Mark Sussman

Professor of Mathematics
Associate Editor, Journal of Computational Physics
VITA
Links to the PhD Thesis/honors undergraduate thesis for previous students
list of publications, available preprints
Department of Mathematics
Florida State University
sussman@math.fsu.edu
Department of Mathematics, Florida State University, Tallahassee, FL 32306
Office: Love 002C, phone: 412-818-9932, fax: 850-644-4053

The research of myself and the students that I advise is at the intersection of Mathematics, Computer Science, Physics, and Engineering. Below are many examples of the applicability of our research on important problems in science and industry.

January 6, 2009, career in Math rated BEST job! (Wall Street Journal, Careers)

United States Patent and Trademark Office

Canvas

Zoom for FSU instructors (select "Zoom")

FSU math zoom quick hints

Qualtrics for FSU instructors

information for campus computer labs

Alphabetical vi quick reference

Calculus Study tips (by: D.A. Kouba, UCD) , tips for free Fortran windows environment on windows. Inexpensive integrated development environment tools for Fortran (windows/MAC) tips for plotting data.

For the research associated with the following illustrations of drops in microfluidic devices, atomization of liquid jets, ship waves, hydrodynamics for flow past a whale, bubbles and drops in complex fluids, hydrodynamics of flow past a human swimmer, flow in a beating heart, and the effect of underwater explosions/implosions on solid platforms, the support of the NSF DMS program, ONR, UTRC, SANDIA labs, SAIC, Xerox, Kodak, and Weidlinger Associates is acknowledged.

Simulations of droplet formation in microfluidic devices.

Three Dimensional Numerical simulation of a 271 micrometer diameter ethanol drop impacting a 30 micrometer ethanol film. Results are in agreement with the experimental results reported by Yarin and Weiss (1995). The Reynolds number is 2227 and the Weber number is 1500. For details of this simulation and more, please see: Yisen Guo, Yongsheng Lian and Mark Sussman, Physics of Fluids, vol 28, 073303 (2016).

Numerical simulation of the head-on collision of a diesel oil drop (cyan) with a water drop (gold) and resulting encapsulation. Weber Number equals 9.6, 45.3, and 58.9 for the top, middle and bottom rows respectively. The computational grid is a block structured dynamic adaptive mesh with 48x288 coarse grid cells and 2 additional levels of adaptivity (effective fine grid resolution is 192x1152, 148 cells per initial drop diameter). Our results are in agreement with the experimental results from R.H. Chen, C.T. Chen, Experiments in Fluids, volume 41, p. 453-461 (2006). We capture the correct transition point for reflexive separation. Simulations are done in 3d axisymmetric (RZ) coordinate system. (work with G. Li, Y. Lian, Y. Guo, M. Jemison, T. Helms, M. Arienti)

Numerical simulation of multiphase flow (click picture for animation): Bending laminar liquid jet in high speed gas cross-flow; velocity ratio 10:1, density ratio 1:1000. Adaptive mesh refinement and Parallel computing. Base grid: 256x128x128 plus 3 levels of refinement. (with M. Arienti (UTRC), V. Mihalef (Rutgers) , M. Soteriou (UTRC)).

Comparison with experiment, which is which!

More comparison with experiment; density ratio is 1:1000, velocity ratio 10:1.

Bending turbulent liquid jet in high speed gas cross-flow; velocity ratio 7:1, density ratio 1:1000. Dynamic Adaptive mesh refinement and parallel computing techniques are used to accelerate the simulation. This simulation was carried out on a single 4 core computer. Base grid 64x16x32 (symmetry assumed at y=0) plus 4 levels of refinement. Simulation uses the ``hybrid level set and volume constraint'' method for representing and updating the gas/liquid interface. The maximum grid size allowed is 16, and the blocking factor is 4. At t=0, there are 88 grids on the finest level containing 161856 cells. At t=1.2 ms, there are 993 grids on the finest level containing 1486656 cells. The pressure projection step consumes 2.1E-5 seconds per cell at t=0 and 3.5E-5 seconds per cell at t=1.2. (with Y. Wang, S. Simakhina, A. Duffy, X. Li (UTRC), H. Gao (UTRC), M. Soteriou (UTRC)).

Illustration of hierarchical grid structure at t=1.2, gas/liquid interface, and velocity along the y=0 slice.

