About Me

Michael Siegel joined the NJIT faculty as an Assistant Professor of Mathematics in 1995, advanced to the rank of Associate Professor in 1998, and on to Professor of Mathematics in 2005. He was also Associate Director and Director of NJIT’s Center for Applied Mathematics and Statistics (CAMS) for 13 years. He is currently the Associate Director for Graduate Studies in the Department of Mathematical Sciences. He is also the university Faculty Athletics Representative (FAR).

Siegel earned his BS in Physics and in Mathematics from Duke University in 1984, and later earned PhD in Mathematics (1989) from New York University’s Courant Institute of Mathematical Sciences. He was also a graduate student in the PhD Program in Physics at Massachusetts Institute of Technology in 1986-87.

In addition to his posts at NJIT, he has been a visiting researcher at the Courant Institute of Mathematical Sciences at NYU and at Oxford University. He had an appointment as Wallenberg Guest Professor at KTH, Stockholm in 2015-2016. Prior to NJIT, he held a National Science Foundation (NSF) Postdoctoral Fellowship and was a Postdoctoral Research Fellow at Ohio State University. He also served as van Karman Instructor in Applied Mathematics at the California Institute of Technology from 1989 to 1991.

Siegel served on the editorial board of the SIAM Journal of Applied Math for nine years. He currently is an Associate Editor for the Journal of Engineering Mathematics.

Siegel has worked with multiple grants, including being a PI or Co-PI on over 20 grants from the NSF since 1996. His research is focused on the analysis and numerical computation of moving boundary problems that arise in fluid mechanics, materials science, and biology. He is the recipient of the NJIT CSLA Excellence in Research Award.

Siegel earned his BS in Physics and in Mathematics from Duke University in 1984, and later earned PhD in Mathematics (1989) from New York University’s Courant Institute of Mathematical Sciences. He was also a graduate student in the PhD Program in Physics at Massachusetts Institute of Technology in 1986-87.

In addition to his posts at NJIT, he has been a visiting researcher at the Courant Institute of Mathematical Sciences at NYU and at Oxford University. He had an appointment as Wallenberg Guest Professor at KTH, Stockholm in 2015-2016. Prior to NJIT, he held a National Science Foundation (NSF) Postdoctoral Fellowship and was a Postdoctoral Research Fellow at Ohio State University. He also served as van Karman Instructor in Applied Mathematics at the California Institute of Technology from 1989 to 1991.

Siegel served on the editorial board of the SIAM Journal of Applied Math for nine years. He currently is an Associate Editor for the Journal of Engineering Mathematics.

Siegel has worked with multiple grants, including being a PI or Co-PI on over 20 grants from the NSF since 1996. His research is focused on the analysis and numerical computation of moving boundary problems that arise in fluid mechanics, materials science, and biology. He is the recipient of the NJIT CSLA Excellence in Research Award.

Education

Ph.D.; New York University; ; 1989

B.S.; Duke University; ; 1984

B.S.; Duke University; ; 1984

2023 Spring Courses

MATH 790D - DOCT DISSERTATION & RES

MATH 790C - DOCT DISSERTATION & RES

MATH 790B - DOCT DISSERTATION & RES

MATH 792B - PRE DOCTORAL RESEARCH

MATH 453 - HIGH-PERF NUMERICAL COMPUTING

MATH 790A - DOCT DISSERTATION & RES

MATH 790E - DOCTORAL DISSERTATION

MATH 790C - DOCT DISSERTATION & RES

MATH 790B - DOCT DISSERTATION & RES

MATH 792B - PRE DOCTORAL RESEARCH

MATH 453 - HIGH-PERF NUMERICAL COMPUTING

MATH 790A - DOCT DISSERTATION & RES

MATH 790E - DOCTORAL DISSERTATION

Past Courses

MATH 332: INTRO COMPLEX VARIABLES

MATH 391: NUMERICAL LINEAR ALGEBRA

MATH 451: METHODS APPL MATH II

MATH 453: HIGH-PERF NUMERICAL COMPUTING

MATH 611: NUMER METH FOR COMPUTATN

MATH 645: ANALYSIS

MATH 689: ADV APPLIED MATH II

MATH 690: ADV APPLIED MATH III

MATH 712: NUMERICAL METHODS II

MATH 713: ADVANCED SCIENTIFIC COMPUTING

MATH 715: MATHEMATICAL FLUID DYNAMICS I

MATH 716: MATHEMATICAL FLUID DYNAMICS II

MATH 745: MATHMATICAL ANALYSIS II

MATH 767: FAST NUMERICAL ALGORITHMS

MATH 791: GRADUATE SEMINAR

MATH 391: NUMERICAL LINEAR ALGEBRA

MATH 451: METHODS APPL MATH II

MATH 453: HIGH-PERF NUMERICAL COMPUTING

MATH 611: NUMER METH FOR COMPUTATN

MATH 645: ANALYSIS

MATH 689: ADV APPLIED MATH II

MATH 690: ADV APPLIED MATH III

MATH 712: NUMERICAL METHODS II

MATH 713: ADVANCED SCIENTIFIC COMPUTING

MATH 715: MATHEMATICAL FLUID DYNAMICS I

MATH 716: MATHEMATICAL FLUID DYNAMICS II

MATH 745: MATHMATICAL ANALYSIS II

MATH 767: FAST NUMERICAL ALGORITHMS

MATH 791: GRADUATE SEMINAR

Research Interests

- Applied mathematics, analysis, and scientific computation for nonlinear PDE's and integro-differential equations, especially as a model for free and moving boundary problems in fluid dynamics.

