Article

Rata, Scott, Suarez Peredo Rodriguez, Maria F, Joseph, Stephy, Peter, Nisha, Echegaray Iturra, Fabio, Yang, Fengwei, Madzvamuse, Anotida, Ruppert, Jan G, Samejima, Kumiko, Platani, Melpomeni, Alvarez-Fernandez, Monica, Malumbres, Marcos, Earnshaw, William C, Novak, Bela and Hochegger, Helfrid (2018) Two interlinked bistable switches govern mitotic control in mammalian cells. Current Biology, 28 (23). 3824-3832.e6. ISSN 0960-9822

Campillo-Funollet, Eduard, Venkataraman, Chandrasekhar and Madzvamuse, Anotida (2018) Bayesian parameter identification for Turing systems on stationary and evolving domains. Bulletin of Mathematical Biology. ISSN 0092-8240

Cusseddu, D, Edelstein-Keshet, L, Mackenzie, J A, Portet, S and Madzvamuse, A (2018) A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology. ISSN 022-5193

Madzvamuse, Anotida and Barreira, Raquel (2018) Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. Discrete and Continuous Dynamical Systems - Series B, 23 (7). pp. 2775-2801. ISSN 1531-3492

Sarfaraz, Wakil and Madzvamuse, Anotida (2018) Domain-dependent stability analysis of a reaction-diffusion model on compact circular geometries. International Journal of Bifurcation and Chaos, 28 (8). p. 1830024. ISSN 0218-1274

Trott, L, Hafezparast, M and Madzvamuse, A (2018) A mathematical understanding of how cytoplasmic dynein walks on microtubules. Royal Society Open Science, 5 (8). p. 171568. ISSN 2054-5703

Frittelli, Massimo, Madzvamuse, Anotida, Sgura, Ivonne and Venkataraman, Chandrasekhar (2018) Numerical preservation of velocity induced invariant regions for reaction-diffusion systems on evolving surfaces. Journal of Scientific Computing. ISSN 0885-7474

Murphy, Laura, Venkataraman, Chandrasekhar and Madzvamuse, Anotida (2018) Parameter identification through mode isolation for reaction-diffusion systems on arbitrary geometries. International Journal of Biomathematics, 11 (4). p. 1850053. ISSN 1793-5245

Frittelli, Massimo, Madzvamuse, Anotida, Sgura, Ivonne and Venktaraman, Chandrasekhar (2017) Preserving invariance properties of reaction–diffusion systems on stationary surfaces. IMA Journal of Numerical Analysis, 2017. pp. 1-36. ISSN 0272-4979

Frittelli, Massimo, Madzvamuse, Anotida, Sgura, Ivonne and Venkataraman, Chandrasekhar (2017) Lumped finite elements for reaction–cross-diffusion systems on stationary surfaces. Computers & Mathematics with Applications, 74 (12). pp. 3008-3023. ISSN 0898-1221

Sarfaraz, Wakil and Madzvamuse, Anotida (2017) Classification of parameter spaces for a reaction-diffusion model on stationary domains. Chaos, Solitons & Fractals, 103. pp. 33-51. ISSN 0960-0779

Tuncer, Necibe and Madzvamuse, Anotida (2017) Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces. Communications in Computational Physics, 21 (3). pp. 718-747. ISSN 1815-2406

Yang, Feng Wei, Venkataraman, Chandrasekhar, Styles, Vanessa and Madzvamuse, Anotida (2017) A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws. Communications in Computational Physics, 21 (1). pp. 65-92. ISSN 1815-2406

Madzvamuse, A and Chung, A H (2016) Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes. Mathematical Modelling of Natural Phenomena, 11 (5). pp. 4-32. ISSN 0973-5348

Upadhyay, Ranjit Kumar, Roy, Parimita, Venkataraman, C and Madzvamuse, A (2016) Wave of chaos in a spatial eco-epidemiological system: generating realistic patterns of patchiness in rabbit-lynx dynamics. Mathematical Biosciences, 281. pp. 98-119. ISSN 0025-5564

