# Michael Siegel

The research of Michael Siegel is focused on the analysis and numerical computation of moving boundary problems in fluid mechanics, materials science, and biology. His research interests include singularity formation on interfaces, the dynamics of drops and bubbles, and the development of numerical methods for interfacial flow with soluble surfactant. He is also developing efficient, nonstiff boundary integral methods for 3D interfacial flow with surface tension.

- PhD, Mathematics, New York University
- MS, Mathematics, New York University
- BS, Physics and Mathematics, Duke University

- NSF Postdoctoral Fellowship, 1992-95.
- NSF Grant, Surfactant Effects on Viscous Fingering, 1997-2001.
- NSF Grant, Analysis and Numerical Computations of Moving Boundaries in Materials Science and Fluid Dynamics, 2001-2005.
- NSF Grant, Focused Research Group: Singularity Formation for the Three-Dimensional Euler Equations and Related Problems (with R. Caflisch, T. Hou and D. Pullin), 2004-2007.
- NSF Grant, Major Research Instrumentation: Acquisition of a Computer Cluster for the Center of Applied Mathematics and Statistics at NJIT (with D. Ahluwalia and M. Ma), 2004-2007.
- NSF Grant, Equipment and Modules for a Capstone Course in Applied Mathematics (with M. Booty, B. Bukiet, L. Kondic, D. Goldman)

- Moving boundary problems in fluid mechanics, materials science, and physiology
- Scientific computation

The research of Michael Siegel is focused on the analysis and numerical computation of moving boundary problems that arise in fluid mechanics, materials science, and physiology. His research in fluid dynamics covers singularity formation on interfaces for inviscid and low Reynolds number (Stokes) flow, the dynamics of drops and bubbles (including the influence of surfactant), and effect of small regularization--such as surface tension--on mathematically ill-posed interfacial flow problems. His studies in materials science primarily involve crystal growth and diffusion controlled moving boundary problems. In physiology, he has studied optimal suturing patterns for skin wounds and formulated models for determining the stress and strain distribution in the heart wall that occur due to changes in heart geometry.

- Singular Perturbation of Smoothly Evolving Hele-Shaw Solutions, (with S. Tanveer), Phys. Rev. Lett. (76), p.419, 1996.
- Singular Effects of Surface Tension in Evolving Hele-Shaw Solutions," (with S. Tanveer and W. Dai), J. Fluid Mech. (323), p.201, 1996.
- Optimal Patterns for Suturing Wounds," (with H. Chaudhry, B. Bukiet, T. Findley, A. Ritter, N. Guzelszu), J. Biomech. (31), p. 101, 1998.
- Surfactant Effects in Steady, Bursting and Cusping Bubbles in Two-Dimensional Stokes Flow, SIAM J. Appl. Math. (59), pp. 1998-2027, 1999.
- Cusp Formation for time-evolving bubbles in two-dimensional Stokes flow, J. Fluid Mech. (412), pp. 227-257, 2000.
- Persistence of memory in drop breakup: The breakdown of universality, (with P. Doshi, I. Cohen, W. W. Zhang, P. Howell, O. A. Basaran, S. Nagel), Science (302), pp. 1185-1188, 2003.
- Evolution of material voids for highly anisotropic surface energy, (with M. Miksis and P. Voorhees), J. Mech. Phys. Solids (52) 6, pp. 1319-1353, 2004.
- Global existence, singular solutions, and ill-posedness for the Muskat problem, (with R. E. Caflisch and S. D. Howison), Comm. Pure Appl. Math. (57) 10 pp. 1374-1411, 2004 (Copyright @ 2004, Wiley).

More information can be found in my Curriculum Vitae.