Selected Publications

Cancer

• Mathematical models of avascular tumour growth
  Roose, T., Chapman, S.J. & Maini, P.K., SIAM Review, to appear (2006). (abstract) (pdf)

Superconductivity

• A hierarchy of models for type-II superconductors
  Chapman, S.J., SIAM Review, 42 , 4, 555-598 (2000). (abstract) (ps.gz)
• Convergence of Meissner minimisers of the Ginzburg-Landau energy of superconductivity as kappa -> infinity
  Bonnet, A., Chapman, S.J. & Monneau, R., SIAM J. Math. Anal., 31, 6, 1374-1395 (2000). (abstract) (ps.gz)
• Macroscopic models of superconductivity
  Chapman, S.J., Proceedings of ICIAM99, OUP (2000). (abstract) (ps.gz)
• Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity
  Aftalion, A, & Chapman, S.J., SIAM J. Appl. Math., 60, 1157-1176 (2000) (abstract) (ps.gz)
• Asymptotic analysis of the bifurcation diagram for symmetric one-dimensional solutions of the Ginzburg-Landau equations
  Aftalion, A, & Chapman, S.J., Europ. J. Appl. Math. 10, 477-495 (1999) (abstract) (ps.gz)
• The motion of superconducting vortices in thin films of varying thickness
  Chapman, S.J. & Heron, D.R., SIAM J. Appl. Math. 58, 1808-1825 (1998) (abstract) (ps.gz)
• Motion and homogenization of vortices in anisotropic type-II superconductors
  Chapman, S.J. & Richardson, G., SIAM J. Appl. Math. 58, 587-606 (1998) (abstract) (ps.gz)
• Vortex pinning by inhomogeneities in type-II superconductors
  Chapman, S.J. & Richardson, G., Physica D 108, 397-407 (1997) (abstract) (ps.gz)
• Bifurcation to vortex solutions in superconducting films
  Boeck, T. & Chapman, S.J., Europ. J. Appl. Math. 8, 125-148 (1997) (abstract) (ps.gz)
• Nucleation of vortices in type-II superconductors in increasing magnetic fields
  Chapman, S.J., Appl. Math. Lett. 10, 29-31 (1997) (abstract) (ps.gz)
• A model for variable thickness superconducting thin films
  Chapman, S.J., Du, Q. & Gunzburger, M.D., Z.A.M.P. 47, 410-431 (1996) (abstract) (ps.gz)
• A mean-field model of superconducting vortices
  Chapman, S.J., Rubinstein, J. & Schatzman, M., Europ. J. Appl. Math. 7, 97-111 (1996)
• Asymptotic analysis of the Ginzburg-Landau model of superconductivity: reduction to a free-boundary model
  Chapman, S.J., Quart. Appl. Math. 53, 601-627 (1995) (abstract) (ps.gz)
• Motion of vortices in type-II superconductors
  Chapman, S.J. & Richardson, G., SIAM J. Appl. Math. 55, 1275-1296 (1995) (abstract) (ps.gz)
• A mean-field model of superconducting vortices in three dimensions
  Chapman, S.J., SIAM J. Appl. Math. 55, 1259-1274 (1995) (abstract) (ps.gz)
• Superheating field of type-II superconductors
  Chapman, S.J., SIAM J. Appl. Math. 55, 1233-1258 (1995) (abstract) (ps.gz)
• Stability of travelling waves in models of superconductivity
  Chapman, S.J., IMA J. Appl. Math. 54, 159-169 (1995) (abstract) (ps.gz)
• A Ginzburg-Landau Type Model of Superconducting/Normal Junctions including Josephson Junctions
  Chapman, S.J., Du, Q. & Gunzburger, M.D., Europ. J. Appl. Math. 6, 97-114 (1995) (ps.gz)
• On the Lawrence-Doniach and Anisotropic Ginzburg-Landau Models for Layered Superconductors
  Chapman, S.J., Du, Q. & Gunzburger, M.D., SIAM J. Appl. Math. 55, 156-174 (1995) (ps.gz)
• Simplified Ginzburg-Landau models for superconductivity valid for high kappa and high fields
  Chapman, S.J., Du, Q., Gunzburger, M.D. & Peterson, J.S., Adv. Math. Sci. Appl. 5, 193-218 (1995) (ps.gz)
• Nucleation of superconductivity in decreasing fields II
  Chapman, S.J., Europ. J. Appl. Math. 5, 469-494 (1994) (abstract) (ps.gz)
• Nucleation of superconductivity in decreasing fields I
  Chapman, S.J., Europ. J. Appl. Math. 5, 449-468 (1994) (abstract) (ps.gz)
• A semi-elliptic system arising in the theory of type-II superconductivity
  Berestycki, H., Bonnet, A. & Chapman, S.J., Comm. Appl. Nonlin. Anal. 1, 1-21 (1994) (abstract) (ps.gz)
• Macroscopic Models of Superconductivity
  Chapman, S.J., Howison, S.D. &; Ockendon, J.R., SIAM Review 34, 529-560 (1992)
• Normal/superconducting transitions in Landau-Ginzburg theory

