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Physicist Harvey Gould and his students create computer simulations to understand the behavior of atoms and molecules in a variety of contexts, especially those that are difficult to study using traditional experimental methods. |
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Virtual realities
Professor Harvey Gould's research
What if fifty people, starting from exactly the same place, begin to walk in completely random fashion? How would they be dispersed in space after an hour has passed?
Physicist Harvey Gould teaches his students how to write interactive Java programs that allow them to simulate "what if" scenarios. Simulations are valuable tools for understanding complex physical systems, like the movement of molecules in a gas, or the alignment of electron spins in a magnet*. The simulations incorporate assumptions about the system of interest as well as one or more parameters that a user can manipulate in a control window. A variety of output information, which can be animated, is displayed in one or more additional windows at the same time.
For example, the random walker scenario, above, contains the following assumptions:
- Movement takes place in a flat, unbounded, two-dimensional plane, free from obstacles.
- More than one walker can occupy the same place at one time.
- The walkers all move at a constant speed with equally sized steps.
And the following variables:
- The user can choose the number of walkers.
- The user can determine the length of time they're allowed to walk.
- Although the program constrains the directions in which the walkers can move (forward, backward, left or right), the user can determine the probability that a walker will move in a particular direction.
In addition to a control window and a graphic visualization window, the program includes a window with a graph showing the number of walkers at specific distances from the origin point. The distance along the x-axis represents the walkers' distances from origin at a given time, while the number of walkers at any given distance is measured along the y-axis. This window updates continuously as the simulation runs.
Computer simulations are helpful to both programmer and user. The programmer must understand the variables and their relationships in order to design a useful simulation. The process of asking how one can convert an abstract idea into a realistic simulation can spur the physicist to view the system from new and useful perspectives, perspectives that might not have been apparent in a purely theoretical approach. Simulations are also useful in situations where a physical process is difficult to manipulate or observe in the laboratory.
From the perspective of users, the simulation's interactive capabilities can spur them to formulate many "what if" questions. In the above example, such questions might include:
- What if the number of walkers increases?
- How does that affect the dispersion pattern?
- How does the pattern change over time?
- What happens if the probability that a walker steps to the right is increased?
Gould is an enthusiastic believer in the importance of physics students learning how to create their own simulations. He is currently at work on the third edition of Introduction to Computer Simulation Methods: Applications to Physical Systems, a popular undergraduate-level textbook designed to teach physics students how to write simulations using Java. He's also helping to develop the Open Source Physics Library, which will make writing simulations much easier. Gould works to bring recent developments in research into the undergraduate curriculum as quickly as possible and to involve students in research.
While computers have greatly enhanced the study of physics through their ability to solve complex mathematical equations and store vast amounts of data, Gould believes that the computer's greatest potential lies in its ability to help us simulate and represent visually the intricacies of the physical world.
* For more about magnets, check out "Having a magnetic moment."
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Additional Resources
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 Random Walk parameter input: the number of walkers, and the probabil- ity that they will walk in each of four directions.
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 Walk simulation. |
 A graph showing the distance of walkers from the origin over time |
| In this simulation, the probability that walkers will move left is slightly higher. Try the Random Walk simulation. (This applet requires Java 1.2+ to be installed on your computer. For a free download, click here.) |
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