6 papers
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…