Chandrasekhar Venkataraman

Lecturer in Mathematical Biology, University of St Andrews


Research

I am an applied mathematician with interests in mathematical biology and numerical analysis. I am interested in nonlinear PDE based models of real world phenomena, especially those in biology, as well as the analysis and approximation of nonlinear PDE.

Along with theoretical studies, I have a number of ongoing collaborations with applied and experimental scientists as well as industrial partners.


Some areas I have worked in are:

  • PDEs on time dependent domains
  • Finite element methods
  • Mathematical cell biology
  • Biological pattern formation
  • Free boundary problems and PDEs on manifolds


My work has received funding from the EPSRC, the Leverhulme Trust and the Japanese Society for the Promotion of Science. I have also received funding to explore knowledge transfer between academia and industry.




Journal Publications


  1. Charles M Elliott, Thomas Ranner and Chandrasekhar Venkataraman. Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 2017.


  2. Feng Wei Yang, Chandrasekhar Venkataraman, Vanessa Styles, and Anotida Madzvamuse. A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws. Communications in Computational Physics, 2017.

  3. Ranjit Kumar Upadhyay, Parimita Roy, Chandrasekhar Venkataraman, and Anotida Madzvamuse. Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit-lynx dynamics. Mathematical Biosciences, 2016.

  4. Feng Wei Yang, Chandrasekhar Venkataraman, Vanessa Styles, Verena Kuttenberger, Elias Horn, Zeno von Guttenberg, and Anotida Madzvamuse. A computational framework for particle and whole cell tracking applied to a real biological dataset. Journal of Biomechanics, 2016.

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

  6. Charles M Elliott and Chandrasekhar Venkataraman. Error analysis for an ALE evolving surface finite element method. Numerical Methods for Partial Differential Equations, 31(2):459-499, 2015.

  7. Wayne Croft, Charles M Elliott, Graham Ladds, Björn Stinner, Chandrasekhar Venkataraman, and Cathryn Weston. Parameter identification problems in the modelling of cell motility. Journal of Mathematical Biology, 71(2):399-436, 2015.

  8. Toshio Sekimura, Chandrasekhar Venkataraman, and Anotida Madzvamuse. A model for selection of eyespots on butterfly wings. PLoS ONE, 10(11):e0141434, 11 2015. [ DOI | http ]

  9. Anotida Madzvamuse, Andy H. W. Chung, and Chandrasekhar Venkataraman. Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2175), 2015. [ DOI ]

  10. Christian Lubich, Dhia Mansour, and Chandrasekhar Venkataraman. Backward difference time discretization of parabolic differential equations on evolving surfaces. IMA Journal of Numerical Analysis, 33(4):1365-1385, 2013. [ DOI | http ]

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

  12. Chandrasekhar Venkataraman, Omar Lakkis, and Anotida Madzvamuse. Global existence for semilinear reaction-diffusion systems on evolving domains. Journal of Mathematical Biology, 64:41-67, 2012. [ http ]

  13. Charles M. Elliott, Björn Stinner, and Chandrasekhar Venkataraman. Modelling cell motility and chemotaxis with evolving surface finite elements. Journal of The Royal Society Interface, 9(76):3027-3044, 2012. [ DOI | http ]

  14. Chandrasekhar Venkataraman, Toshio Sekimura, Eamonn A Gaffney, Philip K Maini, and Anotida Madzvamuse. Modeling parr-mark pattern formation during the early development of amago trout. Physical Review E, 84(4):041923, 2011.


In Proceedings


  1. Konstantinos N Blazakis, Constantino-Carlos Reyes-Aldasoro, Vanessa Styles, Chandrasekhar Venkataraman, and Anotida Madzvamuse. An optimal control approach to cell tracking. In Proceedings of IPTA 2014, pages 74-78, 2015.

  2. Charles M. Elliott, Björn Stinner, Vanessa Styles, and Chandrasekhar Venkataraman. Modelling and simulation of single and multi cell migration in heterogeneous media. In Proceedings of CMBE 2015, 2015.

  3. Feng Wei Yang, Chandrasekhar Venkataraman, Vanessa Styles, and Anotida Madzvamuse. A parallel and adaptive multigrid solver for the solution of the optimal control of geometric evolution laws in two and three dimensions. In Proceedings of CMBE 2015, 2015.

  4. Chandrasekhar Venkataraman, Charles M. Elliott, and Thomas Ranner. Coupled bulk-surface free boundary problems from a model for receptor-ligand dynamics. In Oberwolfach Report No. 55/2015 for the workshop Geometric Partial Differential Equations: Surface and Bulk Processes, 2015.

  5. Chandrasekhar Venkataraman, Omar Lakkis, and Anotida Madzvamuse. Adaptive finite elements for semilinear reaction-diffusion systems on growing domains. In Numerical Mathematics and Advanced Applications 2011: Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011, page 71. Springer, 2013.

  6. Chandrasekhar Venkataraman, Christian Lubich, and Dhia Mansour. Backward difference time discretisation of parabolic partial differential equations on evolving surfaces. In Oberwolfach Report No.15/2013 for the workshop Interfaces and Free Boundaries: Analysis, Control and Simulation, 2013.

Thesis


  • Chandrasekhar Venkataraman. Reaction-diffusion systems on evolving domains with applications to the theory of biological pattern formation. PhD thesis, University of Sussex, June 2011.http ]




Teaching at St Andrews (2015-Present). Current students see mms for course content.



  1. 2016/17: Mathematical Biology I (MT4552) and Pure and Applied Mathematics (MT1003)

  2. 2015/16: Mathematical Biology I (MT4552)

Contact

Mathematical Institute
School of Mathematics and Statistics
North Haugh
University of St Andrews
St Andrews
Fife
KY16 9SS

Email: cv28`at'st-andrews.ac.uk

Phone: 01334 463740