1
Dr. Erwin A. MacN. George
Dept. of Applied Mathematics & Statistics
Stony Brook University
Stony Brook, NY 11794-3600
USA
Telephone: (631) 632-8370
602 Route 25A,
Saint James, NY 11780-1403
USA
Telephone: (631) 584-3274
E-mail : egeorge@ams.sunysb.edu
URL : http://www.ams.sunysb.edu/~egeorge
PROFILE
Skilled research and teaching academic with a master’s in pure mathematics and a doctorate in
applied mathematics. Ten years experience teaching a wide variety of undergraduate and graduate
university mathematics/applie d mathematics/statistics courses. Research Interests: computational
fluid mechanics, numerical analysis, parallel computing, partial differential equations, ordinary
differential equations, biological and medical mathematics, atmospheric science, earth science,
oceanography, mathematics education.
EDUCATION
Ph.D. in Computational Applied Mathematics
Stony Brook University, Stony Brook, NY, USA
Dissertation topic: A Numerical Study of Rayleigh-Taylor Instability
1998-2003
Advisor: Dr. James Glimm
M.A. in Mathematics
Pennsylvania State University, University Park, PA, USA
1994-1996
B.A. with Honours in Mathematics; minor in French
University of Guelph, Guelph, Ontario, Canada
1989-1993
RECENT EXPERIENCE
Postdoctoral Research and Teaching Fe llow
Aug. 2004 – present
Postdoctoral Research Associate
Jan. 2004 – Aug. 2004
Research Assistant
1999 – Dec. 2003
Teaching Assistant
1998 – 2000
Instructor
spring 2000 and
summers 2002-2004
Stony Brook University, Stony Brook, NY, USA

Teach linear algebra, advanced calculus, differential equations, and statistics.

Teaching assistant for numerical analysis and differential equations courses .

Write and grade portions of the Applied Mathematics and Statistics doctoral qualifying exam.

Research assistant/associate on topics such as astrophysical jets, fluid mixing, front tracking,
the level set method, parallel programming, image processing .

Develop front tracking and total variation diminishing computational codes for use on the
parallel computers at Oak Ridge National Laboratory and the National Energy
Research Scientific Computing Centre (NERSC).

Major writer of NERSC computer time request proposal for the Applied Mathematics and
Statistics department.

Affiliate at Brookhaven National Laboratory.
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CV for Dr. Erwin George
Instructor
1996-1998
Teaching Assistant
1994-1996
Pennsylvania State University, University Park, PA, USA

Taught algebra, trigonometry, pre-calculus, ordinary and partial differential equations, and
linear algebra. Was teaching assistant for calculus courses.

Wrote, proofread, and graded examinations for multi -section courses. Proofread workbook
and solutions manual being written by a faculty member for a business calculus course.
PROFESSIONAL ORGANIZATION MEMBERSHIPS
Society for Industrial and Applied Mathe matics;
Society; Mathematical Association of America;
American Mathematical Society;
National Geographic Society.
American Physical
PUBLICATIONS
1.
The influence of scale breaking phenomena on turbulent mixing rates (E. George, J. Glimm,
X. Li, Y. Li, X. Liu. SUBMITTED to Physical Review Letters ).
2.
Self similarity of Rayleigh-Taylor mixing rates (E. George and J. Glimm, Physics of Fluids ,
vol. 17, issue 5, article 054101, May 2005).
3.
Shock wave interactions in spherical and perturbed spherical geomet ries (S. Dutta, E.
George, J. Glimm, J. Grove, H. Jin, T. Lee, X. Li, D. H. Sharp, K. Ye, Y. Yu, Y. Zhang, and M.
Zhao, Nonlinear Analysis , IN PRESS, Elsevier, 2005).
4.
A Numerical study of Rayleigh-Taylor instability (E. George, Doctoral Dissertation , December
2003).
5.
Simulation of fluid mixing in acceleration driven instabilities (E. George, J. Glimm, X. L. Li,
Z. L. Xu, Computational Fluid and Solid Mechanics 2003 [Proceedings of the 2nd MIT
Conference on Computational Fluid and Solid Mechanics, Edited by K.J. Bathe], pp. 908-911,
Elsevier, 2003).
6.
Simplification, conservation and adaptivity in the front tracking method (E. George, J. Glimm,
J. W. Grove, X. L. Li, Y. J. Liu, Z. L. Xu, N. Zhao, Hyperbolic Problems: Theory, Numerics,
Applications [Proceedings of the 9th International Conference on Hyperbolic Problems , Edited
by T. Hou and E. Tadmor], pp. 175-184, Springer-Verlag, 2003).
7.
Numerical methods for the determination of mixing (E. George, J. Glimm, X. L. Li, A.
Marchese, Z. L. Xu, J. W. Grove, D. H. Sharp, Laser and Particle Beams , vol. 21, pp. 437442, 2003. Los Alamos National Laboratory report No. LA-UR-02-1996 ).
8.
A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing rates (E.
George, J. Glimm, X.-L. Li, A. Marchese, Z.-L. Xu, Proceedings of the National Academy of Sciences
[USA], vol. 99, no. 5, pp. 2587-2592, March 2002).
SELECTED PRESENTATIONS

