Alex Barnett: publications, talks, notes
You can access my arxiv preprints here, which is a subset of the complete list given on this page
20. Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map, Alex Barnett and Andrew Hassell, preprint, 48 pages, (math.NA 1112.5665)
19. Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues, Alex Barnett and Andrew Hassell, SIAM J. Numer. Anal. 49, 1046-1063 (2011)
18. A new integral representation for quasi-periodic scattering problems in two dimensions, Alex Barnett and Leslie Greengard, BIT Numer. Math. 51, 67-90 (2011) (preprint PDF 1MB)
17. A few more words about James Tenney: dissonant counterpoint and statistical feedback, Larry Polansky, Alex Barnett, and Mike Winter, J. Math. Music, 5 (2), 63-82 (2011) (preprint PDF 0.9MB)
16. A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations, Alex Barnett and Leslie Greengard, J. Comput. Phys., 229 (19), 6898-6914 (2010). (math.NA 1001.5464)
15. An exponentially convergent nonpolynomial finite element method for time-harmonic scattering from polygons, Alex H. Barnett and Timo Betcke, SIAM J. Sci. Comp., 32 (3), 1417-1441 (2010). (preprint PDF 0.6MB)
14. 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)
13. 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])
12. Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis, A. H. Barnett and P. R. Moorcroft, J. Math. Biol., 57 (1) 139-159 (July 2008). (q-bio.QM/0705.3473)
11. Mechanistic home range models and resource selection analysis: a reconciliation and unification, P. R. Moorcroft and A. H. Barnett, Ecology, 89 (4), 1112-1119 (2008). (q-bio.PE/0612008)
10. Quantum mushroom billiards, A. H. Barnett and T. Betcke, CHAOS, 17, 043123 (2007). (13 pages) (nlin.CD/0611059)
9. Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards, Alex. H. Barnett, Comm. Pure Appl. Math., 59 (10), 1457-1488 (2006). math-ph/0512030
8. 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)
7. 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)
6. 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)
5. Parametric evolution for a deformed cavity, D. Cohen, A. H. Barnett, and E. J. Heller, Phys. Rev. E 63, 46207 (2001),(nlin/0008040)
4. 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)
3. 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)
2. 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)
1. 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)
Robust high-order numerical scattering from multi-layer dielectric gratings using a new integral representation for quasi-periodic fields, A. H. Barnett and L. Greengard, Proceedings of WAVES2011: The 10th International Conference on Mathematical and Numerical Aspects of Waves Propagation (July 2011). (PDF 144kB)
Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them, A. Hassell and A. H. Barnett, submitted, P.S.P.M. proceedings of the International Conference on Spectral Geometry, July 2010, Dartmouth College (Mar 2011) (preprint 1.6MB)
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)
Quasi-orthogonality on the boundary for Euclidean Laplace eigenfunctions, Alex. H. Barnett, technical report, math-ph/0601006
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). Technical report (preprint PDF 275kB)
PhD thesis: Dissipation in Deforming Chaotic Billiards, A. H. Barnett (2000). (.ps.gz 2.6MB)
Undergrad thesis: 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)
Computed eigenmodes of billiards that I produced, Sept 2009, feature in Peter Sarnak's review article, Recent Progress on QUE, and Dana Mackenzie, What's Happening in the Mathematical Sciences, Volume 8 (AMS, to appear, Jan 2011), and Shin-ya Koyama, "Arithmetic quantum chaos and zeta functions", Suurikagaku, vol. 571 (2011) Saiensu-sha, and Shin-ya Koyama, "From primes and zetas to arithmetic quantum chaos" Nihon Hyoronsha (December 2010).
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)
SIAM Annual Meeting, Minneapolis, Jul 9-13, 2012.
Workshop on Geometry of eigenvalues and eigenfunctions, CRM, Montreal, Jun 4-8, 2012
Frontiers in Computational and Applied Mathematics, NJIT, Newark, NJ, May 18-20, 2012
Analysis/PDE Seminar, UNC Chapel Hill, Apr 4, 2012
Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, Feb 10, 2012
"The Fast Fourier Transform: an algorithm that has changed your life",
Applied and Computational Mathematics Seminar, Jan 2012; and
Dartmouth Mathematics Society, Oct 2011.
(demo codes: test_fft.m which calls
cooleytukey.m)
"New Integral Representations for Scattering from Multi-layer Dielectric Gratings", WAVES 2011, Vancouver, BC, Jul 2011. (contributed talk)
ICIAM 2011, Vancouver, BC, Jul 2011. (one talk on periodic integral-equation solvers; co-organized 2 minisymposia)
"The Mathematical Overtones of Music," lecture with demonstrations, JHU Center for Talented Youth, Odyssey Series, May 2011
"How integral equations help you solve PDEs," (PDF 6MB), Applied and Computational Mathematics Seminar, Dartmouth College, May 2011
"Diffraction gratings and photonic crystals: new integral representations for periodic scattering and eigenvalue problems", New England Numerical Analysis Day, UMass Dartmouth, Apr 2011
"Diffraction gratings and photonic crystals: numerical analysis of waves," (PDF 1.5MB), Graduate Open House, Mathematics Dept, Dartmouth College, Apr 2011
NIST DLMF Conference Special functions in the 21st century: theory and applications, Washington DC, Mar, 2011. (not a speaker)
CSC Seminar, SFU, Vancouver, BC, Mar 2011
Numerical Analysis and Scientific Computing Seminar, Courant Institute, NYU, Jan 2011
Applied Mathematics and Computational Science Colloquium, U. Penn, Jan 2011
Conference in honor of 65th birthday of Eric Heller, Harvard, October 2010
Integral Equation Methods, Fast Algorithms and Applications, IMA Hot Topics Workshop, Minnesota, Aug 2010
"A new integral representation of quasi-periodic fields and its application to scattering and Bloch eigenvalue problems", (PDF 5MB, with movies: moving contour and scattered field), Frontiers in Computational and Applied Mathematics, NJIT, Newark, NJ, May 2010
Numerical Solutions of the Painleve Equations, International Centre for Mathematical Sciences, Edinburgh, UK, May 2010
"Robust and efficient computation of two-dimensional photonic crystal band structure using second-kind integral equations", (PDF 3.6MB, movie of band structure), Applied Analysis Seminar, Lousiana State University, Mar 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" (PDF 7MB), Laplacian Eigenvalues and Eigenfunctions: Theory, Application, IPAM, UCLA, Feb 2009.
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).
Notes on Method of Fundamental Solutions convergence in the disc (and other domains), June 2006. (2MB 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, 2001. (ps 113kB).