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Diffusion Phenomenon

Diffusion Phenomenon
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2017-05-06 10:56
FunctionSequenceProbability & Statistics
In collections UQ-Applied Mathematical Analysis
This example demonstrates the diffusion phenomenon. It involves the core mathematical concept of conditional probability in probability and statistics. The construction uses commands such as Sequence, Spline, Polygon, and CurveCartesian in GeoGebra. Suitable for high school or university probability and statistics courses.

GeoGebra Commands & Parameters

  1. Sequence(((2 * random()) * π), i, 1, m) → L_{α2}
  2. Sequence(((2 * random()) * π), i, 1, n) → L_{α1}
  3. Spline({L, M, N, U, S, W, Z}, 3) → f
  4. Sequence((x(f(abs(sin(i)))), y(f(abs(sin(i))))), i, 1, m) → LI2
  5. Sequence(((v_m * cos(Element[L_{α2}, i])), (v_m * sin(Element[L_{α2}, i]))), i, 1, m) → LV2
  6. Sequence(((v_m * cos(Element[L_{α1}, i])), (v_m * sin(Element[L_{α1}, i]))), i, 1, n) → LV1
  7. Spline({D, E, F, G, H, I, J, K}, 3) → e
  8. Sequence((x(e(abs(sin(i)))), y(e(abs(sin(i))))), i, 1, n) → LI1
  9. Polygon(A, B, C, O') → poly1, a, b, c, o'
  10. Sequence((Element[LV1, i] * t) + Element[LI1, i], i, 1, n) → LP1
  11. CurveCartesian(abs((sin(i) * L_x)), abs((sin(i) * L_y)), i, 0, π / 2) → d
  12. Sequence((x(Element[LP1, i]) - (floor(x(Element[LP1, i]) / L_x) * L_x), y(Element[LP1, i]) - (floor(y(Element[LP1, i]) / L_y) * L_y)), i, 1, n) → LQ1
  13. Sequence(sgn(sin((π / L_x * x(Element[LP1, i])))), i, 1, n) → Lsx1
  14. Sequence(sgn(sin((π / L_y * y(Element[LP1, i])))), i, 1, n) → Lsy1
  15. Sequence((Element[LV2, i] * t) + Element[LI2, i], i, 1, m) → LP2
  16. Sequence(O + (If[Element[Lsx1, i] < 1, L_x - x(Element[LQ1, i]), x(Element[LQ1, i])], If[Element[Lsy1, i] < 1, L_y - y(Element[LQ1, i]), y(Element[LQ1, i])]), i, 1, n) → LR1
  17. Sequence(sgn(sin((π / L_x * x(Element[LP2, i])))), i, 1, m) → Lsx2
  18. Sequence(sgn(sin((π / L_y * y(Element[LP2, i])))), i, 1, m) → Lsy2
  19. Sequence((x(Element[LP2, i]) - (floor(x(Element[LP2, i]) / L_x) * L_x), y(Element[LP2, i]) - (floor(y(Element[LP2, i]) / L_y) * L_y)), i, 1, m) → LQ2
  20. Sequence(O + (If[Element[Lsx2, i] < 1, L_x - x(Element[LQ2, i]), x(Element[LQ2, i])], If[Element[Lsy2, i] < 1, L_y - y(Element[LQ2, i]), y(Element[LQ2, i])]), i, 1, m) → LR2