This summer I finished writing my Ph.D. thesis. I interviewed for various research post-docs in Boston, New York and Reading, UK. I decided to go to Columbia University this fall to work with Adam Sobel in the Department of Applied Math and Applied Physics and in the Lamont-Doherty Earth Observatory.

I am working on a project with Janice Coen (NCAR) and Jana Milford (CU BOULDER, Mechanical Engineering Dept). This project is at its beginning, and it looks like it will become my MS thesis. It is a spatiotemporal (time-series) study of a controlled burn outside of Fairbanks, Alaska. Much of the data appears to follow nonstationary patterns.

I would happy to provide more details as the study progresses.

VIGRE: Applied Math UCB
Ferroelectric Materials Lab: Physics UCB
Proteomics Lab: MCDB UCB

I finished up my fractal research that I started last september. This involved some last minute research writing my paper and giving a talk at siam. I also worked for the physics department doing some liquid crystal simulation. In addition to this I make some data analysis scripts for a Proeomics lab.

- Geoff
Ex Astris Scientia

I worked at Lawrence Livermore National Laboratory (LLNL), and this was my second summer doing research on multigrid methods in the LLNL's Center for Applied Scientific Computing. Our problem of choice was the convective transport equation, a hyperbolic PDE of much interest to the lab. During the previous semester we found degraded Algebraic Multigrid performance (supported by VIGRE!) and researching the cause of these inefficiencies was the primary goal of the summer.

This summer I worked at the Geophysical Statistics Project at NCAR.

I dealt with a stochastic model that is set up to blend information from numerical data and satellite measurements into the "true state" of the wind. My task was to find more accurate ways to simulate these true wind states from the model.

It was a good experience to see the more applied end of my research and I'm excited to continue to work at NCAR for one day a week during the semester. This work will also part of my thesis.

During the summer 2002 I continued working on my PhD research. My work involves characterising numerical diffusion in MHD type algorithms for astrophysical computing. At first, we analyzed numerical difusion of one dimensional advection equation with Upwind, Lax, Lax-Wendroff, and VanLeer Schemes. Currently I am extending the same tools to two dimensional wave propagation algorithms.

My advisers are: Ellen Zweibel (APS) and Bengt Fornberg (APPM).
There is more information on my webpage: http://lcd-www.colorado.edu/~zuev/R/

I volunteered my time, computer, and brain to Mesa State College. In return, I received no monies or honors. Or honours. I did, however, get to tinker around with the picture capabilities of MATLAB and learn a tremendous amount about fourier transforms in the area of deblurring.

Essentially, every pixel is represented by a number, so a matrix is rendered of a digitally read-in blurred image. Using fourier transforming techniques, theoretically, one should be able to recover the original image by operating on the 'blurred' matrix, rendering a new matrix which when translated into an image, should be the deblurred (original) image. The project is on-going even though the summer has come to a close. I'll let the department know when a paper is published.

During the summer of 2002 I worked with (1) Oswald Metzen, GmbH, German construction materials manufaturer, and (2) Obermeyer Hydro, Inc., manufacture weirs, control systems, and various other accessories for hydroelectrical systems.

Oswald Metzen licensed a patent on a hops silo to a company called Buehler, which was selling the silo to the New Belgium Brewery in Fort Collins. The Metzen representative sent to supervise construction did not speak English, so I was hired as an interpreter.

Obermeyer Hydro sells spillway gates for dams internationally. Two projects in Germany required Installation supervision, but none of the full time employees speak German. I volunteered to supervise installation in exchange for an all expenses paid Europe trip.

During this past summer, I worked as a software designer at Microsoft Corporation in Redmond WA. I learned a lot about server management issues at the enterprise level.

Part of a new management product is a redesigned user interface (UI). I chose one of the proposed interfaces and designed a prototype to demonstrate the UI. I worked with another intern in designing the specifications for the prototype and our project was demoed at the team meeting at the end of the summer. We got a lot of positive comments from the group (possibly because our demo was the only one without technical difficulties).

I ventured into the area of software testing side briefly - just long enough to write a test plan for the prototype. Unfortunately this position had very few mathematical applications.

This summer has been an exciting and hectic mix of teaching, research, and collaboration with scientists at NCAR. I taught two sections of differential equations during the eight week session. This involved three hours of lecture plus one or two office hours every day. This is the first advanced mathematics course which I have taught and I am grateful to the department for such an opportunity.

As a mentor and tutor for NCAR's SOARs program, I was responsible for two undergraduate scientists. Their research project involved produced three dimensional animations of climate model output.

Finally, in May and August I worked on my numerical model, which is the topic of my research. In September I will go to the "Helmholtz Summerschool for Supercomputing in Climate Modeling" in Berlin.

Metropolis Digital Inc.

