Ari Stern
I am a graduate student in the Department of Applied and Computational Mathematics at Caltech. Before coming to Caltech, I received a B.A. in Mathematics and an M.A. in Mathematics of Finance from Columbia University.
You can click here to get a current copy of my CV [pdf].
Research
My research is in the area of discrete geometric dynamics: developing numerical methods that preserve the essential geometric structure of the physical systems they aim to simulate. The motivating idea behind this work is that, if our discretizations respect these structures (e.g., Lagrangian variational principles, symplectic flow, symmetries, momentum conservation), then we can develop numerical integrators with better global behavior — even at lower computational cost — and with arbitrarily good accuracy.
I am particularly interested in discrete field theories, building on some of the recent advances in discrete mechanics and variational integrators for ODEs, and using the recently developed tools of discrete exterior calculus (DEC). This work also draws on a wide spectrum of mathematical subjects including differential geometry, algebraic topology, Lie group theory, classical mechanics, field theory, and numerical analysis.
Current applications being explored include:
- Computational electromagnetics
- Numerical general relativity
- Constrained dynamics, highly oscillatory problems, and dynamics on multiple time scales
- Simulation for computer graphics
My research advisor is Prof. Jerrold E. Marsden, and I also collaborate closely with Mathieu Desbrun and the Applied Geometry Lab.
Papers Available for Download
A. Stern and E. Grinspun [2008], Implicit-Explicit Variational Integration of Highly Oscillatory Problems, submitted.
A. Stern, Y. Tong, M. Desbrun, and J. E. Marsden [2008], Variational integrators for Maxwell's equations with sources, PIERS Online 4, 711–715. Previously appeared in PIERS Proceedings, 443–447, July 2–6, Cambridge, USA 2008. arXiv:0803.2070 [math.NA].
A. Stern, Y. Tong, M. Desbrun, and J. E. Marsden [2007], Computational Electromagnetism with Variational Integrators and Discrete Differential Forms, submitted, in revision.
A. Stern and M. Desbrun [2006], Discrete geometric mechanics for variational time integrators. In SIGGRAPH '06: ACM SIGGRAPH 2006 Courses, pages 75–80, New York, NY, USA. ACM Press.
Upcoming Scheduled Talks
None right now.
Talks Available for Download
Variational Integrators for Maxwell's Equations with Sources [pdf], given at the Progress in Electromagnetics Research Symposium (PIERS) in Cambridge, MA, Jul. 3, 2008.
Geometric Numerical Integration of Lagrangian Dynamics [pdf], given at the Center for Computational Mathematics Seminar at UCSD, Jun. 17, 2008.
Variational Implicit-Explicit Integrators: Multiple Time Scales without Resonance Instability [pdf], poster presented at the Fourth Annual Structured Integrators Workshop at Stanford, Apr. 24–25, 2008.
Symmetry and Simulation: How Geometry Affects Scientific Computing, from the Solar System to Your Microwave Oven. Part of the Everhart Lecture Series at Caltech, Apr. 2, 2008. Streaming webcast available at Caltech Today Theater.
Discrete Differential Forms for Numerical Relativity [pdf], given at the 24th Pacific Coast Gravity Meeting at UCSB, Mar. 22, 2008.
Geometric Methods in Computational Electromagnetics [pdf], given at the USC Seminar Series, Oct. 11, 2007.
Computational E&M with Variational Integrators and Discrete Differential Forms [pdf], given at the workshop Geometric Mechanics: Continuous and discrete, finite and infinite dimensional, Banff International Research Station, Aug. 13, 2007.
DEC and AVIs for Computational Electromagnetism [pdf], given at the Third Annual Structured Integrators Workshop hosted by USC, Apr. 30, 2007.
Variational Integrators for Problems on Multiple Time Scales [pdf], poster from DyNARUM 2007 workshop, Jan. 23, 2007.
I participated in the course Discrete Differential Geometry: An Applied Introduction at the SIGGRAPH 2006 conference on Jul. 30, 2006. My lecture slides [pdf] and movies [zip], are both available from the Discrete Differential Geometry Forum (which also includes resources from the past two years' courses).
Continuous and Discrete Mechanics with Differential Forms [pdf], CDS 280 (Advanced Topics in Geometric Mechanics) seminar talk.
Computational Resources: LaTeX on Mac OS X
MacTeX
The MacTeX distribution is probably the best and easiest way to use TeX on a Mac. In addition to all the standard TeX tools, packages, and fonts from the TeX Live distribution, MacTeX also includes the excellent front-end programs TeXShop (TeX editor and viewer), LaTeXiT (create a snippet of LaTeX text as a small PDF, for easy embedding in non-LaTeX documents), BibDesk (manage BibTeX bibliographies), and Excalibur (spell-checker that intelligently skips LaTeX commands and checks only the actual text).
Podcast: Using LaTeXiT with Keynote and Illustrator
LaTeX is great for typesetting large documents, or those with lots of mathematical content. But what if you don't want to use LaTeX for your whole document? What if you just want to insert a snippet of LaTeX text into your Apple Keynote presentation, or Adobe Illustrator figure (e.g., adding text labels to a mathematical diagram)? In this demo, I show how to do this using the LaTeXiT utility. These movies are based on a presentation I gave at the CalTeX Mac Fest and at TUG 2007. (Unfortunately, my TUG demo was plagued by technical difficulties, so if you attended, these movies will show you what it should have looked like!)
- Part 1: Introduction to LaTeXiT; Using Keynote with LaTeXiT and LinkBack [12 MB Quicktime]
- Part 2: Creating 2D Figures with Adobe Illustrator and LaTeXiT [14 MB Quicktime]
- Part 3: Creating 3D Figures with Adobe Illustrator and LaTeXiT [6 MB Quicktime]
- Part 4: Adding Transparency to 3D Figures [5 MB Quicktime]
Note: when using LaTeXiT with Illustrator, be sure LaTeXiT is set up to export the format "PDF with outlined fonts" — otherwise Illustrator won't be able to import the correct LaTeX fonts. This option can be found in the "General" tab of the LaTeXiT Preferences window.
FasTeX
FasTeX is a system
of abbreviations for LaTeX commands: for example, beq
becomes \begin{equation}; lel
becomes \left\langle; lld ("left langle
double") becomes \left\langle\!\left\langle. These
abbreviations are automatically expanded as you type, without the need
to input any special commands or escape keys; effectively, it lets you
type LaTeX documents in shorthand. Once learned, it can dramatically
increase speed and reduce typos for people who do a lot of work in
LaTeX. Although TeXShop users typically have to purchase abbreviation
software like TypeIt4Me to use
FasTeX, Emacs (my editor of choice) has built-in abbreviation
facilities.
Emacs and LaTeX
While many Mac users like the excellent TeXShop software for working in LaTeX, I'm a big fan of the Emacs editor for just about any work I do. I use Carbon Emacs, which is a version of Emacs for Mac OS X that includes a number of useful pre-configured packages, such as the powerful AUCTeX package for LaTeX editing.
I have also integrated FasTeX into my Emacs environment, which I
think is great for anyone who uses Emacs and LaTeX. If you'd like
to do this, download the abbreviation file latex-abbrev.el, put the file in your
Emacs load-path, and add the following lines to your
.emacs file:
(add-hook 'LaTeX-mode-hook (lambda () (quietly-read-abbrev-file "latex-abbrev.el") (setq local-abbrev-table LaTeX-mode-abbrev-table) (abbrev-mode t) ))
Contact
Ari Stern
California Institute of Technology
1200 E. California Blvd. M/C 217-50
Pasadena, CA 91125
You can also email me at astern@acm.caltech.edu.