Jerry P. Gollub

My research is in the general area of Nonlinear Physics, which is concerned with the mesoscopic and macroscopic behavior of complex systems. Often these systems are described by nonlinear partial differential equations such as the Navier-Stokes equations of fluid motion. My group has conducted experimental work on the following topics over the years: hydrodynamic instabilities and the transition to chaos and turbulence in fluids; the morphology of growing crystals; the dynamics of nonlinear waves; turbulent convection induced by thermal gradients; thin film flows; and frictional dynamics. Our current projects include spatiotemporal (or space-time) chaos, mixing in fluids, and granular flows. Many Penn students have participated in these projects.

Spatiotemporal chaos: Space-time chaos in extended systems often results from hydrodynamic instabilities. Statistical methods can be effectively used to characterize the nature of these fluctuations and to compare them with theoretical predictions. Recent work in our group has centered on surface waves and on rotating film flows. We discovered that the time averages of chaotic patterns can be strikingly regular. We also discovered novel forms of spatiotemporal chaos, including a localized state in which ordered and fluctuating disordered domains coexist. One current project is concerned with the chaotic breakdown of a quasicrystalline wave pattern that is similar to a 12-fold solid state quasicrystal.

Mixing in fluids: The processes leading to mixing and dispersal of impurities or tracers in hydrodynamic flows are fundamental to many geophysical phenomena. The chaotic stretching and folding of fluid elements can lead to variations on scales much finer than the smallest scales of the velocity field. We are studying these fine structures in two-dimensional turbulence created by magnetic forces acting on a conducting fluid. By also measuring the evolving velocity field, we hope to understand the mixing process. Results to date show strong deviations from the spectral properties predicted by a widely accepted theory.

Granular flows: Understanding the flow of granular materials such as sand is a challenging problem because there are no generally accepted equations of motion. The inelasticity of the collisions that occur between particles is a crucial element in understanding granular flows. The collision rate between particles can even diverge to infinity (for hard particles)! We are studying the way in which inelastic collisions give rise to clustering of particles during flow. In another experiment, we are investigating the frictional forces within a granular layer when it is subjected to a shear force. These phenomena are possibly relevant to earthquake phenomena.

For additional information concerning research projects, please see: http://www. haverford.edu/physics-astro/Gollub/Gollub.html

Positions Held

• John and Barbara Bush Professor of Physics at Haverford College
• Member of the National Academy of Sciences
• Fellow of the American Academy of Arts and Sciences
• Adjunct Professor of Physics at University of Pennsylvania
• Member of the Graduate Group in Mechanical Engineering and Applied= Mechanics, Penn
• Advisory Board of the National Science Resources Center, National Academy of Sciences
• Boards of Editors: Nonlinearity ; Journal of Nonlinear Science (1990-93); Physical Review A (1986-89), and American Journal of Physics (1985-88)
• General Councillor of the American Physical Society (1992-1995)
• Visiting Professor at Paris VII and Ecole Normale (1991 and 1985)
• Provost of Haverford College (1988-90)
• Project Director of the Mid-Atlantic Pew Science Program in Undergraduate Education (1987-90).
• Secretary-Treasurer, Division of Fluid Dynamics of the APS (1985-88)

Selected Publications

1. "Hydrodynamic Instabilities and the Transition to Turbulence," H.L. Swinney and J.P. Gollub, Physics Today (August 1978).
2. "Many Routes to Turbulent Convection," J.P. Gollub and S.V. Benson, J. Fluid Mech. 100, 449 (1980).
3. "Commensurate and Incommensurate Structures in a Nonequilibrium System," M.L. Lowe, J.P. Gollub, and T.C. Lubensky, Phys. Rev. Lett. 51, 786 (1983).
4. "Pattern Competition Leads to Chaos," S. Ciliberto and J.P. Gollub, Phys. Rev. Lett. 52, 922 (1984).
5. "Dendritic and Fractal Patterns in Electrolytic Metal Deposits," Y. Sawada, A. Dougherty, and J.P. Gollub, Phys. Rev. Lett. 56, 1260 (1986).
6. "Wave-Vector Field of Convective Flow Patterns," M. S. Heutmaker and J. P. Gollub, Physical Review A 35, 242 (1987).
7. "Development of Sidebranching in Dendritic Crystal Growth," A. Dougherty, P. D. Kaplan, and J. P. Gollub, Phys. Rev. Lett. 58, 1652 (1987).
8. "Chaotic Particle Transport in Rayleigh-Benard Convection," T.H. Solomon and J.P. Gollub, Phys. Rev. A 38, 6280 (1988).
9. "Steady State Dendritic Growth of NH4Br from Solution," A. Dougherty and J.P. Gollub, Phys. Rev. A. 38, 3043 (1988).
10. "Surface Wave Mode Interactions: Effects of Symmetry and Degeneracy," Simonelli and J. P. Gollub, J. Fluid Mech. 199, 471 (1989).
11. "Self-Affine Fractal Interfaces from Immiscible Displacement in Porous Media," M.A. Rubio, C. Edwards, A. Dougherty, and J.P. Gollub, Phys. Rev. Lett. 63, 1685 (1989).
12. Chaotic Dynamics: An Introduction, G.L. Baker and J.P. Gollub, (Cambridge University Press, 1990 and 1996). (Textbook)
13. "Transport by Capillary Waves, Part II: Scalar Dispersion and the Structure of the Concentration field," R. Ramshankar and J.P. Gollub, Phys. Fluids A 3, 1344 (1991).
14. "Fluctuations and Transport in a Stirred Fluid with a Mean Gradient," J.P. Gollub, J. Clark, M. Gharib, B. Lane, and O.N. Mesquita, Phys. Rev. Lett. 67, 3507 (1991).
15. "Geometry of Isothermal and Isoconcentration Surfaces in Thermal Turbulence," B.J. Gluckman, H. Willaime, and J.P. Gollub, Phys. Fluids A 5, 647 (1993).
16. "Spatiotemporal Dynamics due to Stick-Slip Friction in an Elastic Membrane System" D.P. Vallette and J.P. Gollub, Phys. Rev. A 47, 820 (1993).
17. "Transition to Spatiotemporal Chaos via Spatially Subharmonic Oscillations of a Periodic Front," D. P. Vallette, W.S. Edwards, and J.P. Gollub, Phys. Rev. E 49, R4783-86 (1994).
18. "Three Dimensional Instabilities of Film Flows," J. Liu, J.B. Schneider, and J.P. Gollub, Phys. Fluids A 7, 55-67 (1995).
19. "Statistical Studies of Chaotic Wave Patterns", B. J. Gluckman, C.B. Arnold, and J.P. Gollub, Phys. Rev. E 51, 1128-51 (1995).
20. "Order and Disorder in Fluid Motion", J.P. Gollub, Proc. Nat. Acad. Sci. 92, 6705-11 (1995). (A review of our work over an extended period of time.)
21. "Localized Spatiotemporal Chaos in Surface Waves", A. Kudrolli and J.P. Gollub, Phys. Rev. E 54, R1052-55, 1996.
22. "Inverting Chaos: Extracting System Parameters from Experimental Data", L. Baker, J.P. Gollub, and J.A. Blackburn, submittedto Chaos.
23. "Mixing of a Passive Scalar in Magnetically Forced Two-Dimensional Turbulence", Williams, D. Marteau, and J.P. Gollub, submitted to Physics of Fluids, 1996.
24. "Cluster Formation due to Collisions in Granular Material", Kudrolli, M. Wolpert, and J.P. Gollub, submitted to Physical Review Letters, 1996.