Self similarity of Rayleigh-Taylor mixing rates : Applied Mathematics Seminar, Stony Brook University,

A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing
rates : American Physical Society, Division of Fluid Dynamics Meeting, Dallas, TX , November


October 2004.
2002.
A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing
rates : Society for Industrial and Applied Mathematics 50th Anniversary and Annual Meeting,
Philadelphia, PA, July 2002.
Front tracking in two space dimensions : Applied Mathematics Seminar, Stony Brook
University, June 2000.
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CV for Dr. Erwin George
HONOURS

Department of Energy sponsorship to attend the ACTS (Advanced Computational Testing and Simulation)
Toolkit workshop, October 2001, Lawrence Berkeley National Laboratory.

National Science Foundation VIGRE (Vertically Integrated Grants in Research and Education) Doctoral
Fellowship (2002 - 2003), Department of Applied Mathematics and Statistics, Stony Brook University.

Research Assistantship (1999 - 2002, 2003), Department of Applied Mathematics and Statistics, Stony
Brook University.

Teaching Assistantship (1998 - 2000), Department of Applied Mathematics and Statistics, Stony Brook
University.

Turner Fellowship (1998 - 2002), Department of Applied Mathematics and Statistics, Stony Brook
University.

Teaching Assistantship, Department of Mathematics, Pennsylvania State University (1994 - 1996).

Dean's List, University of Guelph, ( spring 1990, spring 1991).

C, MPI, C++, Fortran77, Fortran90, Unix shell programming, Awk, Perl, HTML .

MATLAB, Maple, Graphics calculators, Lotus 123, Excel.

LaTex, AMS-Tex, emacs, vi, Wordperfect, Word.

