diffusion_sigal_project

globals
[
  tick-delta                      ;; how much we advance the tick counter this time through
  max-tick-delta                  ;; the largest tick-delta is allowed to be
  init-avg-speed init-avg-energy  ;; initial averages
  avg-speed avg-energy            ;; current averages
  fast medium slow                ;; current counts
  percent-fast percent-medium     ;; percentage of the counts
  percent-slow                    ;; percentage of the counts
air-particles perfume-particles
  delta-horizontal-surface   ;; the size of the wall surfaces that run horizontally - the top and bottom of the box
  delta-vertical-surface     ;; the size of the wall surfaces that run vertically - the left and right of the box
]

breed [ particles particle ]

particles-own
[
  speed mass energy          ;; particle info
  last-collision
   step-size
    wall-hits                  ;; # of wall hits during this clock cycle
  momentum-difference        ;; used to calculate pressure from wall hits
  momentum-instant           ;; used to calculate pressure
       
  darkparticle?             
]

to setup
  ca
  set-default-shape particles "circle"
  set max-tick-delta 0.1073
  make-particles
  update-variables
  set init-avg-speed avg-speed
  set init-avg-energy avg-energy
;  setup-plots
;  setup-histograms
;;  do-plotting
  make-box
end 

to
   make-box
  
   ask patches[
    ;; if patches are between (-10,-10) to (-10,-16)...
    if ( pxcor = -10 and pycor <= -10 and pycor >= -16 )
      [set pcolor red]                                 ;; ... draws left edge in red
    ;; if patches are between (-16,-10) to (-16,-16)...
    if ( pxcor = -16 and pycor <= -10 and pycor >= -16 )
      [set pcolor red]                                 ;; ... draws right edge in red
    ;; if patches are between (-10,-10) to (-16,-10)...
    if ( pycor = -10 and pxcor >= -16 and pxcor <= -10 )
      [set pcolor red]                                 ;; ... draws bottom edge in red
    ;; if patches are between (-10,-16) to (-16,-16)...
    if ( pycor = -16 and pxcor >= -16 and pxcor <= -10 )
      [set pcolor red]                                 ;; ... draws upper edge in red
    ]
end 

to go
  ask particles [ move ]
;  ask particles
;  [ if collide? [check-for-collision] ]
;  ifelse (trace?)
;    [ ask particle 0 [ pen-down ] ]
;    [ ask particle 0 [ pen-up ] ]
  tick-advance tick-delta
  if floor ticks > floor (ticks - tick-delta)
  [
    update-variables
;    do-plotting
  ]
  calculate-tick-delta
ask particles [bounce]
  display
end 

to update-variables
  set medium count particles with [color = cyan]
  set slow count particles with [color = cyan]
  set fast count particles with [color = cyan]
  set percent-medium (medium / count particles) * 100
  set percent-slow (slow / count particles) * 100
  set percent-fast (fast / count particles) * 100
  set avg-speed  mean [speed] of particles
  set avg-energy  mean [energy] of particles
end 

to calculate-tick-delta
  ;; tick-delta is calculated in such way that even the fastest
  ;; particle will jump at most 1 patch length in a tick. As
  ;; particles jump (speed * tick-delta) at every tick, making
  ;; tick length the inverse of the speed of the fastest particle
  ;; (1/max speed) assures that. Having each particle advance at most
  ;; one patch-length is necessary for them not to jump over each other
  ;; without colliding.
  ifelse any? particles with [speed > 0]
    [ set tick-delta min list (1 / (ceiling max [speed] of particles)) max-tick-delta ]
    [ set tick-delta max-tick-delta ]
end 

to bounce  ;; particle procedure
  let new-px 0
  let new-py 0

  ;; if we're not about to hit a wall (yellow patch), or if we're already on a
  ;; wall, we don't need to do any further checks
  if shade-of? red pcolor or not shade-of? red [pcolor] of patch-at dx dy
    [ stop ]
  ;; get the coordinates of the patch we'll be on if we go forward 1
  set new-px round (xcor + dx)
  set new-py round (ycor + dy)
  ;; if hitting left or right wall, reflect heading around x axis
  if (abs new-px = 100)
    [ set heading (- heading)
;      set wall-hits wall-hits + 1
  ;;  if the particle is hitting a vertical wall, only the horizontal component of the speed
  ;;  vector can change.  The change in velocity for this component is 2 * the speed of the particle,
  ;; due to the reversing of direction of travel from the collision with the wall

      set momentum-instant  (abs (sin heading * 2 * mass * speed) / delta-vertical-surface)
      set momentum-difference momentum-difference + momentum-instant
 ]

  ;; if hitting top or bottom wall, reflect heading around y axis
  if (abs new-py = 100)
    [ set heading (180 - heading)
      set wall-hits wall-hits + 1
  ;;  if the particle is hitting a horizontal wall, only the vertical component of the speed
  ;;  vector can change.  The change in velocity for this component is 2 * the speed of the particle,
  ;; due to the reversing of direction of travel from the collision with the wall

    set momentum-instant  (abs (cos heading * 2 * mass * speed) / delta-horizontal-surface)
    set momentum-difference momentum-difference + momentum-instant  ]


;  if (darkparticle? = false) [
;  ask patch new-px new-py
;    [ sprout 1 [
;                 set breed flashes
;                 set birthday ticks
;                 set color red - 3 ] ]
end 

to move  ;; particle procedure
  if patch-ahead (speed * tick-delta) != patch-here
    [ set last-collision nobody ]
  jump (speed * tick-delta)
end 

to check-for-collision  ;; particle procedure
  ;; Here we impose a rule that collisions only take place when there
  ;; are exactly two particles per patch.

