4 papers · 1 filter
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…
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…