Mark Sussman

Professor of Mathematics
Associate Editor, Journal of Computational Physics
Links to the PhD Thesis/honors undergraduate thesis for previous students
list of publications, available preprints
Department of Mathematics
Florida State University
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)

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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.

Good book for learning MATLAB: ``MATLAB guide,'' Higham, D.J. and Higham, N.J. (2005 second edition, 2017 third edition, SIAM book).

Numerical Renaissance, simulation, optimization, and control, by Thomas Bewley

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): 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)

Implosion with endcaps included... (click for animation)

Numerical simulation of multiphase flow (click for animation): milk-drop simulation (with V. Mihalef, D. Metaxas, E. Jimenez)

Numerical simulation of multiphase flow: computation of ship waves (with D. Dommermuth; visualized by K. Beason, CS)

Click here for more Movies of flow around a DDG 5415 Navy Ship. Visualization generated by Kevin Beason, CS department

Numerical simulation of multiphase flow: computation of microscale jetting in ink-jet device (with E.G. Puckett and J. Andrews)

Numerical simulation of multiphase flow: non-newtonian (Oldroyd-B) bubbles (with M. Ohta)

Numerical simulation of multiphase flow: wobbly bubble (with M. Ohta)

List of Publications, available preprints, available source code

Journal of Computational Physics (JCP) electronic submission system.

Links to others ...

VISIT (adaptive visualization tool)

Center for Computational Sciences and Engineering, Adaptive mesh methods (LBNL)

Applied Numerical Algorithms Group at LBNL (ANAG); Adaptive mesh methods, fluid/structure interaction

National Renewable Energy Laboratory (NREL); Computational Science.

UINTAH multiscale and multiphysics infrastructure for high performance computing systems.

Structured Adaptive Mesh Refinement Application Infrastructure, LLNL

UCLA Computational and Applied Math (CAM) reports.

Professor Stan Osher, level sets, shock capturing, image processing.

Professor Gerry Puckett, Free Surface modeling of jetting devices.

Google's self driving car.

Peter Mucha - Networks (evolutionary prisoner's dilemma, Community Structure, Medicine, and the Brain.)

Andrew Sommese, Professor Emeritus, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame. Numerical Algebraic Geometry, Homotopy Continuation Method.

Human Longevity INC. Human Genomics, Microbiome, and Stem Cell Therapies.

Aptina imaging.

SUSTAIN: SUrge-STructure-Atmosphere INteraction Facility

Arete Associates; remote sensing solutions.

CFD Research Corporation (CFDRC).

Weidlinger Associates, Applied science, structural integrity.

FARO 3D Measurement, Imaging and Realization Technology.

Ametek: manufactures electronic instruments and electromechanical devices.

Exa corporation. Numerical analysis solutions for the aircraft and automotive industry.

General Atomics: Energy, Defense, Transportation, Unmanned Aircraft Systems.

DynaFlow INC, Multimaterial flow simulation - Research and development. Cavitation phenomena.

AMTEC Modeling and Simulation: Missile systems, UAV/UGV ground systems, and more...


Tesla careers

Makani Power (now part of google): airborne wind power technology

ADINA - Numerical tools for analysis of fluid-structure interaction phenonmena (Automatic Dynamic Incremental Nonlinear Analysis)

Citilabs, traffic flow analysis.

SINTEF: Enabling Low-Emission LNG Systems

Professor Gabriel Weymouth. Nonlinear fluid/structure interactions, High energy breaking waves and air entrainment. "Lily Pad": interactive solid/fluid interaction code. Burst speed underwater vehicle inspired by the Octopus! Flapping Tidal Energy Generator!

Professor Bernhard Muller. CFD applied multiphase flow, fluid structure interaction, computational aeroacoustics, computational thermoacoustics, and low mach number flow

Professor Marilena Greco. Marine Hydrodynamics, CFD, nonlinear free-surface and multiphase flows, fluid-structure interaction, hydroelasticity.

Professor Gang Chen. Land use and climate change, water flow and physicochemical reactions in the porous media, environmental biotechnology, and surface chemistry.

Dr. Michel Bergmann. CFD applied multiphase flow, fluid structure interaction, self propelled swimmers, ship hydrodynamics.

Professor Nicholas Zabaras. Computational Science and Engineering Laboratory. Applied and basis research in the interface of computational mathematics, scientific computing, and materials.

Professor Yabe, Magnesium Civilization - ultimate renewable energy cycle, CIP method, Computational Physics, laser experiments.

Professor Xiao, Laboratory, CFD, Ocean/Atmosphere Simulations.

Dr. Kensuke Yokoi, Blood flow, Contact angle dynamics, splashing, atomization.

Professor Mitsuhiro Ohta, Fluids Engineering Laboratory, Tokushima University.

