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扩散现象

扩散现象
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2017-05-06 10:56
函数数列概率统计
所属专题 UQ-Applied Mathematical Analysis
该范例演示了扩散现象。涉及的核心数学概念包括概率统计中的条件概率。作图要点包括使用了Sequence, Spline, Polygon, CurveCartesian等GeoGebra命令。适合用于高中或大学的概率统计课程。

GeoGebra 命令及参数

  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