Alex Barnett: publications, talks, notes
Updated Aug 2009... (Also download an old publication list with abstracts, dated Jan 2005, PDF).
A Few More Words About James Tenney: Dissonant Counterpoint and Statistical Feedback, Larry Polansky, Alex Barnett, and Mike Winter, submitted, J. Math. Music, 31 pages (Nov 2009) (preprint PDF 0.9MB)
An exponentially convergent nonpolynomial finite element method for time-harmonic scattering from polygons, Alex H. Barnett and Timo Betcke, submitted, SIAM J. Sci. Comp., 20 pages (Aug 2009) (preprint PDF 0.6MB)
Quasi-orthogonality on the boundary for Euclidean Laplace eigenfunctions , Alex. H. Barnett, preprint, math-ph/0601006
Perturbative analysis of the Method of Particular Solutions for improved inclusion of high-lying Dirichlet eigenvalues , Alex H. Barnett, SIAM J. Num. Anal. 47 1952-1970 (2009). (PDF 1.8MB)
Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains, A. H. Barnett and T. Betcke, J. Comput. Phys. 227 (14) 7003-7026 (2008). (0708.3533 [math.NA])
Quantum mushroom billiards, A. H. Barnett and T. Betcke, CHAOS, 17, 043123 (2007). (nlin.CD/0611059)
Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis , A. H. Barnett and P. R. Moorcroft, in press, J. Math. Biol., 57 (1) (July 2008) (submitted May 2007). (q-bio.QM/0705.3473)
Mechanistic home range models and resource selection analysis: a reconciliation and unification, P. R. Moorcroft and A. H. Barnett, Ecology, in press, submitted Nov 2006 (q-bio.PE/0612008)
Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards, Alex. H. Barnett, Comm. Pure Appl. Math., 59 (10), 1457-1488 (2006). math-ph/0512030
Effective scattering coefficient of the cerebral spinal fliud in adult head models for Diffuse Optical Imaging, A. Custo, W. M. Wells III, A. H. Barnett, E. M. C. Hillman, and D. A. Boas, Applied Optics, 45, 4747--55 (2006) (preprint PDF 233kB)
A fast numerical method for time-resolved photon diffusion in general stratified turbid media, Alex H. Barnett, Journal of Computational Physics, 201 771-797 (2004) (preprint PDF 590kB)
Robust inference of baseline optical properties of the human head with 3D segmentation from magnetic resonance imaging, Alex H. Barnett, Joseph P. Culver, A. Gregory Sorensen, Anders Dale, and David A. Boas, Applied Optics 42, 3095-3108 (2003). (preprint version PDF 464kB)
Parametric evolution for a deformed cavity, D. Cohen, A. H. Barnett, and E. J. Heller, Phys. Rev. E 63, 46207 (2001),(nlin/0008040)
Mesoscopic scattering in the half-plane: squeezing conductance through a small hole, A. H. Barnett, M. Blaauboer, A. Mody, and E. J. Heller, Phys. Rev. B 63, 245312/1 (2001),(cond-mat/0008279)
Rate of energy absorption for a driven chaotic cavity, A. H. Barnett, D. Cohen, and E. J. Heller, J. Phys. A 34, 413-437 (2001), (nlin.CD/0006041)
Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions, A. H. Barnett, D. Cohen, and E. J. Heller, Phys. Rev. Lett.85, 1412 (2000) (nlin/0003018)
Substrate-based atom waveguide using guided two-color evanescent light fields, A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, M. Prentiss, Phys. Rev. A. 61, 023608 (2000) (physics/9907014)
Accurate and Robust Computation of Photonic Crystal Band Structure using Second-Kind Integral Equations, A. H. Barnett and L. Greengard, Proceedings of WAVES2009: The 9th International Conference on Mathematical and Numerical Aspects of Waves Propagation (June 2009). (PDF 158kB)
Bayesian estimation of optical properties of the human head via 3D structural MRI, A. H. Barnett, J. P. Culver, A. G. Sorensen, A. M. Dale, and D. A. Boas, Proc. SPIE 5138 (2003). (PS 0.7MB)
Fast computation of the time domain diffusion forward model for optical tomography in the Born approximation, Jonathan S. Stott, Quan Zhang, Alex H. Barnett, and David A. Boas, (2003). (preprint PDF 275kB)
PhD thesis, Dissipation in Deforming Chaotic Billiards, A. H. Barnett (2000). (.ps.gz 2.6MB)
Bayesian Comparison of Models for Images, A. H. Barnett and D. J. C. MacKay, in Maximum Entropy and Bayesian Methods (Kluwer, 1996) p.239--248 (.ps.gz 421kB) (PDF 582kB)
convolution: son et lumiere, for issue 01 of Convolution. A Journal for Experimental Criticism, (October 2009), (preprint PDF 0.5MB)
Cover image for Notices of the AMS, January 2008. Computed eigenmodes numbered 1, 10, 102, 103, 104, 105 of a uniformly hyperbolic billiard, with background of random waves. (Accompanying article by Z. Rudnick)
Numerical Solutions of the Painleve Equations, International Centre for Mathematical Sciences, Edinburgh, UK, May 2010
Dartmouth Mathematics Colloquium, Nov 2009
MIT Applied Math Colloquium, Nov 2009
Dartmouth Math Society, introductory talk for undergraduates, Oct 2009
Computational Optical Sensing and Imaging (COSI) graduate program seminar series, UC Boulder, Sep 2009. (PDF 9MB)
Topological Complexity of Random Sets, AIM workshop, Palo Alto, Aug 2009, (including results on random plane waves)
WAVES2009, Pau, France, Jun 2009. (contributed talk)
Colloquium and PDE/Analysis Seminar (two talks, and 3-week visiting fellowship), ANU, Canberra, Australia, Feb 2009
"Computing eigenmodes on the torus: photonic crystals using second-kind integral equations", Laplacian Eigenvalues and Eigenfunctions: Theory, Application, IPAM, UCLA, Feb 2009. (PDF 7MB).
