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HorizontalCylinder

A horizontal truncated circular cylinder.

Constructor

Full form ```python HorizontalCylinder(R, H, b, t)

and short form 
```python
HorizontalCylinder(R, H) == HorizontalCylinder(R, H, -R, R)

Parameters:

  • R, radius
  • H, height
  • b, bottom boundary, relative to the center
  • t, top boundary, relative to the center

Constraint:

$ -R \le b \le t \le R $

Usage

As for any other Form factor.

Implementation

Class HorizontalCylinder inherits from the interface class IFormFactor .

Form factor is computed as

$$ F(\mathbf{q})=2 L \space \text{sinc}\Big(q_x\dfrac{L}{2}\Big) \int_{b}^{t} \text{d}z \space \sqrt{R^2-z^2} \space \text{sinc}(q_y\sqrt{R^2-z^2}) \exp[iq_z(z-b)] , $$

Volume has been validated against $$V=L \Big( t\sqrt{R^2-t^2}- b\sqrt{R^2-b^2} + R^2 \Big[\text{asin}\Big(\frac{t}{R}\Big) - \text{asin}\Big(\frac{b}{R}\Big) \Big] \Big).$$

More general:

  • Cylinder, if vertical and non-truncated.

Example

Scattering by uncorrelated, oriented horizontal truncated cylinders for horizontal incidence. Rotation around $z$ axis:

Generated by Examples/ff/HorizontalCylinder.py .

History

Introduced in BornAgain 1.20.