During the summer of 2002, I worked as an assistant programmer at MDI in San Jose. MDI specializes in developing and publishing games on next generation console systems. My primary task was to fix bugs in a Sony Playstation2 title to be released in Japan. This work was being done by consultants when I arrived but was assigned to me since I learn a little bit of Japanese at CU and the testers in our Japan office were not pleased with the work of the consultants. After this we also made another version for the Korean market.

Overall it was a very enjoyable summer. I had access to technical material and development hardware from Sony Computer Entertainment and had a chance to practice some real world programming and now have a better understanding what kind of training I need.

I was reluctant at the beginning of the summer to pursue any engineering-related work of any kind, as I recovered from a considerable burnout after a hard semester academically and personally. Having talked with fellow students in applied math, though, I learned about research opportunities within the department, and became quickly interested. Before I knew it, an outstanding opportunity lay before me, and I took advantage of it, and have been working on research-related materials ever since.

My supervising professor, Dr. Lucas Monzon is performing research involving the mathematics behind a new approach at signal approximation and compression. My work demanded that I gain experience using Mathematica, and I have since helped develop a simple 3-D plotting tool for complex numbers. Using this tool and others developed by Dr. Monzon, we were able to gain insight into various applications of the approximation process.

I did two major things, one was teach, the other was study for the PDE prelim.

The teaching was great, I taught the "Connections" class with Erik Fisher, it's a multi-disciplinary class. We talk about math, music, philosophy and physics. We read mostly original sources and discuss them. The kids who take it seem to like it a lot, and so do we. Daniel Jones from music, our own Hans De Sterck, Allan Franklin from physics, and Doug Robertson from CIRES all show up on different days to help Erik and I out.

The other class I taught was calc. 1 for the MEP/MASP Summer Bridge program. The Bridge program is to help the MEP/MASP kids who are entering now as freshmen get a head start on the topics and study habits they'll need to do well here. Rudy used to teach physics for them. It's a great program, if they ever try to recruit you to teach for them, I certainly recommend it.

Studying for the prelim was studying for the prelim. We all grew facial hair for good luck. I think it worked.

NCAR / VIGRE (in profesor Manteuffel's research group):

I spent part of my time in June and July working for VIGRE. I learning a few finite element methods and developed matlab programs that approximated Laplace's equation. I will use this experience in the upcoming semesters to modify the groups FOSPAC pde package, in order to use bi-quadratic approximations not just bi-linears as is the case right now.

I worked for NCAR, during the remaining parts of summer. I was involved with the scientific computation group mainly doing linux administation on some of the large server machines. I also did a little work with some visualization and graphics tools such as NCL. I used these tools to analyze some shallow water test models.

I also gained a great deal of experience for the applied math field this summer by playing a lot of golf. I'm working on getting my handicap below 8 by the end of the fall. Spending time studying for my Fastasy football team was also explored heavily this summer.

I was involved in the creation of an internal (Sun Microsystems, Inc.) software project encompassing order entry, product groupings, resource allocation, billing, contract management, and product delivery. In addition, a large portion of the software is going to be accessed through an ecommerce web portal. The software will be used by Sun throughout the Americas, Europe, and Asia. We used a UML based object oriented approach to the system design which required us to create process flow diagrams to graphically layout the system, and then use case diagrams to give as much system detail as possible.

The use cases and process flows are eventually going to be used by the developers to code the software. Each process flow and use case diagram had to be approved by team leaders in the Americas, Europe and Asia and we used conference calls and web broadcasting to communicate internationally.

On the lighter side, I was fortunate enough to work with some very bright people, both interns and full-time Sun employees. I learned an enormous amount about the business culture, the importance of group dynamics, and the basic ideology of a very successful company.

This summer I returned to the Mathematical Modeling and Analysis group at Los Alamos National Laboratory (LANL) to continue my work with David Moulton on multigrid and numerical upscaling techniques. While multigrid is typically used to solve the large, sparse linear systems arising from discretizations of PDEs, our work focuses on the use of multigrid-style coarsening in numerical upscaling.

Numerical upscaling can be thought of as the determination of the effective material properties of a composite material. If the variation in material properties is at a very fine scale, it can be computationally intractable to perform fully resolved simulations. Thus, we seek to appropriately average the fine-scale operator over coarse-scale regions. We use operator-dependent multigrid coarsening techniques to create coarse-scale discretizations from a fine-scale discretization, and thus our coarse-scale operators include the effects of the fine-scale variations in material properties. From these coarse-scale operators we recover the effective coarse-scale material properties. These can then be used in computationally tractable simulations.

Over the summer, I worked in both the mortgage business and the finance field. The first job consisted of all of the transactions in respect to refinancing and purchasing new homes. Closings, credit reports, etc. The second internship was interesting as well. The company FNStar developed a software application for financial advisors of numerous companies. The application reported and tracked data from all of the clients, scraped data from the internet in order to improve the advisors portfolio modeling for the client, and it also made predictions for client retirement plans. I learned a little about the application and was working in order to sell the product.

