Dan Schult

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Dan Schult

Charles G. Hetherington Professor of Mathematics

Department/Office Information



  • BA, Washington University at St. Louis, 1984 
  • MS, Economics, Princeton University, 1986 
  • PhD, Applied Mathematics, Northwestern University, 1996
  • Spreading, synchronizing and coupled dynamics
  • Network analysis, especially coupled dynamic systems 
  • Nonlinear PDEs and ODEs 
  • Numerical simulation
  • Modeling and dynamical systems
  • Applications to combustion, epidemics, and neuroscience

Open Source Packages: 
NetworkX  - NetworkX is a Python language software package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.
Pygraphviz - PyGraphviz is a Python interface to the Graphviz graph layout and visualization package.

I also have some local server-side web based demonstrations listed on my webpage.

Ken Segall, Matthew LeGro, Steven Kaplan, Oleksiy Svitelskiy, Shreeya Khadka, Patrick Crotty, and Daniel Schult, “Synchronization dynamics on the picosecond time scale in coupled Josephson junction neurons”, 
Physical Review E, Vol. 95, 032220 (2017). 

Kenneth Segall, Siyang Guo, Patrick Crotty, Dan Schult, and Max Miller, 
“Phase-flip bifurcation in a coupled Josephson junction neuron system”, 
Physica B: Condensed Matter, Vol. 455, pg 71-75 (2014). 

Patrick Crotty, Daniel A. Schult and Ken Segall, 
"Josephson Junction simulation of neurons" 
Physical Review E Vol. 82, 011914 (2010). 
Aric Hagberg and Daniel A. Schult, 
"Rewiring networks for synchronization", 
Chaos: An Interdisciplinary Journal of Nonlinear Science 
Vol 18, No 3, 037105, pg 1-7, (2008). 
Aric A. Hagberg, Daniel A. Schult and Pieter J. Swart, 
"Exploring Network Structure, Dynamics, and Function using NetworkX", 
in Proceedings of the 7th Python in Science Conference (SciPy 2008) Pasadena, CA,  
Edited by G Varoquaux, T Vaught, J Millman, pp. 11-15 (2008). 
Aric Hagberg, Daniel A. Schult and Pieter J. Swart, 
"Designing threshold networks with given structural and dynamical properties" 
Physical Review E Vol. 74, No 5, 056116 (2006). 
R. Berry, C. Breward, M. Leeser, J. Ockendon, C.P. Please, D. Schult, J. Shen, 
B.S. Tilley, J. Grand-Maison, R. Jain, K. Maki, G. Miller, and J. Phillips, 
"Mosaic Maps: 2D information from perspective data" 
Proceedings of the Twenty-Second Annual Workshop on Mathematical Problems in Industry 
June 12-16, 2006, pg. 52-75. Appeared June (2007). 
Michele L. Kelley and Daniel A. Schult, 
"Modeling extinction in forced opposed-flow smolder" 
Combustion Theory and Modelling Vol 10, p. 133-143, (2006). 
Melissa A. Decker and Daniel A. Schult, 
"Dynamics of smolder waves near extinction", 
Combustion Theory and Modelling Vol 8, p. 491-512, (2004). 
D.A. Schult, C.A. Spade and V.A. Volpert, 
"Dopant Distribution in Isothermal Frontal Polymerization", 
Applied Math Letters Vol 15, (2002) pp. 749-754. 
James Graham-Eagle and Daniel A Schult, 
"The effect of wind on combustion waves with reactant depletion", 
Proceedings of the Royal Society of London Series A Vol. 457 (2001) pp. 2397-2417. 
D.A. Schult and V.A. Volpert, 
"Linear Stability Analysis of Thermal Free Radical Polymerization Waves", 
Intl Journal of Self-Propagating High-Temperature Synthesis Vol. 8 No 4, 1999. 
J. Graham-Eagle and D.A. Schult, 
"Combustion Waves with Reaction Depletion", 
The ANZIAM Journal Vol. 43 No 1, (2001) pp. 119-135. 
Daniel A. Schult, 
"Matched Asymptotic Expansions and the Closure Problem for Combustion Waves", 
SIAM Journal of Applied Mathematics, Vol. 60 No. 1, (1999) pp. 136-155. 
D.A. Schult, A. Bayliss and B.J. Matkowsky, 
"Traveling Waves in Natural Counterflow Filtration Combustion and Their Stability", 
SIAM Journal of Applied Mathematics} Vol. 58 (1998) pp.806-852. 
A.P. Aldushin, B.J. Matkowsky and D.A. Schult, 
"Buoyancy Driven Filtration Combustion", 
Combustion Science and Technology Vol. 125 (1997) pp.283-349. 
A.P. Aldushin, B.J. Matkowsky and D.A. Schult, 
"Upward Buoyant Filtration Combustion", 
Journal of Engineering Mathematics Vol. 31 (1997) pp.205-234. 
A.P. Aldushin, B.J. Matkowsky and D.A. Schult, 
"Downward Buoyant Filtration Combustion", 
Combustion and Flame Vol. 107 (1996) pp.151-175. 
D.A. Schult, B.J. Matkowsky, V.A. Volpert, and A.C. Fernandez-Pello, 
"Forced Forward Smolder Combustion", 
Combustion and Flame Vol. 104 (1996) pp.1-26. 
A.P. Aldushin, B.J. Matkowsky, D.A. Schult, K.G. Shkadinsky, G.V. Shkadinskaya and V.A. Volpert. 
"Porous Medium Combustion", in 
Springer Lecture Notes in Physics 449, Modeling in Combustion Science 
Eds. J. Buckmaster and T. Takeno, Springer Verlag, 1995, pp.315-324. 
D.A. Schult, B.J. Matkowsky, V.A. Volpert and A.C. Fernandez-Pello, 
"Propagation and Extinction of Opposed Flow Smolder Waves", 
Combustion and Flame Vol. 101 (1995) pp.471-490.