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Alexander H. Barnett

Assistant Professor of Mathematics
329_alexander_barnett

Departments

  • Mathematics

Related Links

Contact Information

Email: alexander.barnett@dartmouth.edu
Phone: 603-646-3178
Office: 6188 Kemeny Hall

Education

B.A. Cambridge University; Ph.D. Harvard University

Areas of Expertise

Efficient computational methods for PDEs: the Dirichlet eigenproblem, high frequency waves, parabolic equations in complex geometries, mathematical physics: spectral properties of quantized chaotic dynamical systems, quantum ergodicity, dissipation, billiard systems, inverse problems in medical imaging: Diffuse Optical Tomography for functional brain imaging, Bayesian statistical inversion methods.

Selected Works

  • "Asymptotic Rate of Quantum Ergodicity in Chaotic Euclidean Billiards," Communications on Pure and Applied Mathematics, 59:10 (October 2006) 1457-1488.
  • Custo, A, W M Wells III, A H Barnett, E M C Hillman, and D A Boas, "Effective Scattering Coefficient of the Cerebral Spinal Fluid in Adult Head Models for Diffuse Optical Imaging," Applied Optics, 45:19 (July 2006) 4747-4755.
  • "A Fast Numerical Method for Time-Resolved Photon Diffusion in General Stratified Turbid Media," Journal of Computational Physics, 201 (2004) 771-797.
  • Barnett, A H, J P Culver, A G Sorensen, A M Dale, and D A Boas, "Robust Inference of Baseline Optical Properties of the Human Head with 3D Segmentation from Magnetic Resonance Imaging," Applied Optics, 42 (2003) 3095-3108.
  • Cohen, D, A H Barnett, and E J Heller, "Parametric Evolution for a Deformed Cavity," Physical Review E, 63:4 (April 2001) 46207.

Current Projects

"Quasi-orthogonality on the Boundary for Euclidean Laplace Eigenfunctions;" "Improved Inclusion Bounds for High-Frequency Dirichlet Eigenvalues via a Generalized Method of Particular Solutions;" "Eigenmodes of Mushroom Billiards"