Chapman, S.J., Howison, S.D., McLeod, J.B., &; Ockendon, J.R., Proc. R. Soc. Edin., 119A, 117-124, (1991)

• S.J. Chapman (1991) - Macroscopic Models of Superconductivity, Oxford University D. Phil. thesis (pdf)

Exponential Asymptotics

• Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations
  King, J.R. & Chapman, S.J., Europ. J. Appl. Math., 12 , 433-463 (2001) (abstract) (ps.gz)
• On the role of Stokes lines in the selection of Saffman-Taylor fingers with small surface tension
  Chapman, S.J., Europ. J. Appl. Math. 10, 513-534 (1999) (abstract) (ps.gz)
• Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations
  Chapman, S.J., King, J.R. & Adams, K.L., Proc. Roy. Soc. Lond. A 454, 2733-2755 (1998) (abstract) (ps.gz)
• On the nonuniversality of the error function in the smoothing of Stokes discontinuities
  Chapman, S.J., Proc. R. Soc. Lond. 452, 2225-2230 (1996) (abstract) (ps.gz)
• Stokes Phenomenon and Matched Asymptotic Expansions
  Olde Daalhuis, A.B., Chapman, S.J., King, J.R., Ockendon, J.R. & Tew, R.H., SIAM J. Appl. Math. 55, 1469-1483 (1995) (abstract) (ps.gz)

Transition to turbulence

• Subcritical transition in channel flows
  Chapman, S.J., J. Fluid Mech. , to appear (2001) (abstract) (ps.gz)

Shear-thinning fluids

• Extrusion of Power-Law Shear-Thinning Fluids with Small Exponent
  Chapman, S.J., Fitt, A.D. & Please, C.P., Int. J. Nonlin. Mech. 32, 187-199 (1997)
• Asymptotics of slow flow of very small exponent power-law shear-thinning fluids in a wedge
  Brewster, M., Chapman, S.J., Fitt, A.D. & Please, C.P., Europ. J. Appl. Math. 6, 559-572 (1995)

Ray Theory and Diffraction/Complex rays

• Scalar wave diffraction by tangent rays
  Tew, R.H., Chapman, S.J., King, J.R., Ockendon, J.R., Smith, B.J. & Zafarullah, I., Wave Motion, 32, 363--380 (2000) (abstract) (ps.gz)
• Edge diffraction of complex rays
  Chapman, S.J., Lawry, J.M.H., Ockendon, J.R. & Saward, V.H., Wave Motion, to appear (2000) (abstract) (ps.gz)
• Ray theory for high-Peclet-number convection-diffusion
  Chapman, S.J., Lawry, J.M.H. & Ockendon, J.R., SIAM J. Appl. Math. 60, 121-135 (1999) (abstract) (ps.gz)
• Edge diffraction of creeping rays
  Chapman, S.J., Ockendon, J.R. & Saward, V.H., J. Acoust. Soc. Am. 107, 1841-1845 (2000) (abstract) (ps.gz)
• On the theory of complex rays
  Chapman, S.J., Lawry, J.M.H., Ockendon, J.R. & Tew, R.H., SIAM Review 41,417-509 (1999) (abstract) (ps.gz)
• On the approximation of the eigenvalues of an annulus using complex rays
  Chapman, S.J., Europ. J. Appl. Math. 10, 225-236 (1999) (abstract) (ps.gz)

Miscellaneous

• Vacuum moulding of a superplastic in two dimensions
  Chapman, S.J., Fitt, A.D. & Pulos, G., IMA J. Appl. Math. 63, 217-246 (1999) (abstract) (ps.gz)
• Vortices and Boundaries
  Chapman, S.J., Hunton, B.J. & Ockendon, J.R., Quart. Appl. Math. 56, 507-519 (1998)
• Dynamics of line singularities
  Carpio, A., Chapman, S.J., Howison, S.D. & Ockendon, J.R., Phil. Trans. R. Soc. Lond. A 355, 2013-2024 (1997) (abstract) (ps.gz)
• Asymptotics of violent surface motion
  Chapman, S.J., Gillow, K.A., Howison, S.D. & Ockendon, J.R., Phil. Trans. R. Soc. Lond. A 355, 679-685 (1997)
• Have we got problems for you
  Chapman, S.J., New Scientist, 2035, 22 June, 38-41 (1996)
• Drums that sound the same
  Chapman, S.J., Am. Math. Month. 102, 124-138 (1995) (abstract) (ps.gz)
• Dissection of rectangles, Möbius bands and tori into squares of different size
  Chapman, S.J., Duke Math. J. 72, 467-485 (1993)

This page last modified by S. J. Chapman
Tuesday, 07-Mar-2006 18:22:00 GMT
Email corrections and comments to chapman@maths.ox.ac.uk