picture

Course Description

Many significant real-life problems today are interdisciplinary in nature, involving physical, biological sciences, and/or social sciences, mathematics, and computer science in an area called computational science. Computing and modeling can often stimulate the insight and understanding that theory and experiment alone cannot achieve. This course prepares students to understand and utilize fundamental concepts of computational science. The course considers two major modeling approaches: system dynamics models and cellular automaton simulations. System dynamics models provide integral views of interacting system components that change with time. To model such dynamic systems, students will employ a tool called Vensim. With this tool, students can create pictorial representations of models, develop relationships, run simulations, and generate graphs of the results. In contrast to system dynamics, cellular automaton simulations provide local views of individuals affecting individuals. The virtual world under consideration consists of a rectangular grid of cells, and each cell has a state that can change with time according to certain rules.

This course does not require computer programming experience. The concept of rate of change is used throughout the course. The course will provide the necessary background for the student to understand the material and confidently succeed in the course. The course covers numerous applications in a wide variety of areas. Each class involving such an application will provide the prerequisite science without overwhelming the students with excessive detail.

In Turkey, we will study the local issues, such as tourism, forest fire, fisheries, and ecology of Dalyan river and we will discuss modeling of these problems.

Textbook:

Shiflet, A. B. and G. W. Shiflet, Introduction to Computational Science: Modeling and Simulation for the Sciences, Princeton University Press, 2006.

Learning Outcomes

  1. To be able to analyze the complex problems with a dynamic behavior as a system.

    1. The students can understand the complexity of problems presented in a textual form.
    2. The students can identify the components of a complex problem.
    3. The students can define the component action and interactions.
  2. To be able to construct a model to represent a complex problem.

    1. The students can construct a simulation model to represent complex relationships of a system with variables, constraints, and formulas.
    2. The students can handle the random behavior of the components.
    3. The students can build computational models in the programming tool of the course.
    4. The students can rectify various types of computational errors in the models.
    5. The students can interpret the outcome of models and identify the role that the components play on these outcomes.
  3. be able to understand complex problems in the immediate environment that can be tackled with the computational modeling.

    1. The students can describe the problem fully in writing.
    2. The students can identify the components of the problem and their actions and interactions.
    3. The students can form a rough model of the problem without data collection.
  4. To be able to report on an application to a complex problem.

    1. The students can write a technical report on computational modeling of a complex problem.
    2. The students can present their findings to an audience in an effective manner.

Grading

it may be taken on a grade or a credit/no-credit basis.
The course grade will assigned on the basis of the following activities:

Course Outline (Tentative schedule)

Week
Day Topics
1
1 Overview of Computational Science
Programming tool: Vensim
Errors in computations
Rate of change
Model: Unconstrained Growth and Decay
2 Systems Dynamics Problems
Constrained Growth and Carrying capacity
Equilibrium and stability
Models: Drug dosage and Skydiving
3 Simulation Techniques
Euler’s method
Runge-Kutta 2 method
4 Models with interactions
Competition
Spread of SARS
Quiz 1
2
5 Predator Prey Model
Introduction
Lotka-Volterra Model
Projects
6 The Carbon Cycle
Flows between subsystems
Fossil fuels
Projects
7 Global warming
Greenhouse effect
Greenhouse gasses
Projects
8 Mercury pollution
Introduction
Projects
Quiz 2
3
9 Cardiovascular Systems
Circulation
Blood pressure
Stroke volume
Blood flow
Projects
10 Managing Fishery
Economics background
Gordon-Schaefer Production function
Projects
11 Monte Carlo (MC) simulation
Random number generators
Generating events from simple distributions
Exercises
12 Calculating area through MC
Introduction
Exercises
Quiz 3
4
13 Random walk
Introduction
Algorithm for Random walk
Average distance covered
Relationship between steps and distance
14 Spreading fire
Introduction
Updating rules
Simulation and Animation
15 Final Day
Project presentations
Final Exam
12 Calculating area through MC
Introduction
Exercises
Quiz 3