- Moving boundary problems in materials science and biology

- Well-posedness theory and singularity formation

- Numerical analysis

- Moving boundary problems in materials science and biology

- Well-posedness theory and singularity formation

- Numerical analysis

In Progress

**Analysis and computations of moving boundary problems**

Michael Siegel's research is primarily on the mathematical analysis and numerical computation of moving boundary problems in fluid dynamics, materials science, and biology. He is developing new boundary integral algorithms for the fast and accurate numerical computation of moving boundaries. This includes multiscale methods for the computation of interfacial flow with surfactant, and electrokinetic flow. He has also developed well-posedness theory for moving boundary problems, and investigated singularity formation.

Technical Report

Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains

arXiv preprint arXiv:2207.07548, July (3rd Quarter/Summer) 2022

Convergence of the boundary integral method for interfacial Stokes flow

Arrive preprint arXiv:2105.07056, May 2021

arXiv preprint arXiv:2207.07548, July (3rd Quarter/Summer) 2022

Convergence of the boundary integral method for interfacial Stokes flow

Arrive preprint arXiv:2105.07056, May 2021

Journal Article

Ma, Manman, & Booty, Michael, & Siegel, Michael (2022). A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions.

Lushnikov, Pavel, & Silantyev, Denis , & Siegel, Michael (2021). Collapse vs. blow up and global existence in the generalized Constantin-Lax-Majda equation.

Yariv, Ehud, & Siegel, Michael (2019). Rotation of a superhydrophobic cylinder in a viscous liquid.

Palsson, Sara, & Siegel, Michael , & Tornberg, Anna-Karin (2019). Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow.

Wang, Qiming, & Ma, Manman, & Siegel, Michael (2019). Deformation and stability of a viscous electrolyte drop in a uniform electric field.

*Journal of Fluid Mechanics, Cambridge University Press*,*943, A47*, 44.Lushnikov, Pavel, & Silantyev, Denis , & Siegel, Michael (2021). Collapse vs. blow up and global existence in the generalized Constantin-Lax-Majda equation.

*Journal of Nonlinear Science*,*31*(5), 56 pages.Yariv, Ehud, & Siegel, Michael (2019). Rotation of a superhydrophobic cylinder in a viscous liquid.

*Journal of Fluid Mechanics*,*880*, R4 1-13 (13 pages).Palsson, Sara, & Siegel, Michael , & Tornberg, Anna-Karin (2019). Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow.

*Journal of Computational Physics*,*386*, 218-247.Wang, Qiming, & Ma, Manman, & Siegel, Michael (2019). Deformation and stability of a viscous electrolyte drop in a uniform electric field.

*Physical Review Fluids*,*4*, 053702. SHOW MORE

Wrobel, Jacek, & Booty, Michael, & Siegel, Michael, & Wang, Qiming (2018). Simulation of surfactant-mediated tipstreaming in a flow-focusing geometry.

Siegel, Michael , & Tornberg, Anna-Karin (2018). A local target specific quadrature by expansion method for evaluation of layer potentials in 3D.

Ambrose, David, & Liu, Yang, & Siegel, Michael (2017). Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension.

Ambrose, David, & Siegel, Michael (2017). Well-posedness of two-dimensional hydroelastic waves.

Wang, Qiming, & Siegel, Michael, & Booty, Michael (2014). Numerical simulation of drop and bubble dynamics with soluble surfactant.

Ambrose, David, & Siegel, Michael, & Tlupova, Svetlana (2013). A small-scale decomposition for 3D boundary integral computations with surface tension.

Malakuti, Kamyar, & Caflisch, Russel, & Siegel, Michael (2013). Detection of complex singularities for a function of several variables.

Booty, Michael, & Papageorgiou, Demetrios, & Siegel, Michael, & Wang, Qiming (2013). Long-wave equations and direct simulations for the breakup of a viscous fluid thread surrounded by an immiscible viscous fluid.

Xu, Kuan, & Booty, Michael, & Siegel, Michael (2013). Analytical and computational methods for two-phase flow with soluble surfactant.

Higley, Michael, & Siegel, Michael, & Booty, Michael (2012). Semi-analytic solutions for 2D elastic capsules in Stokes flow.

Chou, Tom, & Siegel, Michael (2012). A mechanical model of retinal detachment.

Ambrose, David, & Siegel, Michael (2012). A non-stiff boundary integral method for 3D porous media flow with surface tension.

