70 citations · 191 across the 17 of their papers we have counts for
18 papers
Finite element approximation of the enthalpy formulation for Stefan problems on evolving surfaces
Philip J. Herbert, Thomas Sales, Chandrasekhar Venkataraman
We propose, and analyse, a spatially discrete evolving surface finite element method for the approximation of the enthalpy formulation of the two-phase Stefan problem posed on an e…
Free boundary limits of coupled bulk-surface models for receptor-ligand interactions on evolving domains
Amal Alphonse, Diogo Caetano, Charles M. Elliott +1
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting…
Linking discrete and continuous models of cell birth and migration
W. Duncan Martinson, Alexandria Volkening, Markus Schmidtchen +2
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, b…
An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids
Emma Leschiera, Gheed Al-Hity, Melanie S. Flint +4
In recent in vitro experiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol result…
Parallel two-scale finite element implementation of a system with varying microstructures
Omar Richardson, Omar Lakkis, Adrian Muntean +1
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain com…
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…
Lumped finite element method for reaction-diffusion systems on compact surfaces
Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura +1
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathb…
A Bayesian approach to parameter identification with an application to Turing systems
Eduard Campillo-Funollet, Chandrasekhar Venkataraman, Anotida Madzvamuse
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a ri…
A computational approach for mode isolation for reaction-diffusion systems on arbitrary geometries
Laura Murphy, Chandrasekhar Venkataraman, Anotida Madzvamuse
In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model…
A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws
F. Yang, C. Venkataraman, V. Styles +1
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal con…
Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
Charles M. Elliott, Thomas Ranner, Chandrasekhar Venkataraman
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a ma…
Whole cell tracking through the optimal control of geometric evolution laws
Konstantinos N. Blazakis, Anotida Madzvamuse, Constantino-Carlos Reyes-Aldasoro +2
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular…
Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems
Anotida Madzvamuse, Andy H. W. Chung, Chandrasekhar Venkataraman
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to…
Error analysis for an ALE evolving surface finite element method
Charles M. Elliott, Chandrasekhar Venkataraman
We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a m…
Parameter identification problems in the modelling of cell motility
Wayne Croft, Charles M Elliott, Graham Ladds +3
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulation…
Adaptive finite elements for semilinear reaction-diffusion systems on growing domains
Chandrasekhar Venkataraman, Omar Lakkis, Anotida Madzvamuse
We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimat…
Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains
Omar Lakkis, Anotida Madzvamuse, Chandrasekhar Venkataraman
We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising…
Global existence for semilinear reaction-diffusion systems on evolving domains
Chandrasekhar Venkataraman, Omar Lakkis, Anotida Madzvamuse
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed dom…