Professor Yongsheng Lian, Computational Thermi-Fluid Laboratory, University of Louisville.

Professor Qinghai Zhang, School of Mathematical Sciences, Zhejiang University, Hangzhou, China, numerical methods for deforming boundary problems, multiphase/multiphysics flows, mathematical biology.

Professor John Lowengrub, Center for Computational Microstructure, tumor growth, crystal growth,..

Professor Paul Yager, Microfluidics research

Professor Shelley Anna, microfluidics, interfacial fluid mechanics, surfactant transport

Professor Patricia McGuiggan, Adhesion, Friction, Wetting, Interfacial forces ...

Radhakrishnan Lab, Intracellular trafficking, computational structural biology, insilico oncology, targeted drug delivery

Brady Group, California Institute of Technology, Stokesian Dynamics, Complex fluids, interface between continuum mechanics and statistical mechanics

Golestanian Group, Oxford Physics, Condensed matter theory, soft and biological matter, microswimmers, stochastic swimmers

Professor Paul Atzberger, soft materials and complex fluids, molecular biology, microfluidic and nanofluidic devices

Max Planck Institute of Colloids and Interfaces

Professor Reinihard Lipowsky, Membranes and Vesicles, Interfacial Phenomena, Lines and Surfaces, Max Planck Institute

Professor John Bush, Geomphysical and Environmental Fluid Dynamics, Surface Tension-driven Phenomena, Biofluidynamics

Dr. Junseok Kim, phase field methods, adaptive Cahn-Hilliard methods.

Professor Ron Fedkiw, Level Sets, Computer animation, CFD.

Professor Joseph M. Teran, virtual surgery, computational biomechanics, multimaterial interaction.

Doug James, computer graphics, physically based animation, physically based sound rendering, haptic rendering, scientific computing (e.g. reduced order modeling algorithms)

Farhat Research group, aeroelasticity, fluid structure interaction, underwater explosions and implosions, underwater acoustics.

Dr. Mikhail Shashkov, LANL X-div, Moment of fluid, Remap, Mimetic methods

Consortium for advanced simulation of light water reactors (CASL)

Consortium for advanced research on transport of hydrocarbon in the environment (CARTHE)

Professor Thierry Coupez, Center for Material Forming, CEMEF-MINES ParisTech, injection molding, anistropic mesh refinement

Professor Frederic Gibou, Materials Science, Image Segmentation, CFD.

Dr. M. Bussmann, spray based processes, particle deposition and coating processes, control of boiler fouling, wetting and dewetting phenomena.

Professor Marco Picasso, Newtonian and Non-Newtonian free surface flow

James Weir Fluids Laboratory, University of Strathclyde

Professor Tim Colonius, Cavitation and bubble dynamics in Shockwave Lithotripsy

Professor Greg Turk, Computer animation, contact line dynamics, solid fluid interaction.

Professor Suresh Menon, Georgia Tech. Computational Combustion Lab.

Professor Haibo Dong, University of Virginia. The secrets of Dragonfly Flight..

Professor James O'Brien, Computer animation and modeling.

Professor Zoran Popovic, animation and control.

Dr. Stephane Popinet, National Institue of water and atmospheric research, Wellington, New Zealand.

Dr. Viorel Mihalef, Computer animation, solid fluid interaction.

Professor Gretar Tryggvason, multiphase flow: bubbles, drops, sprays.

Professor J.A. Sethian, level set methods, fast marching methods, tumor modeling.

Professor Jonathan Shewchuk, Computational Geometry, ground motion in large basins during strong earthquakes.

Professor Stephen Wise, Tumor modeling.

Professor Stephane Zaleski, Numerical simulations of multi-phase flow.

Professor Arnold Reusken, Numerical simulations of multi-phase flow.

Professor Marsha Berger, 3d Cartesian grid methods for embedded boundaries.

Professor Leslie Greengard, fast multipole method.

Dr. Bjorn Sjogreen, CASC-LLNL, shock capturing methods, high order accurate finite difference methods.

Lecture notes developed by Dr. Bjorn Sjogreen

Dr. Bill Henshaw, CASC-LLNL, overlapping grids+AMR. Twilight zone method.

Aerojet: Company develops missile and space propulsion devices.

ESI group, crash safety simulations.

Dassault Systems: simulate cataract surgery, aerospace, automobile, predict drag on ships towing icebergs,...

Dr. Michael Frank, Sandia, Reversible Computing

NASA Quantum Computing Workshop

Dr. Dave Bacon: Lecture notes on Quantum Computing

FLUENT, CFD tools.

Cognitech, image restoration tools.

Professor John Stockie, Fuel cells, pulp fibers.

Molecular dynamics, crack propagation.

Professor Charles Peskin, Blood circulation and the heart.

