23 citations · 76 across the 26 of their papers we have counts for
31 papers
Homogenization of the Richards equation in porous media: Multiscale modelling of water transport in vegetated soil
Andrew Mair, Mariya Ptashnyk
In this paper we consider the multiscale modelling of water transport in vegetated soil. In the microscopic model we distinguish between subdomains of soil and plant tissue, and us…
The Burgers-FKPP advection-reaction-diffusion equation with cut-off
Nikola Popovic, Mariya Ptashnyk, Zak Sattar
We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction…
Multiscale modelling and analysis of growth of plant tissues
Arezki Boudaoud, Annamaria Kiss, Mariya Ptashnyk
How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular struc…
Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
Katherine Baker, Lehel Banjai, Mariya Ptashnyk
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in…
Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
Maximilian Engel, Felix Hummel, Christian Kuehn +3
We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume…
Derivation of a Fractional Cross-Diffusion System as the Limit of a Stochastic Many-Particle System Driven by Lévy Noise
Esther S. Daus, Mariya Ptashnyk, Claudia Raithel
In this article a fractional cross-diffusion system is derived as the rigorous many-particle limit of a multi-species system of moderately interacting particles that is driven by L…
Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: Nonstandard scaling
John R. King, Jakub Köry, Mariya Ptashnyk
In this paper we undertake a multiscale analysis of nutrient uptake by plant root hairs, considering different scale relations between the radius of hairs and the distance between…
Chemical Kinetics, Markov Chains, and the Imaginary Itô Interpretation
Álvaro Correales, Carlos Escudero, Mariya Ptashnyk
The abstract chemical reaction understood as a Markov chain in continuous time, has been studied in the physical literature for several years. It has been…
Homogenization of biomechanical models of plant tissues with randomly distributed cells
Andrey Piatnitski, Mariya Ptashnyk
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are m…
From individual-based mechanical models of multicellular systems to free-boundary problems
Tommaso Lorenzi, Philip J. Murray, Mariya Ptashnyk
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteris…
Homogenization of degenerate cross-diffusion systems
Ansgar Juengel, Mariya Ptashnyk
Two-scale homogenization limits of parabolic cross-diffusion systems in a heterogeneous medium with no-flux boundary conditions are proved. The heterogeneity of the medium is refle…
Mathematical Modelling of Auxin Transport in Plant Tissues: Flux meets Signalling and Growth
Henry R. Allen, Mariya Ptashnyk
Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such a…
Strong solutions for the Alber equation and stability of unidirectional wave spectra
Agissilaos G. Athanassoulis, Gerassimos A. Athanassoulis, Mariya Ptashnyk +1
The Alber equation is a moment equation for the nonlinear Schrödinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea st…
Multiscale analysis and simulation of a signalling process with surface diffusion
Mariya Ptashnyk, Chandrasekhar Venkataraman
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and i…
Homogenization of some degenerate pseudoparabolic variational inequalities
Mariya Ptashnyk
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic…
Mathematical Modelling and Analysis of the Brassinosteroid and Gibberellin Signalling Pathways and their Interactions
Henry R. Allen, Mariya Ptashnyk
The plant hormones brassinosteroid (BR) and gibberellin (GA) have important roles in a wide range of processes involved in plant growth and development. In this paper we derive and…
Homogenization of a viscoelastic model for plant cell wall biomechanics
Mariya Ptashnyk, Brian Seguin
The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions bet…
Multiscale analysis of signalling processes in tissues with non-periodic distribution of cells
Mariya Ptashnyk
In this paper a microscopic model for a signalling process in the cardiac muscle tissue of the left ventricular wall, comprising non-periodic fibrous microstructure is considered.…
The impact of microfibril orientations on the biomechanics of plant cell walls and tissues: modelling and simulations
Mariya Ptashnyk, Brian Seguin
It is known that the orientation of cellulose microfibrils within plant cell walls has an important impact on the morphogenesis of plant cells and tissues. Viewing the shape of a p…
Homogenization of biomechanical models for plant tissues
Andrey Piatnitski, Mariya Ptashnyk
In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-c…
Periodic homogenization and material symmetry in linear elasticity
Mariya Ptashnyk, Brian Seguin
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic materia…
Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics
Mariya Ptashnyk, Brian Seguin
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a c…
Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures
Mariya Ptashnyk
In this paper we generalize the periodic unfolding method and the notion of two-scale convergence on surfaces of periodic microstructures to locally periodic situations. The method…
Homogenization of oxygen transport in biological tissues
Anastasios Matzavinos, Mariya Ptashnyk
In this paper, we extend previous work on the mathematical modeling of oxygen transport in biological tissues (Matzavinos et al., 2009). Specifically, we include in the modeling pr…