Essential Guide to Photon Scattering Programming in MathCAD

1. PH24010Data Handling and Statistics Photon Scattering program written in MathCAD

2. The Golden Rule of Programming • Applies to all programming • K.I.S.S. principle • Keep • It • Simple • Stupid

3. MathCAD ProgramsStructures • if, otherwise, for, while • Indentation & vertical bars • Watch selection rectangle • <Space> to increase (more lines) • <Insert> to swap sides • No GOTO • Considered harmful

4. MathCAD programsif statement • Better than if() function for complicated cases. • otherwise statement to catch unhandled cases.

5. Programmed if statement • Note: • Comparisons • use of otherwise to catch all cases

6. MathCAD programs – The for loop • Loop extend shown by indent • ‘Result’ array built up • Note syntax of ‘for’ line • Use when you know in advance how many iterations

7. The while loop • Execute statements while a condition is true • Used when you don’t know in advance how many times loop will be executed. • Loop while you are searching • Loop while error is too big • Loop while system is stable

8. A while loop example • Find first member of vector ‘Vec’ greater than threshold, ‘t’ • Written as function • j is index • while loop • return index & value as vector

9. Longer Loops • Use ‘Add Line’ in body of loop to extend scope of loop. • Lines added at vertical bar • <Insert> key swaps sides of selection bar

10. Longer Loops

11. Program ExamplePhoton Scattering #1 • Photon enters box • Travels random distance • Scatter through random angle • Repeat from step 2 until photon leaves box • Record walk for posterity

12. Photon ScatteringProgram to create Walk

13. Program ExamplePhoton Scattering #2 • Store x-y co-ordinates and i (loop count) • Write functions for • Pathlength() • ScatterAngle(q) • InBox(x,y) • Test these functions !!!

14. Photon ScatteringPathLength function • spath is related to ln(2)/mean path • x placeholder is dummy • rexp(1, spath) function returns vector of 1 number from distribution • indexing to extract element 0 from vector

15. Photon ScatteringScatterAngle(q) • Isotropic scatter - uniform • Give 1 angle randomly between –pp • Similar use of built-in random numbers to earlier. • Deal with anisotropy later

16. Photon ScatteringInBox(V) function • Takes x,y as arguments • 2 way logical expression • LoLimit < x < HiLimit • Uses multiplication to form AND • Returns 1 if in box, 0 otherwise

17. Photon ScatteringProgram to create Walk

18. Photon ScatteringUsing the program

19. Photon ScatteringConclusions • 14 line program + functions • Records entire walk • Extract info from result vector • Easy to extend • 3D scatter • Anisotropy • Change ScatterAngle(q)

20. Combining Many Walks • Use stack() to join results together

21. Simple anisotropy • Assume ‘normal’ distribution about angle

22. Many walks with anisotropy