Industrial Applied Mathematics in the Department of Mathematical Sciences

People

Faculty

• Richard Braun, Associate Professor
Nonlinear BVPs and free boundary problems in fluid mechanics and materials science.
• David Colton, Professor
Scattering and inverse scattering; numerical analysis.
• L. Pamela Cook, Professor
Fluid flow: Transonic and viscoelastic flows.
• Tobin Driscoll, Assistant Professor
High-order and spectral methods for differential equations;  radial basis functions;  numerical conformal mapping.
• David Edwards, Associate Professor
Asymptotic and perturbation methods in biochemical, chemical engineering, instrumentation (chemical reactions) and viscoelastic systems.
• George Hsiao, Professor
Boundary integral equations, finite element methods.  Applications in elasticity.
• Peter Monk, Professor
Finite element methods, applications in computational electromagnetism and inverse problems.
• David Olagunju, Associate Professor
Viscoelastic flows, stability, bifurcations, dynamical systems and combsution.
• John Pelesko, Assistant Professor
Perturbation methods, electromagnetics, MEMS and NEMS.
• Rakesh , Associate Professor
Scattering and inverse problems.
• Lou Rossi , Assistant Professor
Neural networks, vortex methods, flow in porous media and fluid mechanics.
• Gilberto Schleiniger, Associate Professor
Fluid flow: Transonic and viscoelastic flows.

• Wagner Muniz
  Computational electromagnetism. Wagner was an RA supported by AFOSR working on a problem of interest to Brooks AFB.
• Rodrigo Platte
  Applied Mathematics, viscoelastic fluid flow. Rodrigo is working on a problem of interest to DuPont.
• Rob Ronkese
  Applied Mathematics. Rob was supported by GIG for his first year.
• Jiguang Sun
  Computational electromagnetism. Jiguang is working with Seagate and is partially supported by them.

Alumni

• Fioralba Cakoni, Industrial Mathematics (GIG) postdoc
Boundary integral equations and coupling BEM-FEM. Applications in electromagnetic and elastic scattering problems. Fioralba accepted a tenure track position at the University of Delaware in the Mathematical Sciences Department.
• Mikhail Khenner, Industrial Mathematics (GIG) postdoc
Computational and theoretical fluid dynamics;  numerical methods for problems with interfaces and free boundaries;  computational materials science. Mikhail accepted a tenure track position at the University of Buffalo in the Mathematics Department.
• Cynthia DeBisschop, Industrial Mathematics (GIG) postdoc.
 Thin film evolution and viscoelastic applications. Formerly Cynthia Spade (until 7/01), Cyndi is now an Assistant Professor at Old Dominion University in the Department of Mathematics and Statistics.
• Bryan Wood
  Applied Mathematics, viscoelastic fluid flow. Bryan finished his PhD in 2003 and moved to a postdoc at Georgetown. He was supported in part by GIG and by DuPont.
• Molly Brazill
  Mathematics. Molly was supported by GIG in her first year, and she finished her MS in 2003.
• Chrissy Getman
  Applied Mathematics. GIG supported. Chrissy did an internship at Merck in Rahway, NJ, for the summer of 2000. She finished her MS in May 2001 and is working for Merck.
• Ellen Phifer
  Applied Mathematics. GIG supported. Ellen did an internship at SmithKline Beecham in King of Prussia, PA, for the summer of 2000. She completed her MS in May 2001, and is currently working for Survice Engineering.
• Homayoun Heidari
  Applied mathematics, fluid mechanics. Homayoun was a Visiting Scholar in parts of January and February 2001.
• Shailesh Naire
  Computational fluid dynamics, draining films. Shailesh's PhD work (2000) was on surfactant transport in a vertical draining film and was partially supported by Dow Corning. He began a visiting assistant professor position at WPI in August 2000.
• Stacie Rueblinger
  Mathematics. Stacie was supported by GIG in her first year.
• Gamze Berensel Tanoglu
  Computational materials science. Gamze's PhD (2000) was in collaboration with NIST scientists in the Materials Science and Engineering Laboratory and the Information Technology Laboratory. She now has a faculty position at the Izmir Institute of Technology (IZTECH) in the Mathematics Department.
• Hope Kyelberg
  Applied Mathematics. Hope was supported by GIG for her first year.
• Sean Christopher
  After a year at UD, Sean took a permanent job at Sunoco in 2000.
• Joe Coyle
  Computational Electromagnetism. Joe completed an internship at Brooks AFB in Summer, 1997. His PhD was completed Summer, 1998; he is now a postdoc at the University of Strathclyde in Glasgow, Scotland.
• Michael Hirsch
  M.S. in Applied Mathematics, 12/98. Now works at the Naval Surface Warface Laboratory in Maryland, where he was an intern in the summer of 1998. Michael had interned there two previous summers as well.
• Jie Zhang
  M.S. in Applied Mathematics, 1997. Jie spent most of the summer of 1996 in the Mathematical and Computational Sciences Division at NIST in Gaithersburg, MD. He is now studying computational fluid dynamics at Northwestern University in the Department of Engineering Sciences and Applied Mathematics under Mike Miksis.