French (read/write/speak).
SKILLS
REFERENCES
1)
Dr. James Glimm (Ph.D. dissertation advisor) - Distinguished Professor and Chair of the Department of
Applied Mathematics and Statistics.
P-138A Mathematics Tower
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook
Stony Brook, NY 11794-3600, USA
Telephone: (631) 632-8355;
FAX:
(631) 632-8490
E-mail:
glimm@ams.sunysb.edu
Home page: www.ams.sunysb.edu/~glimm
2)
Dr. Xiaolin Li (Ph.D. dissertation committee chair) - Professor and Graduate Programme Director, Department of
Applied Mathematics and Statistics.
1-121 Mathematics Tower
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook
Stony Brook, NY 11794-3600, USA
Telephone: (631) 632-8354;
FAX: (631) 632-8490
E-mail:
linli@ams.sunysb.edu
Home page: www.ams.sunysb.edu/~linli
3)
Dr. Alan Tucker (Primary teaching referee) - Distinguished Teaching Professor and Director of Undergraduate
Studies, Department of Applied Mathematics and Statistics.
P-138 Mathematics Tower
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook
Stony Brook, NY 11794-3600, USA
Telephone: (631) 632-8365;
FAX: (631) 632-8490
E-mail:
atucker@notes.cc.sunysb.edu Home page: www.ams.sunysb.edu/~tucker
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TEACHING STATEMENT FOR ERWIN A. MACN. GEORGE
A revolution in my ideas about how mathematics should be taught occurred during my second semester of calculus as an
undergraduate at the University of Guelph. The instructor, Professor Jack Weiner, despite a large class size, was able to
accomplish what I had seen other instructors attempt with only limited success: he engaged every student in the class by
making sure we actively participated in discussions, did and presented examples in class, and provided continuous
feedback on whatever we did not understand, all with a goal of ensuring that we left the classroom with a clear
understanding of the topic that was taught. Needless to say, I have attempted to incorporate Professor Weiner's
approach as an integral part of my classroom teaching style.
My initial experiences with university level teaching, beginning in 1994, involved conducting recitations. It was easy in
that context to thoroughly engage students in a class and get the feedback necessary to ensure that a given topic was
clearly understood by all. During the summer of 1995, my role shifted to that of course instructor, and with this expanded
responsibility, I reflected more carefully on the core reasons for Professor Weiner's success. I had also in the preceding
year taken a course on teaching university level mathematics, using the book How to Teach Mathematics by Steven G.
Krantz. In preparing to teach my first full course, I turned to the ideas expressed in that book and my observations of the
habits of my past good teachers, like Professor Weiner, in determining how to become an effective teacher. Over the
years, those ideas have been refined, and they will continue to be refined since I believe that one of the key attributes of
a successful teacher is the desire to continue to learn new ways of improving one's teaching skills.
I have found the following to be the key principles behind obtaining and maintaining a “Weinerian'' classroom, in which
each student is actively trying to learn and is willing to ask the necessary questions to do so and, furthermore, is leaving
the classroom with not only a clearer idea of the topic taught but also of how to learn. First, one must establish mutual
trust and respect with students. Second, one must be very accessible both in and out of the classroom. Third, one must
have a continuous manner of assessing the level of understanding by students of the course material. Fourth, one must
be extremely knowledgeable and enthusiastic about mathematics, science, and other fields impacted by mathematics.
And finally, on a related note one must be supremely well prepared for each lecture.
The establishment of mutual trust and respect with students comes with being unambiguously clear at the start of a
course about the academic and behavioural expectations, particularly regarding how grades will be assigned. It also
comes with encouraging student questions in and out of class and always answering those questions thoughtfully.
Additionally, it comes with addressing any student concerns immediately, leading naturally to the second key principle of
accessibility.
I find that students react more positively in class when they are sure that any questions will be answered either there or
out of class. I typically have significantly more than the suggested number of office hours, and also have an open door
policy. On a few occasions, I have even taken a class on a “field trip'' to my office at the end of the first lecture just to
emphasize my desire to have them use my office hours. I encourage the use of e-mail for questions and always respond
promptly. I have found this level of attention encourages students to ask more questions than they otherwise would have
done, which in turn allows me to better tailor my course presentation to their benefit.
I believe in the continuous, fair evaluation of student performance. My courses are liberally sprinkled with quizzes and
homework sets due for grading, so that students are required to work continuously and thus keep up with the course
material. This frequent evaluation of students makes midterms and finals seem less daunting to them. It has the added
benefit of keeping me abreast of which topics may need additional attention. A fixed number of the lowest scores of each
student from these copious quizzes and homework sets are discarded, so that he/she is allowed time to adjust to the
rigours of my classroom without penalty. Solutions to quiz, homework, and examination problems are made available to
students in a timely manner. I have found this continuous work policy very helpful in ensuring that students keep up with
