Alfred Clark, Jr. Professor Emeritus of Mechanical Engineering, Mathematics, and Biomedical Engineering Dept. Mechanical Engineering University of Rochester Rochester, NY 14627 (585) 275-4078 |

**Research Interests**

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; transport processes in various contexts including thermocline heat flow during the Pinatubo event, proton transport in fuel cells, diffusion in cell membranes, diffusion through nanoporous membranes, and laser heating of optical materials. For more detailed information, including publications, see my listing in the Department of Mechanical Engineering web pages.

**Teaching Interests**

My primary teaching interests over the years have been in engineering science and applied mathematics. Engineering courses I have taught include Statics (ME 120), Dynamics (ME121), Fluid Dynamics (ME 225), Thermodynamics (ME 123), Heat Transfer (ME 223), Mechanical Systems (ME 213), Compressible Flow (ME 436), and Incompressible Flow (ME 437). In recent years I have taught applied mathematics 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. Many 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 many additional Mathematica notebooks illustrating concepts in Fourier Series and boundary value problems, click here. For Mathematica tutorials click here. 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**

ME 163 - Applied Ordinary Differential Equations

ME 201 / MTH 281 - Applied Fourier Series and Boundary Value Problems

**Biographical Sketch**

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 (1971-72), and two 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.

**Other Interests**

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.

**Representative Publications**

Live links lead to download pages.

"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.

"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 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 , 1995, 2003, 2011, 2013.

“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.

“Highly Permeable Silicon Membranes for Shear Free Chemotaxis and Rapid Cell Labeling,” Henry H. Chung, Charles K. Chan, Tejas S. Khire, Graham A. Marsh, Alfred Clark Jr., Richard E. Waugh, and James L. McGrath, Lab on a Chip, **14**, 2456-2468, 2014.

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