Animation of turbulent jet in a cross flow time up to 1.30ms. (animation is the concatenation of 4 parts)

Numerical simulation of flow past an animated North America Right Whale (click picture for animation). Two levels of adaptivity. This is work with Anna McGregor, Dr. Ross McGregor, Dr. Doug Nowacek from the Duke Marine Labs, Austen Duffy (graduate student, Florida State applied math), and Dr. Gorden Erlebacher (Florida State, Department of Scientific Computing).

Numerical simulation of droplet formation in a T-junction (click picture for animation). Continuous phase fluid travels 10 times faster than the "droplet" fluid. Square cross section 1E-4 cm^2. Effective fine grid resolution: 256x64x32. Contact angle: 135 degrees. Size of the droplets consistently have an effective diameter of 0.011cm which is in agreement with experiment and simulation reported by van der Graaf et al, Langmuir 2006, 22(9), 4144-4152 (continuous phase flow rate v_max=8.3cm/s). This work with Dr. Austen Duffy (recent PhD, Florida State applied math), and Dr. Michael Roper (Florida State, Department of chemistry and biochemistry).

Numerical simulation of droplet formation in a head-on microfluidic device (click picture for animation). Continuous phase fluid (water) enters from the bottom (Q=0.05 micro-liter/min) and dispersed phase fluid (oil) enters from the top (Q=0.1 micro-liter/min). Channel height is 10 microns and channel width is 30 microns. Contact angle is prescribed at 135 degrees. The numerical algorithm predicts a droplet length of 162 microns. Experiments from Figure 7 of Shui et al (Lab on a chip, 2009) show droplets with length 143 microns. Effective fine grid resolution: 128x32x4. This work with Dr. Austen Duffy (recent PhD, Florida State applied math), Matt Jemison (PhD student, Florida State applied math) and Dr. Michael Roper (Florida State, Department of chemistry and biochemistry).

Numerical simulation together with experiments (conducted in M. Ropers' lab) for droplet formation in a T-junction (click picture for animation). Continuous phase fluid (oil) enters from the left (Q=1.3 micro-liter/min) and dispersed phase fluid (water) enters from the top (Q=0.3 micro-liter/min). The channel has a trapezoidal cross section with dimensions close to 185 microns wide by 37 microns high. The contact angle is prescribed at 135 degrees. The numerical algorithm predicts a droplet length of 415 microns. Experiments show a droplet length of 444 microns. Effective fine grid resolution: 128x64x4. This work with Dr. Austen Duffy (recent PhD, Florida State applied math), and Dr. Michael Roper (Florida State, Department of chemistry and biochemistry).

Numerical simulation of vortex rings of a heavy drop falling in a viscous liquid. Simulations agree with experiments reported by Baumann, Joseph, Mohr and Renardy, Phys. of Fluids A, volume 4, p. 567-580 (1992)! (with M. Ohta, Y. Akama, and Y. Yoshida (Muroran Institute of Technology))

Numerical simulation of unstable light drops rising in a viscous liquid. Simulations agree with experiments! (with M. Ohta, Y. Akama, Y. Yoshida (Muroran Institute of Technology))

Morton number=0.2, Eotvos number=52.8

Morton number=0.0002, Eotvos number=19.2

Morton number=0.0002, Eotvos number=21.8

Morton number=0.0002, Eotvos number=22.9

Morton number=2.2, Eotvos number=70.1

Numerical simulation of multiphase flow: Animation and Control of Breaking Waves (with V. Mihalef and D. Metaxas, Rutgers)

Numerical simulation of multiphase flow (click picture for animation): Boiling and solid-fluid interaction (with V. Mihalef, S. Kadioglu, B. Unlusu, D. Metaxas, M.Y. Hussaini)

For this boiling movie, the temperature of the solid changes from hot to cold (click picture for animation).

Numerical simulation of multiphase flow (click picture for animation): solid-fluid interaction, contact line dynamics (with V. Mihalef, S. Kadioglu, D. Metaxas)

Numerical simulation of multiphase flow (click picture for animation): solid-fluid interaction (with V. Mihalef, S. Kadioglu, D. Metaxas)

Numerical simulation of multiphase flow (click picture for animation): underwater explosion, shock waves and solid-fluid interaction (with S. Kadioglu, D. Rubin, J. Wright)

Numerical simulation of multiphase flow (click picture for animation): underwater explosion, shock waves and cavitation effects (with S. Kadioglu, D. Rubin, J. Wright)

Numerical simulation of multiphase flow (click pictures for animation): underwater implosion, shock waves and solid-fluid interaction (with S. Kadioglu, D. Rubin, J. Wright)