the course work and hence know what is going on in class and are willing to participate more.
Being extremely knowledgeable about mathematics, science, and other fields impacted by mathematics ensures that one
has the ability to put what the students are learning into a larger context; something which many students desire as a
motivation for studying some of the abstract ideas in mathematics. I often discuss how the topic being taught impacts
my research or that of my colleagues. And I continually strive to expand my knowledge of all things mathematical so that
I may better situate the topics being taught in a larger context. Related to this principle is my belief that a student should
not only be taught about the subject matter at hand but should also be taught study skills which work best in learning
mathematics. I discuss frequently in class some of the study techniques which work, such as continually doing work and
never falling behind. Also, I have found that my enthusiasm for mathematics and, more generally, learning is contagious
in the classroom.
Being well prepared, for me, means having a variety of ways of presenting material, with a view to gauging via student
feedback which approach is best. One should have thought deeply about the subject one is about to teach as well as how
best to teach it. For example, I think carefully about the balance between presenting finished material versus leading
students to discovery when preparing for a specific class or an entire course. Whenever time and the material permit, I
employ the discovery approach since it engages students more during class and appears to help in their retention of the
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results of that discovery. One should be careful not to follow too inflexible an approach in teaching; adjustments should
be made to incorporate the feedback given by students. And the key way to develop this flexible classroom style is
extensive preparation.
I have taught a wide variety of courses, ranging from pre-calculus to graduate level. Many have involved the use of
technological tools such as programmable graphing calculators and maple, and I am therefore very comfortable with
using technology to enhance my presentation of topics. I am willing to teach a very wide variety of courses, including
those not in my area of expertise. I welcome the challenge of teaching outside my area of expertise as a learning
opportunity. My preference for teaching includes courses on calculus, advanced calculus, linear algebra and applications,
ordinary differential equations, partial differential equation, numerical analysis, abstract algebra, real analysis, complex
analysis and applications, fluid dynamics, and high performance computing. I am also interested in conducting and/or
participating in teaching workshops for graduate students in your department who will be or are teaching. I have a
passion for teaching which I wish to spread to the new generation of graduate students in the mathematical sciences.
TEACHING EXPERIENCE (up to the spring 2005 semester)
POSITION
Instructor
Instructor
Teaching Assistant
Teaching Assistant
Instructor
Instructor
Stony Brook University, Stony Brook, NY (1998 – present)
COURSE
COURSE DESCRIPTION
Elements of Statistics
Use/misuse of statistics in real life; basic measures of
(Applied Math. 102)
central tendency & dispersion, frequency distributions,
probability, binomial & normal distributions, confidence
intervals, hypothesis testing, chi-square test,regression.
Basic properties of matrix algebra, matrix norms, eigenvalues,
Matrix Methods and
solving systems of equations; applications to economics, growth
Models (Applied Math.
models, Markov chains, regression, linear programming.
201)
Computer software packages used.
Direct and indirect methods for the solution of linear & nonlinear
Numerical Analysis
equations. Computation of eigenvalues and eigenvectors of
(Applied Math. 326)
matrices. Quadrature, differentiation, and curve fitting.
Numerical solution of ordinary and partial differential equations.
Homogeneous & inhomogeneous linear differential equations;
Applied Calculus IV:
systems of linear differential equations; power series & Laplace
Differential Equations
transform solutions; partial differential equations, Fourier series.
(Applied Math. 361)
Alliance for Graduate
Education and the
Professoriate Intensive
Mathematics Seminar
Analytical Methods for
Applied Mathematics &
Statistics (Applied
Review of differential equations, advanced calculus, and linear
algebra for undergraduate science students planning to apply to
graduate schools.
(GRADUATE COURSE) Review of techniques of multivariate
calculus, convergence and limits, matrix analysis, vector space
basics, and Lagrange Multipliers.
Math. 501)
POSITION
Instructor
Instructor
Instructor
Teaching Assistant
Pennsylvania State University, University Park, PA (1994 – 1998)
COURSE
COURSE DESCRIPTION
Quadratic equations; equations in quadratic form; word
College Algebra I
problems; graphing; algebraic fractions; negative and rational
(Math. 21)
exponents; radicals.
Relations, functions, graphs; polynomial, rational functions,
College Algebra II and
graphs; word problems; nonlinear inequalities; inverse
Analytic Geometry
functions; exponential, logarithmic functions; conic sections;
(Math. 22)
simultaneous equations.
Trigonometric functions; solutions of triangles; trigonometric
Plane Trigonometry
equations; identities.
(Math. 26)
Techniques of Calculus
(Math. 110)
Teaching Assistant
Instructor
Instructor
Calculus with Analytic
Geometry (Math. 140)
Matrices (Math. 220)
Ordinary and Partial
Differential Equations
(Math. 251)
Functions, graphs, techniques of differentiation & integration,
exponentials, improper integrals, applications.
Functions; limits; analytic geometry; derivatives, differentials,
applications; integrals, applications.
Systems of linear equations; matrix algebra; eigenvalues and