  if count other particles-here = 1
  [
    ;; the following conditions are imposed on collision candidates:
    ;;   1. they must have a lower who number than my own, because collision
    ;;      code is asymmetrical: it must always happen from the point of view
    ;;      of just one particle.
    ;;   2. they must not be the same particle that we last collided with on
    ;;      this patch, so that we have a chance to leave the patch after we've
    ;;      collided with someone.
    let candidate one-of other particles-here with
      [who < [who] of myself and myself != last-collision]
    ;; we also only collide if one of us has non-zero speed. It's useless
    ;; (and incorrect, actually) for two particles with zero speed to collide.
    if (candidate != nobody) and (speed > 0 or [speed] of candidate > 0)
    [
      collide-with candidate
      set last-collision candidate
      ask candidate [ set last-collision myself ]
    ]
  ]
end 

;; implements a collision with another particle.
;;
;; THIS IS THE HEART OF THE PARTICLE SIMULATION, AND YOU ARE STRONGLY ADVISED
;; NOT TO CHANGE IT UNLESS YOU REALLY UNDERSTAND WHAT YOU'RE DOING!
;;
;; The two particles colliding are self and other-particle, and while the
;; collision is performed from the point of view of self, both particles are
;; modified to reflect its effects. This is somewhat complicated, so I'll
;; give a general outline here:
;;   1. Do initial setup, and determine the heading between particle centers
;;      (call it theta).
;;   2. Convert the representation of the velocity of each particle from
;;      speed/heading to a theta-based vector whose first component is the
;;      particle's speed along theta, and whose second component is the speed
;;      perpendicular to theta.
;;   3. Modify the velocity vectors to reflect the effects of the collision.
;;      This involves:
;;        a. computing the velocity of the center of mass of the whole system
;;           along direction theta
;;        b. updating the along-theta components of the two velocity vectors.
;;   4. Convert from the theta-based vector representation of velocity back to
;;      the usual speed/heading representation for each particle.
;;   5. Perform final cleanup and update derived quantities.

to collide-with [ other-particle ] ;; particle procedure
  ;;; PHASE 1: initial setup

  ;; for convenience, grab some quantities from other-particle
  let mass2 [mass] of other-particle
  let speed2 [speed] of other-particle
  let heading2 [heading] of other-particle

  ;; since particles are modeled as zero-size points, theta isn't meaningfully
  ;; defined. we can assign it randomly without affecting the model's outcome.
  let theta (random-float 360)



  ;;; PHASE 2: convert velocities to theta-based vector representation

  ;; now convert my velocity from speed/heading representation to components
  ;; along theta and perpendicular to theta
  let v1t (speed * cos (theta - heading))
  let v1l (speed * sin (theta - heading))

  ;; do the same for other-particle
  let v2t (speed2 * cos (theta - heading2))
  let v2l (speed2 * sin (theta - heading2))



  ;;; PHASE 3: manipulate vectors to implement collision

  ;; compute the velocity of the system's center of mass along theta
  let vcm (((mass * v1t) + (mass2 * v2t)) / (mass + mass2) )

  ;; now compute the new velocity for each particle along direction theta.
  ;; velocity perpendicular to theta is unaffected by a collision along theta,
  ;; so the next two lines actually implement the collision itself, in the
  ;; sense that the effects of the collision are exactly the following changes
  ;; in particle velocity.
  set v1t (2 * vcm - v1t)
  set v2t (2 * vcm - v2t)



  ;;; PHASE 4: convert back to normal speed/heading

  ;; now convert my velocity vector into my new speed and heading
  set speed sqrt ((v1t ^ 2) + (v1l ^ 2))
  set energy (0.5 * mass * (speed ^ 2))
  ;; if the magnitude of the velocity vector is 0, atan is undefined. but
  ;; speed will be 0, so heading is irrelevant anyway. therefore, in that
  ;; case we'll just leave it unmodified.
  if v1l != 0 or v1t != 0
    [ set heading (theta - (atan v1l v1t)) ]

  ;; and do the same for other-particle
  ask other-particle [
    set speed sqrt ((v2t ^ 2) + (v2l ^ 2))
    set energy (0.5 * mass * (speed ^ 2))
    if v2l != 0 or v2t != 0
      [ set heading (theta - (atan v2l v2t)) ]
  ]

  ;; PHASE 5: final updates

  ;; now recolor, since color is based on quantities that may have changed
  recolor
  ask other-particle
    [ recolor ]
end 

to recolor  ;; particle procedure
  ifelse speed < (0.5 * 10)
  [
    set color cyan set size  .40
  ]
  [
    ifelse speed > (1.5 * 10)
      [ set color cyan ]
      [ set color cyan ]
  ]
end 

;;;
;;; drawing procedures
;;;


;; creates initial particles

to make-particles
  create-particles 100
  [
    setup-particle
    random-position
    recolor
  ]
  calculate-tick-delta
end 

to setup-particle  ;; particle procedure
  set speed init-particle-speed
  set mass particle-mass
  set energy (0.5 * mass * (speed ^ 2))
  set last-collision nobody
end 


;; place particle at random location inside the box.

to random-position ;; particle procedure
  setxy ((1 + min-pxcor) + random-float ((2 * max-pxcor) - 2))
        ((1 + min-pycor) + random-float ((2 * max-pycor) - 2))
end 

;to-report last-n [n the-list]
;  ifelse n >= length the-list
;    [ report the-list ]
;    [ report last-n n butfirst the-list ]
;end