Faculty Directory
Alvin Bayliss

Professor of Engineering Sciences and Applied Mathematics


2145 Sheridan Road
Evanston, IL 60208-3109

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Bayliss Research

Alvin Bayliss' Homepage


Engineering Sciences and Applied Mathematics

Electrical Engineering and Computer Science

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Ph.D. Mathematics, New York University, New York, NY

M.S. Mathematics, New York University, New York, NY

B.S. Physics, City College of New York, New York, NY

Research Interests

I work in the numerical solution of partial differential equations, especially those modeling combusion, solid mechanics, wave propagation, and fluid dynamics.  Development of adaptive numerical procedures for both finite differences and spectral methods. Computation and analysis of pattens in combustion, including both gaseous combustion nd solid fuel combustion, a procedure for the synthesis of materials usig highly exothermic reactions.  Analysis and computations of integro-partial dfferential equations modeling nonloal interactions.  An example of such a system involves competing populations where the computation or a scarce resource, e.g., water, food or air, depends on not just the population at a specific point but on a weighted average of the populations in a neighborhood of the point.

Significant Recognition

  • Clarence ver Steeg Graduate Faculty Award
  • McCormick Teaching Award
  • ISI Highly Cited Researcher

Significant Professional Service

  • Associate Editor - Journal of Computational Physics, Applied Numerical Mathematics

Selected Publications

  • Bayliss, A.; Tanzy, M.C.; Volpert, V.A.; Nehrkorn, M.E., “Stability and pattern formation for competing populations with asymmetric nonlocal coupling”, Mathematical Biosciences, (2013)
  • Bayliss, Alvin; Lennon, Erin M.; Tanzy, Matthew C.; Volpert, Vladimir A., “Competing reactions in condensed phase combustion: Wave structure and stability”, Journal of Engineering Mathematics, (2013)
  • Bayliss, Alvin; Lennon, Erin M.; Tanzy, Matthew C.; Volpert, Vladimir A., “Solution of adiabatic and nonadiabatic combustion problems using step-function reaction models”, Journal of Engineering Mathematics, (2013)
  • Bayliss, A.; Volpert, V.A.; Segal, B.L., “Pattern formation in a model of competing populations with nonlocal interactions”, Physica D: Nonlinear Phenomena, (2013)
  • Tzou, J.C.; Ma, Y.-P.; Bayliss, A.; Matkowsky, B.J.; Volpert, V.A., “Homoclinic snaking near a codimension-two Turing-Hopf bifurcation point in the Brusselator model”, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, (2013)
  • J. C. Tzou, A. Bayliss, B. J. Matkowsky and V. A. Volpert, “Stationary and slowly moving localised pulses in a singularly perturbed Brusselator model”, European Journal of Applied Mathematics, (2011)
  • Bayliss, A.; Volpert, V. A.; Lennon, E. M.; Tanzy, M. C.; Mukasyan, A. S., “Combustion of reactive solutions impregnated into a cellulose carrier: Modeling of two combustion fronts”, Chemical Engineering Journal, (2011)
  • JC Tzou, A Bayliss, BJ Matkowsky, VA ..., “Interaction of Turing and Hopf Modes in the Superdiffusive Brusselator Model Near a Codimension Two Bifurcation Point”, ... Modelling of Natural ..., (2010)