Madzvamuse, Anotida and Lubkin, Sharon R (2016) A note on how to develop interdisciplinary collaborations between experimentalists and theoreticians. Interface Focus, 6 (5). p. 20160069. ISSN 2042-8898

Yang, Feng Wei, Venkataraman, Chandrasekhar, Styles, Vanessa, Kuttenberger, V, Horn, E, von Guttenberg, Z and Madzvamuse, Anotida (2016) A computational framework for particle and whole cell tracking applied to a real biological dataset. Journal of Biomechanics, 49 (8). pp. 1290-1304. ISSN 0021-9290

Madzvamuse, Anotida, Ndakwo, Hussaini S and Barreira, Raquel (2016) Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion. Discrete and Continuous Dynamical Systems - Series A, 36 (4). pp. 2133-2170. ISSN 1078-0947

Madzvamuse, Anotida and Chung, Andy H W (2016) The bulk-surface finite element method for reaction-diffusion systems on stationary volumes. Finite Elements in Analysis and Design, 108. pp. 9-21. ISSN 0168-874X

Sekimura, Toshio, Venkataraman, Chandrasekhar and Madzvamuse, Anotida (2015) A model for selection of eyespots on butterfly wings. PLoS ONE, 10 (11). pp. 1-23. ISSN 1932-6203

Blazakis, Konstantinos N, Madzvamuse, Anotida, Reyes-Aldasoro, Constantino-Carlos, Styles, Vanessa and Venkataraman, Chandrasekhar (2015) Whole cell tracking through the optimal control of geometric evolution laws. Journal of Computational Physics, 297. pp. 495-514. ISSN 0021-9991

Tuncer, N, Madzvamuse, A and Meir, A J (2015) Projected finite elements for reaction-diffusion systems on stationary closed surfaces. Applied Numerical Mathematics, 96. pp. 45-71. ISSN 0168-9274

Portet, Stéphanie, Madzvamuse, Anotida, Chung, Andy, Leube, Rudolf E and Windoffer, Reinhard (2015) Keratin dynamics: modeling the interplay between turnover and transport. PLoS ONE, 10 (3). e0121090. ISSN 1932-6203

Madzvamuse, Anotida, Ndakwo, Hussaini S and Barreira, Raquel (2015) Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations. Journal of Mathematical Biology, 70 (4). pp. 709-743. ISSN 0303-6812

Madzvamuse, Anotida, Chung, Andy H W and Venkataraman, Chandrasekhar (2015) Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems. Proceedings of the Royal Society A, 471 (2175). ISSN 1364-5021

Chong, Maureen Siew Fang, Shahrill, Masitah, Crossley, Laurie and Madzvamuse, Anotida (2015) The stability analyses of the mathematical models of hepatitis C virus infection. Modern Applied Science, 9 (3). pp. 250-271. ISSN 1913-1844

Madzvamuse, A and Barreira, R (2014) Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces. Physical Review E, 90 (4). 043307-1. ISSN 1539-3755

Madzvamuse, Anotida and Chung, Andy H W (2014) Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations. Applied Mathematics and Computation, 244. pp. 361-374. ISSN 0096-3003

Madzvamuse, Anotida and George, Uduak (2013) The moving grid finite element method applied to cell movement and deformation. Finite Elements in Analysis and Design, 74. pp. 76-92. ISSN 0168-874X

Lakkis, Omar, Madzvamuse, Anotida and Venkataraman, Chandrasekhar (2013) Implicit--explicit timestepping with finite element approximation of reaction--diffusion systems on evolving domains. SIAM Journal on Numerical Analysis, 51 (4). pp. 2309-2330. ISSN 0036-1429

Lakkis, Omar, Madzvamuse, Anotida and Venkataraman, Chandrasekhar (2013) Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains. SIAM Journal on Numerical Analysis, 51 (4). pp. 2309-2330. ISSN 0036-1429

