Fermions.hs

   1 module Fermions where
   2
   3 type Charge = Float
   4 type Mass = Float
   5 type Vector = (Float, Float, Float)
   6 type Fermion = (Vector, Vector, Mass, Charge)
   7
   8 inBox :: Fermion -> Bool
   9 inBox ((x, y, z), _, _, _) = x <= boxSpan && x >= (-boxSpan) && y <= boxSpan && y >= (-boxSpan) && z <= boxSpan && z >= (-boxSpan)
  10
  11 boxSpan :: Float
  12 boxSpan = 1000
  13
  14 initialState :: Float -> [Fermion]
  15 initialState n = map (\k -> (((k * boxSpan / (n+1)) - boxSpan/2, (sin(pi*k/n)) / 6 * boxSpan, 0), (0, 0, 0), 2, (if (odd (round k::Integer)) then 1 else -1))) [1..n]
  16
  17 getFermionPos :: Fermion -> Vector
  18 getFermionPos (pos, _, _, _) = pos
  19
  20 addVectors :: Vector -> Vector -> Vector
  21 addVectors (x,y,z) (a,b,c) = (x+a, y+b, z+c)
  22
  23 mulVector :: Float -> Vector -> Vector
  24 mulVector n (x,y,z) = (n*x, n*y, n*z)
  25
  26 advanceState :: [Fermion] -> [Fermion]
  27 advanceState fermions = filter inBox (map update fermions)
  28   where
  29   update this@(pos, v, mass, charge) = (newPos, newVelocity, mass, charge)
  30     where
  31     newPos = pos `addVectors` v
  32     newVelocity = updatedVelocity --`addVectors` (forceFromBlackHole this)
  33     updatedVelocity = (foldl addVectors v (map (forceBetween this) fermions))
  34
  35 forceBetween :: Fermion -> Fermion -> Vector
  36 forceBetween (pos1@(x1, y1, z1), _, mass1, charge1) (pos2@(x2, y2, z2), _, mass2, charge2)
  37   | pos1 == pos2 = (0, 0, 0)
  38   | otherwise    = (factor * x, factor * y, factor * z)
  39   where
  40     factor = (-charge1) * charge2 / dist +  mass1 * mass2 / dist
  41     dist = x*x + y*y + z*z
  42     x = x2 - x1
  43     y = y2 - y1
  44     z = z2 - z1
  45
  46 --forceFromBlackHole :: Fermion -> Vector
  47 --forceFromBlackHole ((x, y, z), _, _, _) = (factor * x, factor * y, factor * z)
  48 --  where
  49 --  factor = if dist > boxSpan then -0.1 else 0
  50 ----  factor = if factor' == 1/0 then 10000 else factor'
  51 ----  factor' = (-(exp ((dist - boxSpan)/boxSpan)))
  52 --  dist = sqrt(x*x + y*y + z*z)