Research
There are a wide range of problems being solved in collaboration with industry and national labs.  Research ranges from basic numerical analysis (finite element, boundary element and finite difference convergence theory) and fast methods (multigrid) to applications in materials science (foam evolution, phase transformations in crystalline alloys, approximation of microstructure, visco-elastic phenomena) and electromagnetism (scattering, inverse scattering and ferromagentism).  Graduate students are welcome!
 

Seminar
A variety of application areas and mathematical methods are featured in the Applied Mathematics seminar series.   A weekly seminar calendar gives up-to-date information on this and other seminars in the department.
 

Graduate Program

Courses
Students wishing to study applied mathematics usually enroll in the Applied Mathematics graduate program (see The Graduate Program web pages for more details).  There are a number of courses specifically intended for students interested in this area as well as topics courses.  For example

M611 --  Introduction to Numerical Analysis and Scientific Computation I
M612 --  Intro to Numerical Methods for Partial Differential Equations
M616 --  Introduction to Applied Mathematics I
M617 --  Introduction to Applied Mathematics II
M694 --  Methods of Optimization
M806 --  Functional Analysis
M807 --  Complex Analysis
M810 --  Asymptotic and Perturbation Methods
M812 --  Inverse Problems
M835 --  Partial Differential Equations I
M838 --  Numerical Methods for Partial Differential Equations

Students in Applied Mathematics are also encouraged to take courses outside the department.  Courses in engineering and computer science can build on the foundations offered above. 

Funding
Besides the usual university and departmental funding for TAs and fellows, there is occasional RA support which has sometimes come from companies.

Many of the projects listed here have been at least partially supported by the National Science Foundation under grant numbers 9722854 and 9631287. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Computing Resources
The department operates a four processor Silicon Graphics Origin 2000 parallel computer for the support of research computing.  All faculty and graduate students involved with scientific computing have personal workstations.
 

Projects

Current Projects

Seagate

Recording Heads

Peter Monk (PI), U of Delaware, monk@math.udel.edu

Jiguang Sun, U of Delaware

Lei Wang, Seagate

Jiguang Sun will be developing finite difference and finite element methods to compute the electromagnetic field in the write head of a disk drive. This work is expected to help in the design of novel recording heads. He is supported by Seagate.

DuPont

Growth of oxide crystals

Richard Braun (PI), braun@math.udel.edu

Pat Morris, DuPont

Lee Silverman, DuPont

Mathematical models for the growth of oxide crystals with highly anisotropic surface properties will be developed. The crystals are grown from the vapor to be used for pigmenting purposes. DuPont is supporting the project with an Aid to Educational Program grant.

Completed Projects

DuPont

Capillary viscometry for polymer processing

Bryan Wood, U of Delaware

Pam Cook (PI), cook@math.udel.edu

Gilberto Schleiniger (PI), schleini@math.udel.edu

Emeka Nwankwo, DuPont

Bryan Wood completed his PhD working on the mathematical modeling of the flow of a polymer solution in a small tube; this work is expected to help improve the efficiency of some of DuPont's polymer processes. He was supported by the GIG at U of Delaware and by support in kind from DuPont. The project is being supervised by Pam Cook and Gilberto Schleiniger; they were supported by an ATE grant from DuPont.

