View the Project on GitHub ModelingSimulation/Classic-Papers

Below is a list of “classical” or “seminal” papers, i.e. papers that made some kind of breakthrough and started a new line of research (which may have changed significantly since the paper was written.) The papers are organized by topic, but only loosely because topics overlap. This list is evolving; please send any suggestions (to Aleks Donev, Leif Ristoph, or Miranda Holmes-Cerfon.)

Click here to quickly jump to a topic:

- Numerical Analysis
- Stochastic Analysis, Simulation, and Statistical Mechanics
- Fluid Dynamics
- Mathematical Biology
- Other Topics

- Engquist, Björn, and Andrew Majda. “Absorbing boundary conditions for numerical simulation of waves.”
*Proceedings of the National Academy of Sciences*74.5 (1977): 1765-1766. webpage- Classic paper dealing with absoring boundary conditions for hyperbolic equations
- This topic came up several times in our Fall 2018 meetings.

- Cooley, James W., and John W. Tukey. “An algorithm for the machine calculation of complex Fourier series.”
*Mathematics of computation*19.90 (1965): 297-301. website- Proposed the Fast Fourier Transform, an algorithm to compute the discrete Fourier transform in Nlog(N) operations, instead of the previous N^2 operations. This algorithm revolutionized signal processing and is still widely used today.
- An interesting history of the FFT, which goes back further than Cooley & Tukey (even to the time of Gauss), is

Heideman, Michael, Don Johnson, and C. Burrus. “Gauss and the history of the fast Fourier transform.”*IEEE ASSP Magazine*1.4 (1984): 14-21. website

- Fourier, J. “Théorie analytique de la chaleur (The analytical theory of heat).” (1822, with several later translations.)
- A book in which Joseph Fourier claimed that any function, continuous or discontinuous, could be expanded in sin waves. (We now know this is not entirely true.) Although other authors had made this observation in special cases before him, it is this book that is credited with beginning the development of Fourier series. He also made significant developments in the study of heat flow, and proposed the diffusion equation to model it.
*Does anyone know where to get a pdf of the book?*

- Courant, Richard, Kurt Friedrichs, and Hans Lewy. “On the partial difference equations of mathematical physics.”
*IBM journal of Research and Development*11.2 (1967): 215-234. (English translation of the original work, “Uber die Partiellen Differenzengleichungen der Mathematischen Physik,”*Math. Ann.*100, 32-74(1928).)- The authors introduce finite difference schemes in order to prove the existence of solutions to PDEs, but as a byproduct discover the now-famous CFL condition.
- Peter Lax wrote an interesting review of the paper: Lax, Peter D. “Hyperbolic difference equations: A review of the Courant-Friedrichs-Lewy paper in the light of recent developments.”
*IBM Journal*, March (1967): 235-238.

- Einstein, Albert. “On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat.”
*Annalen der physik*17 (1905): 549-560.- “The” classic paper on Brownian motion, which explains (from a physics perspective) why macroscopic bodies jiggle around at random in a liquid.
- Could also include the related classic papers by Brown, and Perrin (the latter received a Nobel prize for his work.)

- Kirkpatrick, Scott, C. Daniel Gelatt, and Mario P. Vecchi. “Optimization by simulated annealing.”
*Science*220.4598 (1983): 671-680. website- The first reference on annealing schemes for finding deep minima on an energy landscape.

- Marinari, Enzo, and Giorgio Parisi. “Simulated tempering: a new Monte Carlo scheme.”
*Europhysics Letters*19.6 (1992): 451.- The first reference on simulated tempering, i.e. simulated annealing, but the system is kept at equilibrium.
- Could be presented simultaneously with Kirkpatrick et al. (1983.)

- Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). “Equation of State Calculations by Fast Computing Machines”.
*Journal of Chemical Physics.*21 (6): 1087–1092. website- The original paper on Metropolis Monte-Carlo.
- Some interesting history about the authorship.
- Could also present the classic paper by Hastings, too:

Hastings, W. Keith. “Monte Carlo sampling methods using Markov chains and their applications.” (1970): 97-109. website

- Shannon, Claude Elwood. “A mathematical theory of communication.”
*Bell system technical journal*27.3 (1948): 379-423.- Introduced the concept that is now known as Shannon entropy, widely used in almost every field.

- G. E. Forsythe and R. A. Leibler, “Matrix inversion by a Monte Carlo method”.
*Math. Tables Other Aids Comput*., 4 (1950), pp. 127–129.- The authors describe a method proposed by Ulam and Von Neumann for solving a linear system Ax = b using Monte Carlo sampling. The method of Ulam and Von Neumann has inspired many modern approaches to approximately solve Ax = b when the dimension d of the solution vector x is extremely high and when the only feasible solvers operate with O(1) or O(d) computational cost. The original paper is short and sweet, weighing in at just over two pages.

