• Ph.D. Applied Mathematics, The Dynamical Creation of Microstructure in Material Phase Transitions, Advisor: Philip J. Holmes, Cornell University, 1991
• M.S. Applied Mathematics, California Institute of Technology, 1989
• M.Sc. Thesis, Galerkin Methods for Parabolic Differential Equations, University of Pretoria, South Africa, 1985
• B.Sc. Hons. Applied Mathematics, University of Pretoria, 1983
• B.Sc. Applied Mathematics, Mathematics & Physics University of Pretoria, 1982

• Employment:
  • 1995–Present Staff Member, Mathematical Modeling and Analysis Group T-7, LANL.
  • June 2002–July 2003 Acting Deputy Director, Center for Nonlinear Studies, LANL.
  • 2001–Present Executive Committee, Center for Nonlinear Studies, LANL.
  • 1999–2001 Project Leader: Computational Modeling of Complex Perovskites (with Motorola)
  • 2000–2002 Project Leader: Multiscale Dimensional Reduction of Massive Bioinformatics Datasets (with Efeckta Technologies)
  • 1992–1995 Research Associate, Courant Institute of Mathematical Sciences, New York University, New York.
  • 1991–1992 Post Doctoral Associate, Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh.

Research Interests:

• Multiscale analysis of dynamics on technological, social and biological networks; epidemiological modeling; wavelet-based multiresolution analysis; nonlinear principal component analysis of large datasets; mesoscopic structures associated with structural phase transformations; dynamics and hysteresis in martensites, perovskites, ferroelectrics and foams; applications of wavelets and homogenization to multiscale problems in solid-state and materials science; nonlinear partial differential equations; scientific computing with Python.

Selected Recent Publications:

1. J.M. Ball, P.J. Holmes, R.D. James, R.L. Pego & P.J. Swart, On the Dynamics of Fine Structure, J. Nonlinear Science 1,1–71(1991).
2. P.J. Swart & P.J. Holmes , Energy minimization and the formation of microstructure in dynamic anti-plane shear , Arch. Rational Mech. Anal  121, 37–85(1992) .
3. K. Bhattacharya, R.D. James & P.J. Swart, Relaxation in shape-memory alloys , Acta Materialia  45:11, 4547–4568 (1997).
4. M. Avellaneda & P.J. Swart, Calculating the performance of piezoelectric composites for hydrophone applications: An effective medium approach , The Journal of the Acoustical Society of America 103: 3,1449–1468(1998) .
5. W.C. Kerr, M.G. Killough, A. Saxena, P.J. Swart & A.R. Bishop, Role of Elastic Compatibility in Martensitic Texture Evolution , Phase Transitions  69,247–270(1999) .
6. Y. Jiang, P.J. Swart, A. Saxena, M. Asipauskas & J.A. Glazier, Hysteresis and Avalanches in Foam Rheology Simulations , Phys. Rev.  E59:2,5819–5832(1999) .
7. T.J. Yang, U. Mohideen, V. Gopalan & P.J. Swart, Observation and mobility study of single 180 degrees domain wall using a near-field scanning optical microscope , Ferroelectrics  222 ,609 (1999) .
8. T.J. Yang, U. Mohideen, V. Gopalan & P.J. Swart, Direct Observation of Pinnning and Bowing of a Single Ferroelectric Domain Wall , Phys. Rev. Lett.  82:20,4106–4109(1999) .
9. D. Louca, H. R¨oder, J.L. Sarrao, D.A. Dimitrov, J.M. Wills, P.J. Swart & A.R. Bishop, The local atomic structure and phonons in Ba0.5Sr0.5TiO3, J. Phys. Chem. Solids  61:2,239–242(2000) .
10. D. Brandon, I. Fonseca & P.J. Swart, Oscillations in a dynamical model of phase transitions, Proc. Royal Soc. Edinburgh A131:1,59-81(2001).
11. NetworkX, A software package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks,   (2005).