eigenvectors; linear systems of differential equations.
First- and second-order equations; special functions; Laplace
transform solutions; higher order equations; Fourier series;
partial differential equations.
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RESEARCH STATEMENT FOR ERWIN A. MACN. GEORGE
My research primarily examines various aspects of the fluid mixing problem Rayleigh-Taylor instability. This classic fluid
instability occurs when a perturbed interface between two fluids of differing densities is subjected to a steady
gravitational acceleration directed from the heavy to the light fluid, resulting in bubbles of light fluid and spikes of heavy
fluid each penetrating into the opposite phase. It arises in a wide variety of important scenarios, such as supernova
explosions, the geological evolution of underground salt domes and volcanic islands, and inertial confinement fusion
(where it can degrade the energy yield of the fusion target). Rayleigh-Taylor instability has been widely studied
experimentally, theoretically, and numerically at universities and laboratories around the world. However it remains a
difficult phenomenon to correctly model via theoretical or numerical simulation techniques, and good experiments are
difficult to conduct. Part of my research involves working on a non-diffusive front tracking code and a diffusive total
variation diminishing (TVD) level-set code for use in studying three-dimensional Rayleigh-Taylor instability numerically. I
will discuss the two main results (so far) from my dissertation and subsequent research.
Most numerical simulations of incompressible flow Rayleigh-Taylor instability greatly under-predict the experimentallydetermined value of the acceleration rate of the bubble envelope, one of the most important macroscopic properties of
the flow. Theory and experiment agree in their determination of this mixing rate, but most numerical simulations underdetermine the rate by a factor of two. We examined reasons for this discrepancy. For weakly compressible flow, the front
tracking simulations have mixing rates in or near the experimental range. In contrast, the untracked TVD simulations
have mixing rates far below the experimental range. Front tracking simulations have no interfacial mass diffusion; TVD
simulations and other simulations which under-determine the mixing rate do. We demonstrate that the lower mixing rate
found in weakly compressible untracked simulations is caused primarily by a reduced buoyancy force due to numerical
interfacial mass diffusion. Quantitative evidence includes results from a time dependent Atwood number analysis of a TVD
diffusive simulation, which yields a diffusively-renormalized mixing rate coefficient for the diffusive simulation in
agreement with experiment. Moreover, we achieve approximate agreement of mixing rates among experiments, theory,
and all properly reinterpreted weakly compressible simulations.
We also studied the effect of compressibility on Rayleigh-Taylor mixing rates. We uncover late time trends of decreasing
mixing rate with increasing compressibility for isothermally-initialized simulations. A time dependent Atwood number
analysis of these simulations reveals the cause of this trend to be a reduced buoyancy force due to the vertical fluid
density stratification which becomes more significant with increasing compressibility. Renormalization of the mixing rate
curves (plotting bubble height vs. Agt2, where A is Atwood number, g is the magnitude of the gravitational acceleration,
and t is time) of high, moderate, and low compressibility simulations using the time dependent Atwood number, results in
improved self-similar t2 scaling of all curves and improved agreement between the mixing rate curves of diffusive and
non-diffusive simulations. Our results suggest a previously-unobserved universal scaling to Rayleigh-Taylor mixing rate
curves across a range of compressibilities.
My research has involved improving a hybrid interface maintenance scheme in the front tracking code, designed to limit
artificial smoothing effects during front propagation. More recently, I have also been part of a team implementing an
even more effective locally hybrid interface maintenance scheme. One result of these improvements has been RayleighTaylor simulations with mixing rates slightly above the experimental range. My current research examines the impact of
surface tension and other physical effects on the mixing rates of the new locally hybrid simulations. I have also been
assessing turbulence models and their relevance to our simulations.
Development of improved front tracking treatments for modelling fluid mixing is and will continue to be a central part of
my research efforts in the short term. I will also develop new multi-phase flow theoretical models and/or improve on
existing models, with the data from large scale simulations providing some insight during the development of these new
and/or improved models. For example, to my knowledge, a buoyancy-drag ordinary differential equations model for the
growth rate of the mixing zone in compressible Rayleigh-Taylor instability has yet to be developed, and I will devise one
which is well supported by data from experiments and simulations. My proposed work should improve our understanding
of the multitude of scientific and technological instances of multi-phase mixing; and, for example, this additional
knowledge may be harnessed in improving the efficiency of technological applications which involve multi-phase fluid
mixing. In the longer term, I expect to expand my research to a wider range of fluid flow phenomenon, such as flows
associated with earth and atmospheric sciences.
Other current research interests include numerical linear algebra, ordinary and partial differential equations, parallel
computing, biological & medical mathematics, numerical analysis, earth and atmospheric sciences, and mathematics
education.