AstroPower

Crystal Growth on a Substrate

Mikhail Khenner, U of Delaware

Richard Braun (PI), braun@math.udel.edu

Michael Mauk, AstroPower

Theory is being developed for crystal growth of a not-necessarily thin film on a substrate with a mask. The fully nonlinear surface geometry was taken into account with a geometric growth model including surface diffusion and condensation from the vapor; the anistropic case was studied as well. The anisotropic case is now being considered. This started out as a follow-on project from the MPI 1999 meeting held at UD. Rich is partially supported by, and Mikhail was fully supported by NSF GIG DMS-9631287 during his stay at UD. The paper that appeared from this project is "A Model for Anisotropic Epitaxial Lateral Overgrowth," M. Khenner, R.J. Braun and M.G. Mauk, J. Crystal Growth 241, (2002) 330-346.

Air Force

On the Mathematical Basis of the Linear Sampling Method

David Colton (PI), colton@math.udel.edu

Fioralba Cakoni, U of Delaware

The linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. The first version of the linear sampling method is more flexible, being able to treat the aforementioned cases as well as partially coated obstacles. However, its mathematical foundation is less well established. In this paper we provide arguments giving a mathematical justification of the first version of the linear sampling method. Fioralba is supported by NSF GIG DMS-9631287; David is supported by AFOSR.

DuPont

A Theoretical Formulation for Rapid, Unambiguous Polymer Characterization using Flow-Referenced Capillary Viscometers

Pam Cook (PI), cook@math.udel.edu

Emeka Nwankwo, DuPont

Gilberto Schleiniger, U of Delaware

Bryan Wood, U of Delaware

The behavior of a polymer solution in a small tube has been studied and a paper has been submitted for publication. Pam and Gilberto have been supported by ATE grants from DuPont and Bryan is supported by DuPont and NSF GIG DMS-9631287.

Air Force

The direct and Inverse Scattering Problems for Partially Coated Obstacles

Peter Monk (PI), monk@math.udel.edu

Fioralba Cakoni, U of Delaware

David Colton, U of Delaware

The direct and inverse scattering problems for partially coated obstacles is considered. The method of integral equations of the first kind is used to solve a scattering problem for the Helmholtz equation where the scattered field satisfies mixed Dirichlet-impedance boundary conditions on the Lipschitz boundary of the scatterer $D$. Then the inverse scattering problem of determining $D$ from a knowledge of the far field pattern of the scattered field is solved by using the linear sampling method. Numerical examples are given showing the performance of the linear sampling method in this case. This work will appear in Inverse Problems; Peter is partially by, and Fioralba is fully supported by, NSF GIG DMS-9631287. Peter and David are supported by AFOSR.

AstroPower

Crystal Growth on a Substrate

Mikhail Khenner, U of Delaware

Richard Braun (PI), braun@math.udel.edu

Micheal Mauk, AstroPower

Crystal growth of a not-necessarily-thin film on a substrate with a mask is studied. The fully nonlinear surface geometry is taken into account with an isotropic geometric growth model including surface diffusion and condensation from the vapor. The results have been submitted for publication. This is a follow-on project from the MPI 1999 meeting held at UD. Rich is partially supported by, and Mikhail is fully supported by, NSF GIG DMS-9631287. The paper from this isotropic model is "An Isotropic Model for Crystal Growth from Vapor on a Patterned Substrate," M. Khenner, R.J. Braun and M.G. Mauk, J. Crystal Growth, 235 (2002) 425-438.

Dow Corning

Bounded film evolution with variable surface properties

Cynthia DeBisschop, now at Old Dominion University

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

In this project, theory is being developed for a thin film on a plate with nonlinear surface properties. The results are of interest to Dow Corning and will allow us to tackle a wider range of problems of interest to them. Dow Corning is partially supporting Rich; Rich is partially supported by, and Cyndi was fully supported by, NSF GIG DMS-9631287.

Air Force

The Linear Sampling Method for Anisotropic Media

David Colton (PI), colton@math.udel.edu

Fioralba Cakoni, U of Delaware

Houssem Haddar, U of Delaware

We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end we extend the linear sampling method from the isotropic case to the case of anisotropic media. In the case when the coefficients are real we also show that the set of transmission eigenvalues forms a discrete set. This work will appear in Journal of Computational and Applied Mathematics; Fioralba is supported by NSF GIG DMS-9631287; David is supported by AFOSR.

