# Computational Modeling at Carleton

**Fractal Art**

**What is a fractal?**

**Projects listed below were last updated in October, 2006. More recent activities are detailed above.**

## Interdisciplinary Computational Modeling Workshop, April 2006

Multiple oganizations at Carleton (including CISMI and HHMI) co-sponsored a workshop for faculty and staff from across the college on April 20-21, 2006. Bob Panoff , from the National Computational Science Institute, facilitated the workshop. The workshop was organized by Susan Singer (Biology) and Arjendu Pattanayak and Bill Titus (Physics/Astronomy). The goal of the workshop was to provide an in-depth introduction to how computational modeling can be used across the curriculum to enrich student learning. Participants learned about the many models and software packages (including animation features in Excel) to help them integrate modeling into their classes. Curricular projects of various types emerged from this workshop.

## Interdisciplinary Computational Modeling Course

Susan Singer (Biology), Arjendu Pattanayak , and Bill Titus (Physics/Astronomy) received summer 2006 HHMI curricular funds to develop a project-oriented modeling course open to students from all disciplines. The course will start with general principles and tools, including ideas common to all quantitative disciplines about the elements of successful models. Students will be exposed to analytical and computational techniques. Background information about the general behavior of nonlinear deterministic systems and probabilistic systems will be included. The first part of the course will also include several case studies, highlighting applications of modeling to real systems. The latter part of the course will focus on applications of these ideas to specific projects, with students working in interdisciplinary teams with an appropriate faculty advisor. Project examples include the dynamics of epidemics on networks, ecological and climate dynamics, and the use of fractals to model pattern formation. This course will be offered as IDSC 217 for the first time in spring 2007.## New Course at Intersection of Computer Science & Economics

David Liben-Nowell (Computer Science) used summer 2006 HHMI curriculum funds to develop a new upper-level course that addresses problems arising at the boundaries of economics and computer science. Within the last few years, an area of interdisciplinary research combining these perspectives has emerged. David is developing a course that investigates questions of this nature:- How much slower are road travel times when individual selfishly select the fastest routes vs. when a centralized authority commands each individual route?
- In economics, competing agents who choose strategies are said to be in
*Nash equilibrium*if each agent's chosen strategy is the best possible response to the strategies of other agents. Can one efficiently compute*Nash equilibria*?

David would like students to recognize the limitations of models traditionally studied in economics or computer science, understand and formulate richer models that draw on both fields, and apply these models to new problems. Game theory will serve as a primary tool throughout the course.

David also used HHMI funding to attend the 7^{th} ACM Conference on Electronic Commerce in Ann Arbor, MI in June 2006.

## Computational Modeling Exercises for Environmental Chemistry

With HHMI funding in summer 2006, Will Hollingsworth (Chemistry) is**designing new computational modeling activities for his introductory environmental chemistry course**(Chem 128). The exercises are aimed at helping students better understand the basics of chemical reaction rates (kinetics) and their application to environmental problems (including atmospheric ozone chemistry, see model at right). Will has been using two modeling programs: STELLA (more info) and VENSIM . He has been learning VENSIM, transferring modeling exercises from STELLA to VENSIM, and creating new Vensim models for student learning. Both of these programs will allow students to do interactive modeling of dynamic systems, including chemical reactions and environmental systems.

Modeling of chemical reaction rates deals with the fundamental molecular steps in a chemical reaction. The focus is on exactly solvable expressions which apply for only the simplest cases. In contrast, models for environmental systems look more broadly at changes over time in much more complicated and macroscopic systems, without the benefit of exact mathematics or full system understanding. Dynamic system software, such as Vensim, allows students to create an important bridge between these two extremes. When exact mathematics are not possible in modeling environmental systems, a faithful representation of the system's time behavior can be determined through approximation. With Vensim, it is easy for the students to build visually intuitive models that can be easily adapted and altered to see how sensitive results are to changes in one or more key variables.