Professor John Strain, Tree Based redistancing.

Professor Li-Tien Cheng, research on biomolecules, wave propagation, materials science, and image processing.

Professor Bin Dong, research on wavelets, optimization (compressed sensing), inverse problems and medical imaging, image processing and analysis.

Professor Steve Ruuth, PDEs on surfaces, segmentation on surfaces.

Professor Isaac Ginis, Hurricane tracking, coupled ocean atmosphere modeling.

Professor M.Y. Hussaini, Computational Science and Engineering.

SAIC, Numerical Flow Analysis Tool. Planing boat!

National Maritime Research Institute, CFD.

Deep water Engineering Research Center, Harbin Engineering University.

Institute of Aerospace Thermodynamics - droplet dynamics, jet break-up, evaportation.

Artium Technologies - Spray diagnostics, particulate monitoring, cloud research - aircraft icing and cloud droplet measurements.

School of Physics, Astronomy and Computational Sciences, George Mason University.

Italian Ship Model Basin (INSEAN).

Center for Turbulence Research

Group for Research and Applications in Statistical Physics (GRASP)

Professor Alain Berlemont, director of research for droplets and sprays at CORIA

Professor Osman Basaran, Reilly Professor of Fluid Mechanics, Purdue: surfactant effects, electro-separation, microfluidics, drops

Professor Alexander Oron, Associate Professor Technion: free boundary problems in hydrodynamics, instabilities of thin liquid films

Professor Nikiforakis, The laboratory of computational dynamics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Professor Changhong Hu, research on water waves and floating bodies

CSIRO manufacturating and infrastructure technology

"Why do Math?" web site! Medicine, Engineering, and many more examples

PETSc homepage; parallel libraries for solving PDEs

Overture: Object-oriented tools for solving PDEs in complex geometries

COMSOL unifying multiphysics simulation environment

Autodesk - CAD/CAM design software, 3D printing. Fire simulation and more!

Professor Randall J. LeVeque Books and Lecture Notes


Please send any comments, questions or requests for more information to me at

CODE.ORG great resource for learning how to program

CODECADEMY great resource for learning how to program

DISLIN scientific plotting software library - very powerful!

NCAR graphics


CYGWIN installation homepage


UWIN homepage



ECLIPSE - FREE IDEs for C++ and other languages

Tutorial for GIT version control program

Stanford free online course on machine learning

C++ tutorial

SEI CERT C++ Coding Standard: Rules for Developing Safe, Reliable, and Secure Systems in C++ (2016 Edition)

Fortran tutorial

Free Fortran for Windows + Fortran Documentation

Scientific Tools for Python

Pictures from trip to Muroran, Japan (2006)

online dictionary.

online Thesaurus.

Growing Citrus fruits in Tallahassee (Satsuma Orange, Kumquats, Calamondin Orange

Live dynamic wind map everywhere on the globe!

Tallahassee Morcom Aquatic Center.

Tomahawk Diving: Learn to dive from 1 or 3 meter springboards and up to 10 meter platforms.

Tallahassee windsurfing club (Shell Point Sailboard Club SPSC)

Shell point shore based tower Station SHPF1

Shell point tides (tides4fishing)

Shell point tides (tideschart)

NOAA Tallahassee Regional Airport weather observations

Arctic Sea Ice News

NOAA weather forecast and history

El nino southern oscillation (ENSO) outlook

An introduction to the El Nino Southern Oscillation

Negative versus Positive Lightning strikes

Hannah Park

Fernandina beach surf report (pipeline surfshop)

New Smyrna Beach Daily Surf Report

St. Augustine Surf Report

Mr. Surf's Panama City Surf Report

Fluid Surf Shop Fort Walton Beach Surf Report

Innerlight Surf Shop Pensacola Surf Report


Storm Surf predictions (buoy 41012 for Saint Augustine)

St George Island Surf Cam

Intel Higher Education Professor Programs

IBM's Brain-Inspired Computer Chip Comes from the Future (IEEE Spectrum)

Research opportunities: Defense Threat Reduction Agency (recent announcement)

Research opportunities: Aeronautics Research Mission Directorate

Research opportunities: Department of Energy Office of Science

Research opportunities: Office of Naval Research

Research opportunities: DESI "Laser-Powered Bat Drones"

Research opportunities: Army Research Laboratory

Research opportunities: Air Force Office of Scientific Research

Research opportunities: National Science Foundation

Research opportunities: Simons Fellows Program

Research opportunities: National Aeronautics and Space Administration

Research opportunities: National Institutes of Health

Research opportunities: Petroleum Research Fund

Research opportunities: W.M. Keck Foundation

Research opportunities: Chan Zuckerberg Initiative

Four properties of powerful teachers (Chronical of higher education)