Math in the News: 5/2/11
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Math in the News: 5/2/11

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In this issue of Math in the News we look at the wildfires in Texas. Why are they so prevalent this year? How can mathematical models help in predicting the path of a fire?

In this issue of Math in the News we look at the wildfires in Texas. Why are they so prevalent this year? How can mathematical models help in predicting the path of a fire?

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Math in the News: 5/2/11 Presentation Transcript

  • 1. 5/2/11
  • 2. Texas Wildfires
    • Making Predictions
    • The large number of wildfires in Texas this year is due to a number of factors:
      • Drought conditions
      • Geography of Texas
      • Low humidity and strong winds
  • 3. Texas Wildfires
    • Making Predictions
    • The path of a wildfire is also affected by trees, grass, and other environmental factors.
    • The movement of wildfires through the landscape is somewhat random and can be modeled using random numbers.
  • 4. Texas Wildfires
    • Making Predictions
    • One way that fire science experts model the behavior of a wildfire is to use a “random walk” simulation.
    • Imagine an ant on a coordinate grid and the random walk it would take across it.
  • 5. Texas Wildfires
    • A Random Walk Simulation
    • You can create a random walk using an Excel spreadsheet.
    • The data in the table, represented in the graph, was generated using a random number formula.
  • 6. Texas Wildfires
    • A Random Walk Simulation
    • Add two column headings, x and y, to A1 and B1.
    • Start at the origin. Enter 0 in A2 and B2.
    • Enter this formula (shown for A3) in subsequent rows:
    • =A2+RANDBETWEEN(-2,2)
    • Graph the data.
  • 7. Texas Wildfires
    • A Random Walk Simulation
    • You can refine the simulation by including additional variables. For example, this random walk includes wind speed, direction, and a forest line in the path of the fire. Although it is still a random walk, the external variables have an influence.
  • 8. Texas Wildfires
    • A Wave Model Simulation
    • Another model used by fire science experts is a wave model.
    • Think of a water wave, or a ripple in a pond.
  • 9. Texas Wildfires
    • A Wave Model Simulation
    • Using Huygens Principle, at any point along the wave front, the wave is made up of small wavelets that each can generate its own wave form.
  • 10. Texas Wildfires
    • A Wave Model Simulation
    • Huygens Principle accounts for the behavior of waves when they meet different boundaries.
  • 11. Texas Wildfires
    • A Wave Model Simulation
    • The “wave” behavior of wildfires can be seen as a wildfire, thought of as a “wave front,” approaches a tree line.
  • 12. Texas Wildfires
    • A Wave Model Simulation
    • The tree line acts as a boundary that affects the movement of the wave.
  • 13. Texas Wildfires
    • A Wave Model Simulation
    • Taking the wave nature of wildfires into account, and modifying the random walk, results in a path like this, which is a reasonably accurate model of the path of a wildfire.
  • 14. Texas Wildfires
    • Making Predictions
    • Why are wildfire mathematical models important? The path of a wildfire is not an abstract line in space, but a real location, where people live. Being able to predict the behavior of a fire has important implications.