Academic research

For the decade prior to becoming an entrepreneur (2002—2012), I enjoyed the lifestyle of a curious academic. My research in this period was motivated by a range of applications in biophysics, and focused on continuum field theory and numerical algorithms. This page links to descriptions of my work, and serves as a sampling of my scientific writing and talks.

Primary investigations

Cardiac mechanics

–

Modelling the active mechanical response of the heart

Modelling the active mechanical response of ventricular myocardium.

Chondrocyte physiology

–

An electrophysiological model for the chondrocyte

Better understanding the cell type responsible for the synthesis of cartilage.

Multiphase flow in porous media

–

Adaptive multiphase flow through porous media

A robust, error-controlled implementation that’s human readable.

Automated mechanics

–

Automated algorithms for finite strain elasticity

Automated finite element methods reduce tedium and errors.

Robust methods for flows

–

Robust methods for modelling biological flow

Accurate and efficient modelling of aneurysm growth.

Phase transfer in batteries

Phase transfer in battery materials

Modelling mechanical phenomena associated with ion transport.

Energetics of tumours

–

Modelling the energetics of growing tumours

Modelling the bio-chemo-mechanics of tumour growth.

Tissue growth and development

–

Modelling tissue growth and development

A continuum theory of multiphase mixtures for modelling biological growth.

Curiosities along the way

Navier-Stokes formulation

Some thoughts on the Navier-Stokes equations

Theoretically equivalent formulations aren’t always equal in practice.

Numerical relativity

Finite element methods in general relativity

Differential geometry and numerical methods for 4D spacetime.

Shape reconstruction

Variational level sets in shape reconstruction from unorganised data sets

Level sets in shape reconstruction from unorganised data sets.

Journal articles

  1. “The roles of K+ currents in human articular chondrocyte electrophysiology: A computational perspective”
    H. Narayanan, M. M. Maleckar, R. B. Clark, J. R. Wilson, W. R. Giles
    Under preparation
  2. “An adaptive finite element method for fluid-structure interaction” [preprint]
    K. Selim, A. Logg, H. Narayanan, M. G. Larson
    Submitted
  3. “In silico estimates of the free energy changes in growing, avascular, tumor spheroids” [postprint] [preprint]
    H. Narayanan, S. N. Verner, K. L. Mills, R. Kemkemer, K. Garikipati
    Journal of Physics: Condensed Matter
    Vol. 22(19), 2010
  4. “The micromechanics of fluid-solid interactions during growth in porous soft biological tissue” [postprint] [preprint]
    H. Narayanan, E. M. Arruda, K. Grosh, K. Garikipati
    Biomechanics and Modeling in Mechanobiology
    Vol. 8(3), pp. 167–181, 2009
  5. “The continuum elastic and atomistic viewpoints on the formation volume and strain energy of a point defect” [postprint] [preprint]
    K. Garikipati, M. Falk, M. Bouville, B. Puchala, H. Narayanan
    Journal of the Mechanics and Physics of Solids
    Vol. 54(9), pp. 1929–1951, 2006
  6. “Biological remodelling: Stationary energy, configurational change, internal variables and dissipation” [postprint] [preprint]
    K. Garikipati, J. Olberding, H. Narayanan, E. M. Arruda, K. Grosh, S. Calve
    Journal of the Mechanics and Physics of Solids
    Vol. 54(7), pp. 1493–1515, 2006
  7. “A continuum treatment of growth in biological tissue: The coupling of mass transport and mechanics” [postprint] [preprint]
    K. Garikipati, E. M. Arruda, K. Grosh, H. Narayanan, S. Calve
    Journal of the Mechanics and Physics of Solids
    Vol. 52(7), pp. 1595–1625, 2004

Chapters in books

  1. “A computational framework for nonlinear elasticity” [postprint] [preprint]
    H. Narayanan
    Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K-A. Mardal, G. N. Wells (Eds.)
    Chap. 27, pp. 527–544, 2012
  2. “A comparison of some finite element schemes for the incompressible Navier-Stokes equations” [postprint] [preprint]
    K. Valen-Sendstad, A. Logg, K-A. Mardal, H. Narayanan, M. Mortensen
    Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K-A. Mardal, G. N. Wells (Eds.)
    Chap. 21, pp. 395–417, 2012
  3. “Characterization and modeling of growth and remodeling in tendon and soft tissue constructs” [postprint] [preprint]
    E. M. Arruda, S. Calve, K. Garikipati, K. Grosh, H. Narayanan
    Mechanics of Biological Tissue, G. A. Holzapfel, R. W. Ogden (Eds.)
    Chap. 5, pp. 63–75, 2006
  4. “Material forces in the context of biotissue remodelling” [postprint] [preprint]
    K. Garikipati, H. Narayanan, E. M. Arruda, K. Grosh, S. Calve
    Mechanics of Material Forces, P. Steinmann, G. A. Maugin (Eds.)
    Chap. 8, pp. 77–84, 2005

