

Fatima, T., Muntean, A. & Ptashnyk, M., 2012, In : Applicable Analysis. 91, 6, p. 1129-1154 26 p.

Research output: Contribution to journalArticle

2011
29 Citations (Scopus)

Enhanced zinc uptake by rice through phytosiderophore secretion: a modelling study

Ptashnyk, M., Roose, T., Jones, D. L. & Kirk, G. J. D., Dec 2011, In : Plant, Cell & Environment. 34, 12, p. 2038-2046 9 p.

Research output: Contribution to journalArticle

phytosiderophores
Zinc
zinc
secretion
uptake mechanisms
2010
53 Citations (Scopus)

A dynamic model of nutrient uptake by root hairs

Leitner, D., Klepsch, S., Schnepf, A., Ptashnyk, M., Marchant, A., Kirk, G. J. D. & Roose, T., 1 Feb 2010, In : New Phytologist. 185, 3, p. 792-802 11 p.

Research output: Contribution to journalArticle

root hairs
dynamic models
nutrient uptake
Food
Soil
44 Citations (Scopus)

Boundedness of solutions of a haptotaxis model

Marciniak-Czochra, A. & Ptashnyk, M., Mar 2010, In : Mathematical Models and Methods in Applied Sciences. 20, 3, p. 449-476 28 p.

Research output: Contribution to journalArticle

Haptotaxis
Boundedness of Solutions
Logistics
Logistic Growth
Describing Function
8 Citations (Scopus)

Derivation of a macroscopic model for nutrient uptake by hairy-roots

Ptashnyk, M., Dec 2010, In : Nonlinear Analysis: Real World Applications. 11, 6, p. 4586-4596 11 p.

Research output: Contribution to journalArticle

Nutrients
Roots
Water
Slip Condition
Stokes System
19 Citations (Scopus)
19 Citations (Scopus)
dual porosity
sorption
porosity
solutes
solute
13 Citations (Scopus)

Homogenization of long-range auxin transport in plant tissues

Chavarría-Krauser, A. & Ptashnyk, M., Dec 2010, In : Nonlinear Analysis: Real World Applications. 11, 6, p. 4524-4532 9 p.

Research output: Contribution to journalArticle

Auxin
Homogenization
Tissue
Cell
Range of data
2008
50 Citations (Scopus)

Derivation of a macroscopic receptor-based model using homogenization techniques

Marciniak-Czochra, A. & Ptashnyk, M., 1 Jan 2008, In : SIAM Journal on Mathematical Analysis. 40, 1, p. 215-237 23 p.

Research output: Contribution to journalArticle

Homogenization
Receptor
Membranes
Cell
Biomolecules
23 Citations (Scopus)

Modelling in vitro growth of dense root networks

Bastian, P., Chavarría-Krauser, A., Engwer, C., Jäger, W., Marnach, S. & Ptashnyk, M., 2008, In : Journal of Theoretical Biology. 254, 1, p. 99-109 11 p.

Research output: Contribution to journalArticle

Nutrients
Roots
Food
Growth
Modeling
2007
18 Citations (Scopus)

Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities

Ptashnyk, M., 15 Jun 2007, In : Nonlinear Analysis. 66, 12, p. 2653-2675 23 p.

Research output: Contribution to journalArticle

Pseudoparabolic Equations
Memory Term
Quasilinear Equations
Variational Inequalities
Existence of Solutions
4 Citations (Scopus)

Pseudoparabolic equations with convection

Ptashnyk, M., 1 Dec 2007, In : IMA Journal of Applied Mathematics. 72, 6, p. 912-922 11 p.

Research output: Contribution to journalArticle

Pseudoparabolic Equations
Convection
Existence of Solutions
Uniqueness
Discretization
2006
5 Citations (Scopus)

Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations

Ptashnyk, M., Oct 2006, In : Applicable Analysis. 85, 10, p. 1285-1299 15 p.

Research output: Contribution to journalArticle

Quasilinear Hyperbolic Equation
Pseudoparabolic Equations
Cross-diffusion
Singular Limit
Regular Solution