Interim Chair and Professor
Ph.D., University of Texas at Austin,1991
Low-gravity fluid physics
One of the most striking and beautiful behaviorsin the world around us is the way systems in nature take their shape.This process of pattern formation is exhibited in a wide range ofcases, including: sand, flames, lasers, fracture, river networks, chemical reactions, and growing organisms (morphogenesis). In many instances, the patterns share common features governed by the physics ofnonlinear systems. The goal of our work is to understand the fundamentallyimportant behaviors exhibited by pattern formingsystems.
Our studies presently focus on experiments in the emerging area of low-gravity fluid physics. Experiments in fluids provide the best understood pattern forming examples since the governing equations and control parameters of fluid systems are known, experimental conditions can be well-defined and easilycontrolled, and the patterns can be readily visualized.Low gravity fluid physics explores novel phenomena that arisewhen the influence of gravity (e.g. buoyancy, sedimentation) issuppressed. Our NASA-sponsored studies currently provide terrestrial scientific support for future space experiments.
One area under investigation is the dynamics of flow driven by interfacial (surface tension) forces. These flows exhibit a rich variety of patterns; we seek to understand how the cellular patterns in these flowsbecome disordered as the system is driven further from thermodynamic equilibrium. We are interested in characterizing the effects of the patterns on transport and mixing, and we are exploring ways to extend techniques of "controlling chaos" to the spatially extended structures that arise in these experiments.A second area under study is pattern formation driven by noise.Most work on nonequilibrium phenomena has concerned systems with deterministic (time-independent or time-periodic) driving.We are studying flows driven by acceleration fluctuations; a narrow-band noise model determines the acceleration profile,permitting the driving to be varied smoothly from a purely deterministicto a completely stochastic regime. These studies model the effects of"g-jitter" that arise in space experiments.
In the future, we plan to initiate investigations of pattern formation in material science and biology; potential areas of study includeinstabilities and defects in thin organic films and the role of spatiotemporalchaos in cell differentiation.
- "Complex-ordered patterns in shaken convection", J.L. Rogers, Werner Pesch, Oliver Brausch, and M.F. Schatz; Physical Review E 71, 066214, June (2005).
- "Secondary Instabilities of Hexagonal Patterns in a Bénard-Marangoni Convection Experiment," D. Semwogerere and M.F. Schatz, Phys. Rev. Lett 93, 124502 (2004).
- "Optical Manipulation of Microscale Fluid Flow," N. Garnier, R. O. Grigoriev, and M.F. Schatz, Phys. Rev. Lett. 054501 (2003).
- "Pattern Formation in Vertically-Oscillated Convection," J. L. Rogers, W. Pesch, and M.F. Schatz, Nonlinearity, C1 (2003).
- "Evolution of Hexagonal Patterns from Controlled Initial Conditions in a Benard-Marangoni Convection Experiment", D. Semwogerere and M. F. Schatz, Phys. Rev. Lett. 88, 054501 (2002).
- " Huygens' Clocks", M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, Proc. R. Soc. Lond. A 458, 563-579 (2002).
- "Convective Instability of Strained Layer Step-Flow", N. Israeli, D. Kandel, M. F. Schatz, and A. Zangwill, Surface Science 494, L735-L740 (2001).
- "Experiments on Thermocapillary Instabilities", M. F. Schatz and G. P. Neitzel, Annum. Rev. Fluid Mech. 33, 93-127 (2001).
- "Superlattice Patterns in Vertically Oscillated Rayleigh-Bénard Convection", J.L. Rogers, M.F. Schatz, O. Brausch, and W. Pesch, Phys. Rev. Lett. 85, 4281 (2000).
- "Measurements of Surface-Wave-Damping in a Container", D.R. Howell, B. Buhrow, T. Heath, C. McKenna, W. Hwong and M.F. Schatz, Phys. Fluids, 12, 322 (2000).
- "Rayleigh-Bénard Convection in a Vertically Oscillated Fluid Layer", J.L. Rogers, M.F. Schatz, J.L. Bougie and J.B. Swift, Phys. Rev. Lett. 84, 87 (2000).
- "Long-wavelength instability in surface-tension-driven Benard convection," S. J. VanHook, M. F.Schatz, J. B. Swift, W. D. McCormick and H. L. Swinney,Physical Review Letters, 75, 4397 (1995).
- "Onset of surface-tension-driven Benard convection," M. F. Schatz, S. J. VanHook, J. B. Swift, W. D. McCormick and H. L.Swinney, Physical Review Letters, 75, 1938 (1995).
- "Instability in a spatiallyperiodic open flow," M. F. Schatz, D. Barkley, and H. L. Swinney, Physics of Fluids, 7, 344 (1995).
- "Purification of silicone oils for fluid experiments," M. F. Schatz and K. Howden, Experiments in Fluids, 19, 359 (1995).
- "Secondary instability in plane channel flowwith spatially periodic perturbations," M. F. Schatz and H. L. Swinney, Physical Review Letters, 69, 434 (1992).