Conference proceedings

  1. “Experimental and computational investigation of viscoelasticity of native and engineered ligament and tendon” [postprint] [preprint]
    J. Ma, H. Narayanan, K. Garikipati, K. Grosh, E. M. Arruda
    Cellular, Molecular and Tissue Mechanics
    IUTAM Symposium Bookseries
    Vol. 16, pp. 3–17, 2010
  2. “Collaborative computational frameworks and the growth problem” [postprint] [preprint]
    H. Narayanan, K. Garikipati, A. Logg
    The Mathematics of Growth and Remodelling of Soft Biological Tissues
    Mathematisches Forschungsinstitut Oberwolfach Reports
    Vol. 5(3), pp. 2247–2249, 2008
  3. “Mathematical modelling of solid tumor growth” [postprint] [preprint]
    K. Garikipati, H. Narayanan, K. Grosh, E. M. Arruda
    The Mathematics of Growth and Remodelling of Soft Biological Tissues
    Mathematisches Forschungsinstitut Oberwolfach Reports
    Vol. 5(3), pp. 2235–2238, 2008

Other academic writing

  1. “A continuum theory of multiphase mixtures for modelling biological growth” [postprint] [preprint]
    H. Narayanan
    Doctoral Dissertation, University of Michigan
    2007
  2. “Variational level sets in shape reconstruction from unorganised data sets” [preprint]
    H. Narayanan
    Project Report, University of Michigan
    2005

Selected talks at conferences

  1. “A continuum model for the active mechanical response of the myocardium” [slides]
    Tenth World Congress on Computational Mechanics
    São Paulo, Brazil, July 2012
  2. “The role of K+ channels in human articular chondrocyte electrophysiology” [slides]
    Cardiac Modelling Seminar at Simula Research Laboratory
    Oslo, Norway, July 2011
  3. “An automated computational framework for hyperelasticity” [slides]
    Fourth European Conference on Computational Mechanics
    Paris, France, May 2010
  4. “A goal-oriented error-controlled solver for biomedical flows” [slides]
    Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics
    Cambridge, MA, June 2009
  5. “Collaborative computational frameworks and the growth problem” [slides]
    Workshop on the Mathematics of Growth and Remodelling of Soft Biological Tissues
    Mathematisches Forschungsinstitut Oberwolfach, Germany, September 2008
  6. “Reshaping tumour growth” [slides]
    University of Michigan Engineering Graduate Student Symposium
    Ann Arbor, MI, November 2007
  7. “A continuum theory of multiphase mixtures for modelling biological growth” [slides]
    Doctoral Dissertation Defence
    Ann Arbor, MI, October 2007
  8. “The numerical implications of multi-phasic mechanics assumptions underlying growth models” [slides]
    Ninth U.S. National Congress on Computational Mechanics
    San Fransisco, CA, July 2007
  9. “Finite element methods in general relativity” [slides]
    University of Michigan Engineering Graduate Student Symposium
    Ann Arbor, MI, November 2006
  10. “Viscoelastic and growth mechanics in engineered and native tendons” [slides]
    43rd Annual Technical Meeting of the Society of Engineering Science
    University Park, PA, August 2006
  11. “The numerical implications of fluid incompressibility in multiphasic modelling of soft tissue growth” [slides]
    Seventh World Congress on Computational Mechanics
    Los Angeles, CA, July 2006
  12. “Tendon growth and healing: The roles of reaction, transport and mechanics” [slides]
    15th U.S. National Congress on Theoretical and Applied Mechanics
    Boulder, CO, June 2006
  13. “Computational modelling of mechanics and transport in growing tissue” [slides]
    Eighth U.S. National Congress on Computational Mechanics
    Austin, TX, July 2005
  14. “Simulations of coupled mechanics and transport in growing soft tissue” [slides]
    Third M.I.T. Conference on Computational Fluid and Solid Mechanics
    Cambridge, MA, June 2005
  15. “Multi-scale simulations of the mechanics of transport and growth in soft tissue” [slides]
    41st Annual Technical Meeting of the Society of Engineering Science
    Lincoln, NE, October 2004
  16. “Material forces in the context of biological tissue remodelling” [slides]
    Seventh U.S. National Congress on Computational Mechanics
    Albuquerque, NM, July 2003
  17. “A continuum treatment of growth in tissue” [slides]
    Second M.I.T. Conference on Computational Fluid and Solid Mechanics
    Cambridge, MA, June 2003