Air Force

The Linear Sampling Method for Anisotropic Media: Part II

Fioralba Cakoni (PI), ccakoni@math.udel.edu

Houssem Haddar, U of Delaware

We reconsider the linear sampling method for solving the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. We extend the results of a previous paper concerning with the same problem to the case where the norm of the real part of the matrix that describes the physical properties of the medium is less than one. This work is in Preprint No. 2001-026, Mathematical Sciences Research Institute, University of California at Berkeley; Fioralba is supported by NSF GIG DMS-9631287.

Dow Corning

Vertical bounded film evolution with variable surface properties

Homayoun Heidari, Sharif University of Technology, Iran (visiting RPI and UD)

Richard Braun (PI), braun@math.udel.edu

Amir Hirsa, Rensselaer Polytechnic Institute

Steven Snow, Dow Corning

Shailesh Naire, University of Nottingham, UK

In this project, theory is being developed for a thin film on a vertical plate with nonlinear surface properties. The results are of interest to Dow Corning and will allow us to make very detailed comparison with experiments that have been developed at RPI. Dow Corning is supporting Rich and Homayoun; Rich is partially supported by NSF GIG DMS-9631287.

SmithKline Beecham

Summer 2000 Internship

Ellen Phifer, U of Delaware

Larry Greller, SmithKline Beecham

Frank Tobin, SmithKline Beecham

Ellen Phifer spent the summer analyzing and improving upon a variable tension spline curve-fitting package. The resulting code was incorporated into MATLAB and will be used by mathematical biologists at SmithKline Beecham in their analysis of sparse data sets. Her studies were directed by Larry Greller and Frank Tobin.

Merck

Summer 2000 Internship

Chrissy Getman, U of Delaware

Mathematical Problems in Industry Workshop 2000

Richard Braun, braun@math.udel.edu

Pam Cook

David Edwards, edwards@math.udel.edu

Peter Monk

Petr Plechac

Gilberto Schleiniger

Don Schwendeman, Rensselaer Polytechnic Institute

The Department of Mathematical Sciences hosted the 16th annual Mathematical Problems in Industry workshop June 5-9, 2000. Thank you to NIST for valuable support once again!

Mathematical Problems in Industry Workshop 1999

Richard Braun, braun@math.udel.edu

Pam Cook

David Edwards

Peter Monk

David Olagunju

Gilberto Schleiniger

Don Schwendeman, Rensselaer Polytechnic Institute

The Department of Mathematical Sciences hosted the 15th annual Mathematical Problems in Industry workshop in early June 1999. The MPI workshop has been held at Rensselaer Polytechnic Institute for the last 13 years (with one exception, when it was held at the University of New Mexico). We were very excited about this week-long international workshop where industrial problems are presented and studied. The workshop was partially supported by a grant from the Mathematical and Computational Sciences Division at the National Institute of Standards and Technology; thank you NIST!

Brooks Air Force Base

Inverse problem for detection of underground objects

Joe Coyle, cassidy@math.udel.edu

Peter Monk, monk@math.udel.edu

David Colton (PI), colton@math.udel.edu

Richard Albanese, Brooks AFB

Joe Coyle spent the summer of 1997 at Brooks AFB in San Antonio, TX, under the supervision of Richard Albanese studying inverse problems related to the detection of underground objects. This work has formed a substantial part of his PhD thesis with Peter Monk.

Dow Corning

Gravitationally-driven drainage of a thick film with a tangentially-immobile surface

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

Udo Pernisz, Dow Corning

In this project, theory was necessary for an experiment that Steven Snow and Udo Pernisz developed at Dow Corning. Their experiment can produce detailed information about the dhape of a film suspended from a wire frame and draining vertically into a bath. In a limiting regime of the experiments, the surface of the film can be made tangentially immobile. We have have developed a theory for this case where we use singular pertubation and computational methods to solve the problem.

From this work we have written a Dow Corning internal report (I0000-1998-45018 by Braun, Snow and Pernisz) and a paper has appeared (J. Colloid Interface Sci. 219 (1999) 225-240). This material is based upon work supported in part by the National Science Foundation under Grant No. 9631287.