Booty, Michael, & Siegel, Michael (2010). A hybrid numerical method for interfacial fluid flow with soluble surfactant .

Lott, Dawn, & Siegel, Michael, & Chaudhry, Hans, & Prestigiacomo, Charles (2009). Computational fluid dynamic simulation to assess flow characteristics of an in-vitro aneurysm model: A validation study.

Siegel, Michael, & Caflisch, Russel (2009). Calculation of complex singular solutions to the 3D incompressible Euler equations.

Young, Yuan-Nan, & Booty, Michael, & Siegel, Michael, & Li, Jie (2009). Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid.

Papageorgiou, Demetrious, & Kas-Danouche, Said, & Siegel, Michael (2009). Nonlinear interfacial stability of core-annular flows in the presence of surfactants.

Hameed, Mohammad, & Siegel, Michael, & Young, Yuan-Nan, & Li, Jie, & Booty, Michael, & Papageorgiou, Dimitri (2008). Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid.

*Physical Review Fluids*,*3*(11), 1-29.Siegel, Michael , & Tornberg, Anna-Karin (2018). A local target specific quadrature by expansion method for evaluation of layer potentials in 3D.

*Journal of Computational Physics*,*364*, 365-392 (27 pages).Ambrose, David, & Liu, Yang, & Siegel, Michael (2017). Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension.

*Mathematics of Computation*,*86*, 2745-2775.Ambrose, David, & Siegel, Michael (2017). Well-posedness of two-dimensional hydroelastic waves.

*Proceedings of the Royal Society of Edinburgh*,*147*(3), 529-570.Wang, Qiming, & Siegel, Michael, & Booty, Michael (2014). Numerical simulation of drop and bubble dynamics with soluble surfactant.

*Physics of Fluids*,*26*, 052102 (26 pages).Ambrose, David, & Siegel, Michael, & Tlupova, Svetlana (2013). A small-scale decomposition for 3D boundary integral computations with surface tension.

*Journal of Computational Physics*,*247*, 168-191.Malakuti, Kamyar, & Caflisch, Russel, & Siegel, Michael (2013). Detection of complex singularities for a function of several variables.

*IMA Journal of Applied Mathematics*,*78*(4), 714-728.Booty, Michael, & Papageorgiou, Demetrios, & Siegel, Michael, & Wang, Qiming (2013). Long-wave equations and direct simulations for the breakup of a viscous fluid thread surrounded by an immiscible viscous fluid.

*IMA Journal of Applied Mathematics*,Xu, Kuan, & Booty, Michael, & Siegel, Michael (2013). Analytical and computational methods for two-phase flow with soluble surfactant.

*SIAM Journal on Applied Mathematics*,*73*(1), 523-548.Higley, Michael, & Siegel, Michael, & Booty, Michael (2012). Semi-analytic solutions for 2D elastic capsules in Stokes flow.

*Proceedings of the Royal Society A*,*468*, 2915-2938.Chou, Tom, & Siegel, Michael (2012). A mechanical model of retinal detachment.

*Physical Biology*,*9*, 046001 (9 pages).Ambrose, David, & Siegel, Michael (2012). A non-stiff boundary integral method for 3D porous media flow with surface tension.

*Mathematics and Computers in Simulation/Elsevier*,*82*(doi:10.1016/j.matcom.2010.05.018), 968-983.Booty, Michael, & Siegel, Michael (2010). A hybrid numerical method for interfacial fluid flow with soluble surfactant .

*Journal of Computational Physics, Elsevier*,*229*, 3864-3883.Lott, Dawn, & Siegel, Michael, & Chaudhry, Hans, & Prestigiacomo, Charles (2009). Computational fluid dynamic simulation to assess flow characteristics of an in-vitro aneurysm model: A validation study.

*Journal of Neurointerventional Surgery/British Medical Journals*,*1*, 100-107.Siegel, Michael, & Caflisch, Russel (2009). Calculation of complex singular solutions to the 3D incompressible Euler equations.

*Physica D*,*238*, 2368-2379.Young, Yuan-Nan, & Booty, Michael, & Siegel, Michael, & Li, Jie (2009). Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid.

*Physics of Fluids*,*21*, 072105.Papageorgiou, Demetrious, & Kas-Danouche, Said, & Siegel, Michael (2009). Nonlinear interfacial stability of core-annular flows in the presence of surfactants.

*Journal of Fluid Mechanics/Cambridge University Press*,*626*, 415-448.Hameed, Mohammad, & Siegel, Michael, & Young, Yuan-Nan, & Li, Jie, & Booty, Michael, & Papageorgiou, Dimitri (2008). Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid.

*Journal of Fluid Mechanics*,*594*, 307-340.COLLAPSE

Chapter

Booty, Michael, & Siegel, Michael, & Anna, Shelley (2015). A hybrid numerical method for interfacial flow with soluble surfactant and its application to an experiment in microfluidic tipstreaming, M.T. Rahni, M. Karbaschi, and R. Miller (Eds.),

*CRC Press*. Boca Raton, Florida: CRC Press