- Purcell, Edward M. “Life at low Reynolds number.”
*American journal of physics*45.1 (1977): 3-11; and Vandenberghe, Nicolas, Jun Zhang, and Stephen Childress. “Symmetry breaking leads to forward flapping flight.”*Journal of Fluid Mechanics*506 (2004): 147-155.- These are two papers on the fundamental fluid dynamical constraints of biological locomotion. The first explains why very small organisms must undergo time-irreversible (non-reciprocal) reconfigurations in order to move, and the second shows why at larger scales even symmetric bodies undergoing symmetric motions can locomote.

- Sutera, Salvatore P., and Richard Skalak. “The history of Poiseuille’s law.”
*Annual review of fluid mechanics*25.1 (1993): 1-20; and Murray, Cecil D. “The physiological principle of minimum work: I. The vascular system and the cost of blood volume.”*Proceedings of the National Academy of Sciences*12.3 (1926): 207-214.- These are two classics that were motivated by flow in biological vessels and vessel networks but whose results are very general. They cover how Poiseuille experimentally discovered his famous laws about pipe flow and how Murray used these relations to theoretically predict the geometry of optimal branched networks.

- Reynolds, Osborne. “III. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels.”
*Proceedings of the Royal society of London*35.224-226 (1883): 84-99.- This is the first clear observation of turbulence. It is a purely experimental paper and so might be paired with one of the more theoretical ones below.

- Kolmogorov, Andrei Nikolaevich. “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers.”
*Proc. R. Soc. Lond. A*434.1890 (1991): 9-13; Kolmogorov, Andrei Nikolaevich. “Dissipation of energy in the locally isotropic turbulence.”*Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences*434.1890 (1991): 15-17.- This is translation into English of Kolmogorov’s derivation of his famous law about energy across scales in isotropic turbulence. (I cannot vouch that this be comprehensible to non-experts!)

- Lorenz, Edward N. “Deterministic nonperiodic flow.”
*Journal of the atmospheric sciences*20.2 (1963): 130-141.- This is Lorenz’s classic discovery of deterministic chaos in a model of atmospheric flows.

- Prandtl, Ludwig. “Motion of fluids with very little viscosity.” (1928).
- This is a translation into English of one of Prandtl’s first papers on boundary layer theory, which revolutionized high Reynolds number fluid dynamics almost immediately.

- Courant, Richard. “Soap film experiments with minimal surfaces.”
*The American Mathematical Monthly*47.3 (1940): 167-174; Keller, Joseph B. “Surface tension force on a partly submerged body.”*Physics of Fluids*10.11 (1998): 3009-3010; Vella, Dominic, and L. Mahadevan. “The “cheerios effect”.”*American journal of physics*73.9 (2005): 817-825.- The first two are not-so-related classics in fluid statics: Courant’s work on soap films as area-minimizing surfaces and Keller’s beautiful generalization of Archimedes’ Principle to include surface tension effects.
- The third is an application of Keller’s paper, to explain why Cheerios tend to clump together in a bowl of milk.

- Taylor, Geoffrey Ingram. “Dispersion of soluble matter in solvent flowing slowly through a tube.”
*Proc. R. Soc. Lond. A*219.1137 (1953): 186-203. website- Showed that when a tracer diffuses in a shear flow, its effective diffusion coefficient is significantly enhanced by the shear. This phenomenon is known as “Taylor dispersion”, and the result is widely used to understand the transport properties of biological and industrial flows.

- Hodgkin, Alan L., and Andrew F. Huxley. “A quantitative description of membrane current and its application to conduction and excitation in nerve.”
*The Journal of physiology*117.4 (1952): 500-544. website- Perhaps the most classic paper of all in math biology.

- Huxley, Andrew F. “Muscle structure and theories of contraction.”
*Prog. Biophys. Biophys. Chem*7 (1957): 255-318.- First explanation of how muscle works; “Huxley’s 1957 scheme.”

- Del Castillo, J., and B3 Katz. “Quantal components of the end‐plate potential.”
*The Journal of physiology*124.3 (1954): 560-573. website- A classic paper on synaptic transmission, which shows that experimental data on synaptic transmission gives strong support to the concept that neurotransmitter is randomly released in packets that the authors call “quanta.”

- Peskin, Charles S., Garrett M. Odell, and George F. Oster. “Cellular motions and thermal fluctuations: the Brownian ratchet.”
*Biophysical journal*65.1 (1993): 316-324. website- First paper that explains how Brownian ratchets can work in molecular biology. Now, ratchets are of interest in materials science.

- Turing, Alan Mathison. “The chemical basis of morphogenesis.”
*Bulletin of mathematical biology*52.1-2 (1990): 153-197. website- Proposes that a reaction-diffusion system of PDEs can explain patterns (e.g. stripes, spots, spirals) found in many biological systems.

- J.C. Maxwell “On physical lines of force,”
*Philosophical Magazine*, 90:S1, (1861): 11-23. website- Charlie says of this: “The best modeling and simulation ever was when Maxwell invented the displacement current purely for mathematical reasons (conservation of charge) and was then able to predict the speed of electromagnetic waves from static measurements alone, and the speed turned out to be that of light!”