Heat Flow and Diffusion -- Markov Chains -- TI-92

The TI-92 material for this module has two parts. This part discusses modeling diffusion using Markov chains. The other part discusses modeling diffusion using simulation. Click here to go to the section on modeling by simulation.

The two TI-92 help modules below provide basic help for working with sequences.

• Graphing one or more sequences.
• Making a table of sequence values.

For the five-celled organism in this section we use five sequences to keep track of the fraction of the substance found in each cell.

• The sequence u₁(n) keeps track of the fraction of the substance in the leftmost cell.
• The sequence u₂(n) keeps track of the fraction of the substance in the second cell from the left.
• The sequence u₃(n) keeps track of the fraction of the substance in the middle cell.
• The sequence u₄(n) keeps track of the fraction of the substance in the second cell from the right.
• The sequence u₅(n) keeps track of the fraction of the substance in the rightmost cell.

The TI-92 screen shows how the Y= screen is set up for an example in which all of the substance starts out in the leftmost cell.

The two screens below show some results as a graph and as a table.

You can use the ideas developed here and in the laboratory material on simulation to study questions like the ones raised in the narrative part of this module.