Alfred Clark, Jr.
Professor of Mechanical Engineering, Mathematics, and Biomedical Engineering
Dept. Mechanical Engineering
University of Rochester
Rochester, NY 14627
My research interests have included the following: hydrodynamics of superfluids; astrophysical fluid dynamics, including solar magnetic fields and solar rotation; tsunami propagation; wind-driven lake circulations; microcirculatory blood flow; oxygen transport to tissue; diffusion in membranes; transport of ADP and ATP in skeletal muscle; mathematical models of infectious diseases. For more detailed information, including publications, see my listing in the Department of Mechanical Engineering web pages.
My primary teaching interests are in applied mathematics. In recent years I have taught courses in diffusion (ME 405), dynamical systems (ME 406), Fourier series and boundary value problems (ME 201/MTH 281), complex variables (ME 202/MTH 282), numerical analysis (ME 211), advanced topics in ordinary differential equations (ME 401), partial differential equations (ME 402), and elementary ordinary differential equations (ME 163). Links to web pages for some of these courses are given below. Most of my recent courses have contained considerable computer work using the software Mathematica, with the primary goal being the dynamical visualization of mathematical processes (click here to see an example: a movie showing the partial sums of the Fourier series of a square wave, with the Gibbs phenomenon showing up clearly). For the dynamical systems course, I have written a software package called DynPac, which runs under Mathematica. It is a comprehensive package for solving systems of nonlinear ordinary differential equations, and for visualizing their solutions.
Links to Mathematics Courses Recently Taught
I was born in Tennessee in 1936. I lived subsequently in Ohio, Pennsylvania, and, for most of my pre-college years, in Bartlesville Oklahoma, where I graduated from high school in 1954. A lifelong addiction to computers began with a summer job with Phillips Petroleum in 1956, for which I programmed a Datatron in machine language on punched paper tape. I received a B.S. in Engineering Sciences from Purdue University in 1958. In 1963 I received a Ph.D. from M.I.T. in Applied Mathematics, with a minor in Physics. After a year postdoc at M.I.T., I came to Rochester in 1964, and have been here ever since, except for an academic leave at the University of Colorado in 1971-72. I also have had two academic leaves in the Medical School at Rochester, connected with my work in microcirculation and oxygen transport. I survived five years as Department Chair of Mechanical Engineering from 1972-1977. In the years since, I have concentrated on teaching and research, with somewhat more emphasis on teaching.
Hiking, birdwatching, photography, visiting historic sites, playing keyboard, rollercoasters, fountain pens, New York Yankees, quality cookies, and reading about any or all of the following: polar exploration, American colonial history, American utopias, American literature, history of aviation, mountaineering, history of mathematics, and computers.
"On the Theory of Shallow Water Waves," C.C. Lin and A. Clark, Jr., Tsing Hua Journal of Chinese Studies, Special No. 1, 54-62, 1959.
"On the Hydrodynamics of Superfluid Helium," Ph.D. dissertation, Massachusetts Institute of Technology, 257 pages, 1963.
"Some Kinematical Models for Small-Scale Solar Magnetic Fields," Physics of Fluids 9, 485-492, 1966.
"Solar Differential Rotation and Oblateness," A. Clark, Jr., J.H. Thomas, and P.A.A. Clark, Science 164, 290-291, 1969.
"Trapped Gravity Waves and the Five-Minute Oscillations of the Solar Atmosphere," J.H. Thomas, P.A.A. Clark, and A. Clark, Jr., Solar Physics 16, 51-66, 1971.
"Spin-Down of a Boussinesq Fluid of Small Prandtl Number in a Circular Cylinder," T. Sakurai, A. Clark, Jr., and P.A.A. Clark, Journal Fluid Mechanics 49, 753-773, 1971.
"Radiative Damping of Trapped Gravity Waves in the Solar Atmosphere," P.A.A. Clark and A. Clark, Jr., Solar Physics 30, 319-325, 1973.
"Spin-Up," E.R. Benton and A. Clark, Jr., Annual Review of Fluid Mechanics 6, 257-280, 1974.
"Thermal Models of Sunspots," Solar Physics 62, 305-330, 1979.
"Complex Analysis in Forth," Forth Dimensions 3, 125, 1981.
"The Capture of Spatially Homogeneous Chemical Reactions in Tissue by Freezing," A. Clark, Jr. and P.A.A. Clark, Biophysical Journal 42, 25-30, 1983.
"Oxygen Delivery from Red Cells," A. Clark, Jr., W.J. Federspiel, P.A.A. Clark, and G.R. Cokelet, Biophysical Journal 47, 171-181, 1985.
"Local Oxygen Gradients Near Isolated Mitochondria," A. Clark, Jr. and P.A.A. Clark, Biophysical Journal 48, 931-938, 1985.
"How Large is the Drop in PO2 between Cytosol and Mitochondrion?," A. Clark, Jr., P.A.A. Clark, R.J. Connett, T.E.J. Gayeski, and C.R. Honig, American Journal of Physiology (Cell Physiology) 252, C583-C587, 1987.
"A Primer on Roller Coaster Dynamics, Part I. Plane and Fancy," RollerCoaster! Magazine, Vol. IX, Issue 3-4, pp. 30-37, 1988.
"A Simple Model of Aerobic Metabolism. Applications to Work Transitions in Muscle," C. Funk, A. Clark, Jr., and R.J. Connett, American Journal of Physiology (Cell Physiology) 258, C995-C1005, 1990.
"Arteriovenous O2 Diffusion Shunt is Negligible in Resting and Working Gracilis Muscles," C.R. Honig, T.E.J. Gayeski, A. Clark, Jr., and P.A.A. Clark, American Journal of Physiology (Heart and Circulatory Physiology) 261, H2031-H2043, 1991.
"Analysis of Lateral Diffusion from a Spherical Cell Surface to a Tubular Projection," D.A. Berk, A. Clark, Jr., and R.M Hochmuth, Biophysical Journal 61, 1-9, 1992.
“DynPac,” A Dynamical Systems Software Package Running Under Mathematica 3, 4 and 5, 1995, 2003.
“Thermocline Flux Exchange During the Pinatubo Event,” D.H. Douglass, R.S. Knox, B.D. Pearson, and A. Clark, Jr., Geophysical Research Letters, 33, L19711, doi:10.1029/2006GL026355, 2006.
“Catalyst Utilization in the Oxygen Electrode of a Proton Exchange Membrane Fuel Cell – Analytical Model and Experimental Validation,” K.C. Neyerlin, W. Gu, H.A. Gasteiger, J. Jorne, and A. Clark, Jr., Journal Electrochemical Society, 154, B279-B287, 2007.
“Membrane mobility of β2 integrins and rolling associated adhesion molecules in resting neutrophils,” T.R. Gaborski, A. Clark, Jr., R.E. Waugh, and J.L. McGrath, Biophysical Journal 95, 4934-4947, 2008.
“Computational and experimental analysis of diffusive molecular separations with molecularly thin nanoporous membranes,” J.L. Snyder, A. Clark, Jr., D.Z. Fang, T.R. Gaborski, C.C. Striemer, P.M. Fauchet, and J.L. McGrath, Journal of Membrane Science, 369, 119-129, 2011.