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greenberg
James M. Greenberg, Professor Emeritus
Ph.D., Brown University
E-mail: greenber@andrew.cmu.edu
Office: Wean Hall 6124
Phone: 412-268-3554


Research:

My research interests lie in the areas of hyperbolic conservation laws, phase field models, viscoelastic flows, and most recently higher order traffic models. Recent publications have involved a judicious blend of computational and analytical work. For animations on shallow water equations click here.

Selected Publications:

Greenberg, J.M. and Hartig, Daniel, "A New Lagrangian Shallow Water Circulation Model"
The paper is available for download in PDF format.


2dim08

Serial Codes

Parallel Codes

Greenberg, J.M., Laurent Gossee, "Chirplet Approximation of Band-Limited, Real Signals Made Easy"
The paper is available for download in PDF format.

Greenberg, J.M., C. Greene and S.P. Hastings, "Remarks on a 25 Year Old Theorem on Two-Dimensional Cellular Automata.", International Journal of Unconventional Computing, Volume 1, Number 4, 2005
The paper is available for download in PDF format.

Greenberg, J. M. and Benjamin Heineike, "Malaria", CMU Center for Nonlinear Ananlysis Report No. 04-CNA-011, Submitted to Journal of Mathematical Biology
The paper is available for download in Postscript and PDF formats.

Greenberg, J. M., Li, Jian and Wang, Zhisong, "New Approaches for Chirplet Approximation", IEEE Transactions of Signal Processing, Volume 55, No. 2, 734-741, February 2007
The paper is available for download in PDF format.

Greenberg, J. M., "Congestion Redux", SIAM J. Appl. Math, Vol. 64, No. 4, (2004), 1175-1185.
The paper is available for download in PDF format.

Greenberg, J. M., "Phase Transitions with Semi-Diffuse Interfaces", CMU Center for Nonlinear Analysis Report No. 01-CNA-014, J. Diff. Eqs. 189 (2003), 161-182
The paper is available for download in Postscript and PDF formats.

Greenberg, J. M., Klar, A., Rascle M., "Congestion on Multilane Highways", CMU Center for Nonlinear Analysis Report No. 01-CNA-011, SIAM Jour. Appl. Math. 63 (2002), 818-833
This paper is available for download in PDF format. Animations may be found here.

B.Argall, E. Cheleshkin, J.M. Greenberg, C. Hinde, and P.J. Lin, "A Rigorous Treatment of a Folow-the-Leader Traffic Model with Traffic Lights Present", CMU Center for Nonlinear Analysis Report No. 01-CNA-007, SIAM Jour. Appl. Math. 63 (2002), 149-168
This paper, along with the mpeg movies, may be found at http://www.math.cmu.edu/users/plin/21380/traffic.html

Greenberg, J. M., "Extensions and Amplifications of a Traffic Model of Aw and Rascle", CMU Center for Nonlinear Analysis Research Report No. 00-CNA-010, SIAM Jour. Appl. Math. Vol. 62, No. 3, 729-745 (2001)
The paper is available for download in PDF format. Two movies in mpeg format are available for viewing (movie1 and movie2).

Greenberg, J. M., "Melt Fracture Revisited", CMU Center for Nonlinear Analysis Research Report No. 00-CNA-004 and EJAM Vol.12, 465-477 (2001).
The paper is available for download in Postscript and PDF formats. Two movies in mpeg format are available for viewing (movie1 and movie2).

Greenberg, J. M., "Estimates and Computations for Melting and Solidification Problems", CMU Center for Nonlinear Analysis Research Report No. 99-CNA-019, Mathematical Modelling and Numerical Analysis Vol. 35, No. 4, 607-630 (2001).
The paper is available for download in Postscript and PDF formats. Here is a movie in mpeg format, and here you can see parts of it in your web browser.

Greenberg, J. M., MacCamy, R. C., and Coffman, C. V., "On the Long-Time Behavior of Ferroelectric Systems", CMU Center for Nonlinear Analysis Research Report No. 97-NA-011, September 1997, Physica D 134, 362–383 (1999).

Greenberg, J. M. and Owen, D., "Antiplane Shear Flows in Visco-Plastic Solids Exhibiting Isotropic and Kinematic Hardening", SIAM J. of Appl. Math 58, 6, 1996–2023 (1998).
The paper is available for download in Postscript, DVI, and PDF formats.

"Elastic Phase Transitions - A New Model", Physica D 108, 209–235 (1997).

Greenberg, J. M. and LeRoux, A. Y., "Analysis and Approximation of Conservation Laws with Source Terms", SIAM J. Numerical Analysis, 34, 1980–2007 (1997).

Greenberg, J. M., LeRoux, A. Y., Baraille, R., and Noussair, A., "Analyse et approximation de lois de conservation avec terme source", C. R. Acad. Sci. Paris, 321, Serie I, 1073–1076 (1995).

Greenberg, J. M. and Demay, Y., "A Simple Model of the Melt Fracture Instability", Euro. J. of Applied Mathematics, Vol. 5, 337–357 (1994).

Greenberg, J. M. and Nachman, A., "Continuum Limits for Discrete Gases with Long- and Short-Range Interactions", Communications on Pure and Applied Mathematics, Vol. XLVII, 1239–1281 (1994).

Greenberg, J. M. and Peszek, R., "Continuum Limits of Interacting Partaicle Systems", Physica D 65, 172–190 (1993).

Greenberg, J. M. and Peszek, R., "Time Periodic Solutions to a Class of Quasilinear Wave Equations", Arch. Rat. Mech. and Anal. 122, 35–52 (1993).