Condensation Simulation

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SIMIODE

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Published on September 11, 2016 10:30:04 AM ● Video Link: https://www.youtube.com/watch?v=0mkK5J-d2pY

Duration: 10:00

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Simulation of 200 particles bouncing in a square region in which the particles condense on the bottom edge.

Consider the random motion of 200 particles in a 50 by 50 square with vertices (0,0), (0,50), (50,50), (0,50) in a plane. At each iteration, n = 0, 1, 2, . . . each particle moves 1 unit in one direction only, due north, due east, due south, or due west, and it must move.

Particles are initially randomly distributed on points with integer coordinates. The number of condensed particles is tallied at each iteration.

If a particle comes in contact with the west, east, or north wall it bounces off by returning to the position just before the bump. If the particle comes in contact with the south or bottom wall it condenses and stays exactly at the position of contact, thus depleting the number of particles which are still randomly moving in the square. Here we show an image of each iterations of the particles and the plot of the number of condensed particles at each iteration.

Viewers can collect data from this simulation and validate their differential equation models.

This material is in support of teaching differential equations using modeling: SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations.

Source: 1-47-S-Condensation Modeling Scenario at https://www.simiode.org/resources/2412