Gilmore, Stephen J, Vaughan, Benjamin L, Madzvamuse, Anotida and Maini, Phlip K (2012) A mechanochemical model of striae distensae. Mathematical Biosciences, 240 (2). pp. 141-147. ISSN 1879-3134

Hetzer, Georg, Madzvamuse, Anotida and Shen, Wenxian (2012) Characterization of Turing diffusion-driven instability on evolving domains. Discrete and Continuous Dynamical Systems - Series A, 32 (11). pp. 3975-4000. ISSN 1078-0947

Crossley, Laurie, Garrett, Caroline A, Hafezparast, Majid and Madzvamuse, Anotida (2012) From the cell membrane to the nucleus: unearthing transport mechanisms for Dynein. Bulletin of Mathematical Biology, 74 (9). pp. 2032-2061. ISSN 1522-9602

Venkataraman, Chandrashekar, Lakkis, Omar and Madzvamuse, Anotida (2012) Global existence for semilinear reaction-diffusion systems on evolving domains. Journal of Mathematical Biology, 64 (1-2). pp. 41-67. ISSN 0303-6812

George, Uduak Z, Stéphanou, Angélique and Madzvamuse, Anotida (2012) Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell. Journal of Mathematical Biology, 66 (3). pp. 547-593. ISSN 0303-6812

Barreira, R, Elliott, C M and Madzvamuse, A (2011) The surface finite element method for pattern formation on evolving biological surfaces. Journal of Mathematical Biology, 63 (6). pp. 1095-1119. ISSN 0303-6812

Venkataraman, Chandrasekhar, Sekimura, Toshio, Gaffney, Eamonn A, Maini, Philip K and Madzvamuse, Anotida (2011) Modeling parr-mark pattern formation during the early development of Amago trout. Physical Review E (PRE), 84 (4). 041923 1-13. ISSN 1539-3755

Madzvamuse, Anotida, Gaffney, Eamonn A and Maini, Philip K (2010) Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains. Journal of Mathematical Biology, 61 (1). pp. 133-164. ISSN 0303-6812

Mackenzie, J A and Madzvamuse, A (2009) Analysis of stability and convergence of finite-difference methods for a reaction-diffusion problem on a one-dimensional growing domain. IMA Journal of Numerical Analysis, 31 (1). pp. 212-232. ISSN 0272-4979

Madzvamuse, Anotida and Maini, Philip K (2007) Velocity-induced numerical solutions of reaction-diffusion systems on continuously deforming domains. Journal of Computational Physics, 225 (1). pp. 100-119. ISSN 00219991

Sekimura, Toshio, Madzvamuse, Anotida and Maini, Philip K (2007) Pigmentation pattern formation in butterfly wings: Global patterns of fore- and hind-wing. Mathematical Modeling of Biological Systems, 1. pp. 147-154.

Madzvamuse, Anotida (2007) A modified backward Euler scheme for advection-reaction-diffusion systems. Mathematical modeling of biological systems. Mathematical Modeling of Biological Systems, 1. pp. 183-190.

Madzvamuse, Anotida (2006) Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. Journal of Computational Physics, 214 (1). 239 - 263. ISSN 0021-9991

Madzvamuse, Anotida, Maini, Philip K and Wathen, Andrew J (2005) A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains. Journal of Scientific Computing, 24 (2). pp. 247-262. ISSN 1573-7691

Madzvamuse, Anotida, Wathen, Andrew J and Maini, Philip K (2003) A moving grid finite element method applied to a model biological pattern generator. Journal of Computational Physics, 190 (2). pp. 478-500. ISSN 0021-9991

Nijhout, H Frederik, Maini, Philip K, Madzvamuse, Anotida, Wathen, Andrew J and Sekimura, Toshio (2003) Pigmentation pattern formation in butterflies - experiments and models. Comptes Rendus Biologies, 326 (8). pp. 711-727. ISSN 1631-0691

Madzvamuse, Anotida, Thomas, Roger D K, Maini, Philip K and Wathen, Andrew J (2002) A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves. Bulletin of Mathematical Biology, 64 (3). pp. 501-530. ISSN 0092-8240

Madzvamuse, Anotida, Maini, Philip K, Wathen, Andrew J and Sekimura, Toshio (2002) A predictive model for color pattern formation in the butterfly wing of Papilio dardanus. Hiroshima Mathematics Journal, 32. pp. 325-336.