Workshop on Numerical and Analytical Methods for Wave Scattering, Manchester, UK, June 2008
Mathematical Aspects of Quantum Chaos, CRM (Univ. de Montreal), June 2008
Frontiers in Computational and Applied Mathematics (FACM08), NJIT, Newark, NJ; submitted poster, May 2008
``Eigenmodes and quantum chaos: Lost on the frequency axis? Check your Dirichlet-to-Neumann map!'' (PDF 17MB), McGill Applied Math Seminar, Montreal, Mar 2008
Applied Math Seminar, U. Delaware, Nov 2007
Numerical analysis seminar, Manchester, UK, July 2007
Three inivited minisymposia talks at ICIAM 2007 meeting, Zurich, Switzerland, Jul 2007.
UMass Amherst, Applied Mathematics Seminar, Nov 2006. (PDF 14MB).
``Quantum mushrooms and scars: what is the high frequency limit of cavity eigenmodes?'', Dartmouth Physics Colloquium, Oct 2006. (PDF 11MB, streaming video)
``High-frequency cavity modes: fast methods and quantum chaos'', SIAM Annual Meeting, Boston, Jul 2006. (PDF 5MB)
''Numerical study of the asymptotic rate of quantum ergodicity in chaotic billiards'', Joint MIT/Harvard Analysis Seminar, Mar 2006. (PDF 7.6MB).
Three lectures on quantum ergodicity and quantum chaos to Dartmouth Geometry Topology Seminar, Feb 2006.
''High-frequency cavity modes: efficient algorithms, and quantum chaos'', Computations in Science Seminar, Mathematics/Physics, U. Chicago, Nov 2005. (PDF 14MB).
``High-frequency cavity modes: efficient computation and applications'', Oxford U. Computing Laboratory, June 2005. (PDF 11MB).
Institute of Sound and Vibration Research, U. Southampton, UK, June 2005.
``High-frequency cavity modes: efficient computation and applications'', New Jersey Institute of Technology, Feb 2005. (PDF 9.5MB).
``Eigenfunctions of the Laplacian: quantum ergodicity, chaos, and fast numerical methods'', invited talk, Applied Mathematics Colloquium, Columbia University, Oct 2004. (PDF 11MB).
``Quantum ergodicity and billiards'', Courant Instructor Day, CIMS, Sept 2004. (PDF 4.3MB)
``Asymptotic ergodicity of eigenfunctions in a uniformly hyperbolic billiard'', invited presentation, Workshop on Semi-classical Theory of Eigenfunctions and PDEs, CRM (Univ. de Montréal) and Fields Institute (Toronto), June 2004. (PDF 5.1MB)
``Ergodicity of quantum eigenfunctions in classically chaotic systems'', invited talk, Applied Math Seminar, Yale, Mar 2004. (PDF 4.3MB)
``Ergodicity of quantum eigenfunctions in classically chaotic systems'', Applied Math Lab Seminar, CIMS, Feb 2004. (PDF 4.2MB)
``Bayesian estimation of optical properties of the human head via 3D structural MRI'', European Conference on Biomedical Optics, Munich, June 2003. (PDF 1.4MB)
``Forward models and Bayesian inference in diffuse optical brain imaging'', invited talk, Theoretical & Computational Biology Seminar Series, Mount Sinai School of Medicine, May 2003. (PDF 2.1MB)
``Noninvasive imaging of the brain with diffusing light pulses'', invited talk, Applied Math Seminar, CIMS, Nov 2002. (PDF 1.2MB)
``Forward and inverse wave problems: Quantum billiards and brain imaging'', Instructors' Day, CIMS, Sept 2002. (PDF 3.2MB)
``Inferring baseline optical properties of the human head'', Photon Migration Imaging group talk, MGH, May 2002. (PDF 646kB)
``How can quantum-classical correspondence help you find the modes of a drum?'' (poster), Dynamics Days, Baltimore, January 2002.
``How can quantum-classical correspondence help you find the modes of a drum?'', invited talk, Courant Institute of Mathematical Sciences, New York University, December 2001.
``Application of Statistical Methods to Wind Forecasting for Wind Power Generation'', invited talk. Radford Neal, Dept of Statistics, University of Toronto, September 2001. (PDF 9.7MB)
``Deformations of Chaotic Billiards and a New `Wall Formula' for Heating Rate'', Pan-American Advanced Study Institute, Ushuaia, Argentina, October 2000 (PDF 361kB) (.ps.gz 227kB)
``Dielectric Waveguides for 1D Atom Traps'' (poster presentation), Cambridge Area Atomic and Molecular Physics 3rd Open House, Harvard-Smithsonian Center for Astrophysics, May 1998. (.ps 350kB)
``Bayesian Comparison of Models for Images'', MAXENT94 (14th Maximum Entropy Workshop), Cambridge, England, June 1994.
1D band structure of single periodic scatterer in Schrodinger equation, June 2008. (0.5MB PDF).
Linearizing the photonic band structure eigenvalue problem using the Dirichlet-to-Neumann map, May 2008. (87kB PDF).
Greens functions for the wave equation, December 2006, (140kB PDF).
Spring Break Puzzler on stochastic processes, March 2005, (30kB PDF), with insightful answer from Jonathan Goodman.
Ill-posed inference and sampling from a high-dimensional sheet-like distribution. (ps 116kB). Introducing Bayesian inference, and presenting a mixed Gaussian-approximation/MCMC method (originally notes for David Boas, June 2002).
Embryonic research proposal for statistical methods in wind forecasting (ps 113kB).