Aside from the internships, I have also been working on a couple of compositions on keyboard/piano. I finished a song called "Suicidal Ambitions" which has no relation to the literal meaning. It stands for the breaking off of one's own passion and forming a new one. The song is nifty, however, in the fact that it covers 9 different genres symbolizing a series of events that happened to me and some friends that I hung out with from the last christmas break to spring break.

I'm also in the process of working on a "Soundtrack that does not have a movie" which is coming out slowly, yet nicely. It'd actually be cool to play a couple of pieces at this next christmas get together, similar to last year. That's about it for the summer,

Sun Microsystems / MVT Development:

The Applied Math Department at CU has given me the opportunity to lead a development team that has added new 3D graphics capabilities and greater flexibility to the MVT (Mathematics Visualization Toolkit). The applet/application is used in order to complete labs that are required for undergraduate Calculus 3 and Differential Equations classes. Sun Microsystems employed me as an intern Java devloper/manager for the duration of the project. This summer opportunity extended my list of job skills far beyond that of a meager programmer, and helped to enlarge my network of contacts in academia and industry. I also got the opportunity to travel to Dillard University in New Orleans to help integrate MVT technology into their cirriculum.

The experience has benefited me in several ways. The project gave me the opportunity to become an intern-manager, which is a very unique situation given the current job market. The success and failures I experienced in management throughout the summer helped me to become a more effective leader. My Java programming skills were certainly focused, which has given me much intuition about what can be done and a notion of how quickly things can be accomplished. The interation with the people at Sun gave me corporate exposure that gave me valuable datapoints that will influence my career decisions after graduation. In conclusion, it was a very beneficial summer full of new challenges and experiences that helped to shape my future.

National Center for Atmospheric Research, Boulder, CO
Climate & Global Dynamics Division, Climate Modeling Section

I spent this summer doing numerical analysis and solving mathematical schemes. My boss, Dr. Bill Collins, one of the head scientists at NCAR, took me on as a student assistant directly responsible to him. In the current Community Climate Model (CCM) created by NCAR, the treatment of upwelling long wave radiation throughout the atmosphere is crudely approximated in the current code. Bill and my job was to come up with a new mathematical scheme, which contains a more detailed treatment, specifically of the Planck Law for radiation, and also a more accurate function to model the transmission between atmospheric layers, including a new relation between the optical depth of the atmosphere and the corresponding temperature.

My job was to run some numerical tests (using Mathematica) on the new scheme that Bill concocted, to see if it would be a plausible addition to the climate code. After determining that the scheme does indeed work, my job then moved to more of a programming position, as it was now necessary to code the scheme up in FORTRAN. After getting the code to work, then it was modified to read in actual data for variables such as the optical depth, wavenumber, and temperature. Then the outputed Intensity was compared with the real life flux observed out the top of the atmosphere, and behold, it agreed very well! So this is the gist of what I did, however Bill has other projects for me over the course of the next couple years.

During the summer of 2002 I worked at the European Organization for Nuclear Research (CERN) in Geneva, Switzerland. This was made possible by a Research Experience for Undergraduates (REU) program through the University of Michigan, funded by the National Science Foundation and Ford Motor Company. At CERN I was a part of the CERN Summer Student program; we attended three hours of lecture every morning on diverse particle physics topics, and worked on research projects in the afternoons. For my research project, I worked with a group from the ATLAS (A Toroidal LHC ApparatuS) Collaboration to develop a conditions database.

One of the main physics goals of the ATLAS detector is to discover and study the Higgs Boson, believed to give mass to matter. One of the characteristic decays of this particle results in four muon tracks; in order to do accurate physics, these tracks must be measured very precisely. The ATLAS detector is on the order of 40 meters high, but we hope to obtain tracking resolution within the 10-micron level. Monitored Drift Chambers make up the Muon Spectrometer, which is designed to meet this challenge of precision tracking. Mechanical stresses, temperature gradients, and other factors, however, can cause the chambers to shift; these shifts must be recorded, and those data used to make corrections in the resulting muon tracks.

To this end, alignment devices will be installed on the muon chambers and their support structures. Each alignment device has many calibration constants associated with it, and the actual alignment data are produced by the interaction of many such alignment devices. To keep track of the alignment devices, their relationships, and associated constants, I constructed a conditions database using Microsoft Access, Visual Basic for Applications, and Microsoft JET SQL. This database is currently in use at the H8 test beam facility for the Muon Spectrometer End-Caps at the CERN Prvesin site. In order to allow more scalability and automated interface with control programmes, we also began a parallel development in mySQL.