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## NetLogo Models Library: |

If you download the NetLogo application, this model is included. (You can also run this model in your browser, but we don't recommend it; details here.) |

This model is the simplest gas model in the suite of GasLab models. The particles are moving and colliding with each other with no external constraints, such as gravity or containers. In this model, particles are modeled as perfectly elastic ones with no energy except their kinetic energy -- which is due to their motion. Collisions between particles are elastic. Particles are colored according to their speed -- blue for slow, green for medium, and red for high.

This model is one in a series of GasLab models. They use the same basic rules for simulating the behavior of gases. Each model integrates different features in order to highlight different aspects of gas behavior.

The basic principle of the models is that gas particles are assumed to have two elementary actions: they move and they collide --- either with other particles or with any other objects such as walls.

The basic principle of all GasLab models is the following algorithm (for more details, see the model "GasLab Gas in a Box"):

1) A particle moves in a straight line without changing its speed, unless it collides with another particle or bounces off the wall. 2) Two particles "collide" if they find themselves on the same patch (NetLogo's View is composed of a grid of small squares called patches). In this model, two particles are aimed so that they will collide at the origin. 3) An angle of collision for the particles is chosen, as if they were two solid balls that hit, and this angle describes the direction of the line connecting their centers. 4) The particles exchange momentum and energy only along this line, conforming to the conservation of momentum and energy for elastic collisions. 5) Each particle is assigned its new speed, heading and energy.

Initial settings: - NUMBER-OF-PARTICLES: the number of gas particles. - TRACE?: Draws the path of one individual particle. - COLLIDE?: Turns collisions between particles on and off. - INIT-PARTICLE-SPEED: the initial speed of each particle -- they all start with the same speed. - PARTICLE-MASS: the mass of each particle -- they all have the same mass.

As in most NetLogo models, the first step is to press SETUP. It puts in the initial conditions you have set with the sliders. Be sure to wait till the SETUP button stops before pushing GO. The GO button runs the models again and again. This is a "forever" button.

Monitors: - PERCENT FAST, PERCENT MEDIUM, PERCENT SLOW monitors: percent of particles with different speeds: fast (red), medium (green), and slow (blue). - AVERAGE SPEED: average speed of the particles. - AVERAGE ENERGY: average kinetic energy of the particles.

Plots: - SPEED COUNTS: plots the number of particles in each range of speed (fast, medium or slow). - SPEED HISTOGRAM: speed distribution of all the particles. The gray line is the average value, and the black line is the initial average. The displayed values for speed are ten times the actual values. - ENERGY HISTOGRAM: the distribution of energies of all the particles, calculated as (m*v^2)/2. The gray line is the average value, and the black line is the initial average.

Initially, all the particles have the same speed but random directions. Therefore the first histogram plots of speed and energy should show only one column each. As the particles repeatedly collide, they exchange energy and head off in new directions, and the speeds are dispersed --- some particles get faster, some get slower, and the plot will show that change.

What is happening to the numbers of particles of different colors? Why are there more blue particles than red ones?

Can you observe collisions and color changes as they happen? For instance, when a red particle hits a green particle, what color do they each become?

Why does the average speed (avg-speed) drop? Does this violate conservation of energy?

This gas is in "endless space" -- no boundaries, no obstructions, but still a finite size! Is there a physical situation like this?

Watch the particle whose path is traced in the drawing. Notice how the path "wraps" around the world. Does the trace resemble Brownian motion? Can you recognize when a collision happens? What factors affect the frequency of collisions? What about the "angularity" of the path? Could you get it to stay "local" or travel all over the world?

In what ways is this model an "idealization" of the real world?

Set all the particles in part of the world, or with the same heading -- what happens? Does this correspond to a physical possibility?

Try different settings, especially the extremes. Are the histograms different? Does the trace pattern change?

Are there other interesting quantities to keep track of?

Look up or calculate the *real* number, size, mass and speed of particles in a typical gas. When you compare those numbers to the ones in the model, are you surprised this model works as well as it does? What physical phenomena might be observed if there really were a small number of big particles in the space around us?

We often say outer space is a vacuum. Is that really true? How many particles would there be in a space the size of this computer?

Could you find a way to measure or express the "temperature" of this imaginary gas? Try to construct a thermometer.

What happens if there are particles of different masses? (See "GasLab Two Gas" model.)

How would you define and calculate pressure in this "boundless" space?

What happens if the gas is inside a container instead of a boundless space? (See "Gas in a Box" model.)

What happens if the collisions are non-elastic?

How does this 2-D model differ from the 3-D model?

Set up only two particles to collide head-on. This may help to show how the collision rule works. Remember that the axis of collision is being randomly chosen each time.

What if some of the particles had a "drift" tendency -- a force pulling them in one direction? Could you develop a model of a centrifuge, or charged particles in an electric field?

Find a way to monitor how often particles collide, and how far they go, on average, between collisions. The latter is called the "mean free path". What factors affect its value?

In what ways is this idealization different from the one used to derive the Maxwell-Boltzmann distribution? Specifically, what other code could be used to represent the two-body collisions of particles?

If *more* than two particles arrive on the same patch, the current code says they don't collide. Is this a mistake? How does it affect the results?

Is this model valid for fluids in any aspect? How could it be made to be fluid-like?

Notice the use of the `histogram`

primitive.

Notice how collisions are detected by the turtles and how the code guarantees that the same two particles do not collide twice. What happens if we let the patches detect them?

This model was developed as part of the GasLab curriculum (http://ccl.northwestern.edu/curriculum/gaslab/) and has also been incorporated into the Connected Chemistry curriculum (http://ccl.northwestern.edu/curriculum/ConnectedChemistry/)

This was one of the original Connection Machine StarLogo applications (under the name GPCEE) and is now ported to NetLogo as part of the Participatory Simulations project.

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

- Wilensky, U. (1997). NetLogo GasLab Free Gas model. http://ccl.northwestern.edu/netlogo/models/GasLabFreeGas. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Copyright 1997 Uri Wilensky.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was developed at the MIT Media Lab using CM StarLogo. See Wilensky, U. (1993). Thesis - Connected Mathematics: Building Concrete Relationships with Mathematical Knowledge. Adapted to StarLogoT, 1997, as part of the Connected Mathematics Project. Adapted to NetLogo, 2002, as part of the Participatory Simulations Project.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2002.

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