Chapter 15 Partial Differential Equation Models

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Chapter 15Partial Differential Equation Models

• Method of Lines
• One Dimensional Diffusion
• Example Triangular Initial Data Distribution
• Number of Transitions Activity

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Example One Dimensional Diffusion (PDE)
lower than neighbors
in between neighbors
higher than neighbors
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One Dimensional Diffusion (Cond)
higher than neighbors
lower than neighbors
tend to flatten out
u
in between neighbors
x
x
over time
x
x
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DEVS Implementation of 1D Diffusion
oneDimCellSpace
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DEVS Implementation of 1D Diffusion sloping
initial state
oneDimCellSpace
length and height 11 and speed 10, 11 cells
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Definition and Measurement of Activity
Continuous segment
Piecewise Continuous Segment
Activity sum of ranges. Avg Activity Af
for wave with amplitude A and frequency f
computational efficiency occurs when number of
transitions reflects number of threshold crossings
activity in monotonic region reflects avg rate
of change
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activity distribution
activity 35.5 (area of space with arrows)
length and height 11 and speed 10, 11
cells Since there is some oscillartion arround
5.5, I used the first time to hit 5.5 in the
table.The oscillation is about 3 times the
quantum.
DEVS transitions Activity/quantum
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q .01
q .001
q .0001
As quantum gets smaller, the DEVS transitions
gets closer to the predicted activity. The reason
can be found in the distribution over cells which
moves from uniform to the sharp curve predicted.
The uniform distribution, at lower quanta is due
to increased oscillation as cells adjust to their
neighbors in big steps.