Sekimura, T, Madzvamuse, A, Wathen, A J and Maini, P K (2000) A model for Colour Pattern formation in the Butterfly wing of Papilio dardanus. Proceedings B: Biological Sciences, 267 (1446). pp. 851-859. ISSN 1471-2954

Thomas, R D K, Madzvamuse, A, Maini, P K and Wathen, A J (2000) Growth patterns of noetiid ligaments: implications of developmental models for the origin of an evolutionary novelty among arcoid bivalves. Geological Society Special Publication (117). pp. 279-289. ISSN 03058719

Book Section

Blazakis, K, Reyes-Aldasoro, C C, Styles, V, Venkataraman, C and Madzvamuse, A (2015) An optimal control approach to cell tracking. In: Louis, Alfred K, Arridge, Simon and Rundell, Bill (eds.) Proceedings of the Inverse Problems from Theory to Applications Conference (IPTA2014). IOP Publishing Ltd, pp. 74-77. ISBN 9780750311069

Venkataraman, C, Lakkis, O and Madzvamuse, A (2013) Adaptive finite elements for semilinear reaction-diffusion systems on growing domains. In: Cangiani, Andrea and et al, (eds.) Numerical mathematics and advanced applications 2011: proceedings of ENUMATH 2011. Springer, Berlin, pp. 71-82. ISBN 9783642331336

Conference or Workshop Item

Madzvamuse, Anotida, Leube, Rudolf E, Othmer, Hans and Merkel, Rudolf (2015) Coupling geometric PDEs with physics, cell morphology, motility and pattern formation. In: Coupling geometric PDEs with physics, cell morphology, motility and pattern formation, 13th July 2015 to 18th December 2015.

Yang, F, Venkataraman, C, Styles, V and Madzvamuse, A (2015) A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions. In: 4th International Conference on Computational and Mathematical Biomedical Engineering - CMBE2015, 29 June-1 July 2015, Paris, France. (Accepted)

Yang, Feng Wei, Madzvamuse, Anotida and Venkataraman, Chandrasekhar (2015) Whole cell tracking and movement reconstruction through an optimal control problem. In: Seminar at iBiDi, Munich, Germany, 8 June, 2015, Munich, Germany.

Madzvamuse, A, Thomas, R D K, Sekimura, T, Wathen, A J and Maini, P K (2003) The moving grid finite element method applied to biological problems. In: Morphogenesis and Pattern Formation in Biological Systems.

Sekimura, T, Madzvamuse, A, Wathen, A J and Maini, P K (2002) Pigmentation pattern formation in the butterfly wing of Papilio dardanus. In: Mathematical Modelling and Computing in Biology and Medicine: Proceedings of the 5th European Conference for Mathematics and Theoretical Biology Conference.

Maini, P K, Crampin, E J, Madzvamuse, A, Wathen, A J and Thomas, R D K (2002) Implications of domain growth in morphogenesis. In: Mathematical Modelling and Computing in Biology and Medicine: Proceedings of the 5th European Conference for Mathematics and Theoretical Biology Conference.

Conference Proceedings

Madzvamuse, Anotida, Gerisch, Alf and Barreira, Raquel (2018) Cross-diffusion in reaction-diffusion models: analysis, numerics and applications. Published in: ECMI 2016: Progress in Industrial Mathematics at ECMI 2016. 26 385-392. Springer ISBN 978-3-319-63081-6

Edited Special Journal Issue

Leube, Rudolf, Madzvamuse, Anotida, Merkel, Rudolf and Othmer, Hans, eds. (2016) Coupling geometric partial differential equations with physics for cell morphology, motility and pattern formation. Interface Focus, 6 (5). ISSN 2042-8898