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Stephen H. Davis (born 7 September 1939) is an American applied mathematician working in the fields of Fluid Mechanics and Materials Science. Davis is the McCormick School Institute Professor and the Walter P. Murphy Professor of Applied Mathematics at Northwestern University. Davis has been listed as an ISI Highly Cited researcher in Engineering.
Davis received his B.E.E in Electrical Engineering from the Rensselaer Polytechnic Institute in 1960 and the M.S. and PhD in Mathematics in 1962 and 1964, respectively. He was a Research Mathematician at the RAND Corporation from 1964 to 1966, a Lecturer in Applied Mathematics at Imperial College London for 1966-1968, and Assistant, Associate, and Full Professor of Mechanics at the Johns Hopkins University from 1968-1978. He joined the Northwestern faculty in January 1979. He was Assistant then Associate Editor of the Journal of Fluid Mechanics from 1969-1989 and the Editor from 2000-2009. He has been the Editor of the Annual Review of Fluid Mechanics since 1999.
Davis is known for introducing new mathematical methods in Fluid Mechanics and Material Science, confronting issues beyond the frontiers of the fields, and obtaining fundamental understandings of mechanisms of behavior in anticipation of future needs.
In Fluid Mechanics, Davis first studied the instability of time-dependent flows including Stokes Layers and first identified and studied dynamic instabilities driven by variations in surface tension along interfaces. He gave the first nonlinear theory of film rupture by instabilities driven by van der Waals attractions and the first coupling of evaporation and thin film instabilities. He gave the first analytic theory of moving contact lines leading to the understanding of the dynamics and instabilities of droplet spreading. His review article (RMP) laid out how long-wave asymptotic theory would be the basis of research worldwide in the analysis of thin- films, droplet spreading, and micro/nano -science flows.
Davis has studied the dynamics of metallic foams and devised a unique numerical simulation based on a network model that can be used to follow in time a regular foam as it becomes disorganized. In Material Science, Davis pioneered the coupling of morphological instabilities and material anisotropy and was the first to give results for rapid solidification in which thermodynamic disequilibrium generates banding. He has written a book “Theory of Solidification” for Cambridge University Press. Further, he was the first to use long-wave theories to describe the destabilization of deposited solid films and their evolution to quantum dots through coarsening via the derivation of convective Cahn-Hilliard equations. He has given growth laws for nano-wire evolution by bulk or surface diffusion (stepwise growth).
Finally, Davis has pioneered the study of the interaction of fluid and solidification finding ways of using imposed motion to delay morphological instability and showing how freezing can modify the modes of convection. He recently has outlined a method of freezing a metallic foam so as to produce a porous solid with uniform permeability.