Dow Corning

Limiting cases of gravitationally-driven drainage of thick film

Shailesh Naire

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

In this project, theory was necessary for an experiment that Steven Snow and Udo Pernisz developed at Dow Corning. Their experiment can produce detailed information about the shape of a film suspended from a wire frame and draining vertically into a bath. Shailesh Naire has extended the work on the case of a tangentially-immobile film (see below) to include more realistic physical effects. Finite surface viscosity, the Marangoni effect, and surfactant transport have been added. A "flat film" limit has been studied. Shailesh has solutions from analytical and computional approaches that bound the fastest and slowest draining limits of the experiments.

This work has appeared electronically in the SIAM Journal on Applied Mathematics (61 (2000) 889-913), and has resulted in the Dow Corning internal report (1999-I0000-41799). This material is based upon work supported in part by the National Science Foundation under Grant No. 9631287.

Dow Corning

Insoluble surfactant model for gravitationally-driven drainage of a thick film

Shailesh Naire

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

In this project, theory was necessary for an experiment that Steven Snow and Udo Pernisz developed at Dow Corning. Their experiment can produce detailed information about the shape of a film suspended from a wire frame and draining vertically into a bath. Shailesh Naire has extended the work still further. Finite surface viscosity, the Marangoni effect, and surfactant transport have been added, and the case where the film is patched onto the static meniscus has been studied. He also has found interesting dynamics in the evolution of the film shape and other dependent variables. These 1+1-d computations have appeared in the Journal of Colloid and Interface Science (230 (2000) 91-106). This material is based upon work supported in part by the National Science Foundation under Grant No. 9631287.

Dow Corning

Gravitationally-driven drainage of a thick film in 3D

Shailesh Naire, now going to the University of Nottingham, UK

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

Dow Corning

Gravitationally-driven vertical film drainage with variable surface properties

Shailesh Naire, now at Divsion of Theoretical Mechanics, University of Nottingham, UK

Richard Braun (PI), braun@math.udel.edu

Steven Snow, Dow Corning

Shailesh added nonlinear surface properties to the one-dimensional film problem and the results have appeared in print (Phys. Fluids 13, (2001) 2492-2502). Dow Corning supported Shailesh and Rich; this material is based upon work supported in part by the National Science Foundation under Grant No. 9631287.

Shailesh completed a set of 2+1 dimensional computations and the results have been submitted to the Journal of Fluid Mechanics. Dow Corning supported Shailesh and Rich; this material is based upon work supported in part by the National Science Foundation under Grant No. 9631287.

National Institute of Standards and Technology

Effect of initial conditions in phase-field modeling of dendritic growth

Jie Zhang, now at Northwestern University

Richard Braun, , braun@math.udel.edu

Bruce Murray, SUNY Binghamton

Jeff McFadden, NIST

In this internship, Jie spent two months of the summer of 1996 at the NIST Gaithersburg, MD, site. There he worked with Bruce Murray (then of NIST) and Jeff McFadden in the Applied and Computational Mathematics Division of the Information Technology Laboratory. Jie also attended a short course on diffuse-interface modeling of phase change.

Jie studied the effect of different initial conditions on the subsequent evolution Governed by a phase field model of solidification. Jie computed the solidification of an undercooled melt in a thermally-insulated box with initial conditions for the thermal field that could be discontinuous, have only a continuous temperature field, or have a continuous first derivative as well. He found that the smoother the initial condition for the temperature field was, the less likely it would be that unphysical spreading of the interfacial region would occur. This is practically useful in computation of dendritic microstructures and the results will soon be available in postscript form.

Jie did this project for MS thesis in the Math Sciences Department. He is now attending the Northwestern Department of Engineering Sciences and Applied Mathematics and is studying for his PhD there.

Thomson CSF, France

Inverse scattering of electromagnetic waves from obstacles

Cristoph Labreuch, Thomson CSF

Peter Monk, monk@math.udel.edu

David Colton (PI), colton@math.udel.edu

Drs Colton and Monk were visited for a year by Christoph Labreuch, an employee of Thomson CSF, to study the identification of objects using inverse scattering of electromagnetic waves. This work formed the bulk of Christoph's PhD thesis.

Equipment for the Lab

Peter Monk, monk@math.udel.edu

Pam Cook, cook@math.udel.edu

Richard Braun, braun@math.udel.edu

An SGI Octane with an R10000 cpu, an SGI Indigo2 with an R10000 cpu, and a Pentium III machine are in an office suite in Ewing Hall. Shailesh wasvworking away and Peter and Joe collaborating.

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Last Updated: 11/12/01
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