Connected Chemistry 4 Number and Pressure

globals
[
  tick-delta                 ;; how much we advance the tick counter this time through
  max-tick-delta             ;; the largest tick-delta is allowed to be
  box-edge                   ;; distance of box edge from axes
  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
  total-particle-number
  labels?                    ;; show ID of particles
  collisions?
  instant-pressure           ;; the pressure at this tick or instant in time
  pressure-history           ;; a history of the four instant-pressure values
  pressure                   ;; the pressure average of the pressure-history (for curve smoothing in the pressure plots)
  wall-hits-per-particle     ;; average number of wall hits per particle
  maxparticles
  particles-to-add           ;; keeps track of particles to add after pressing ADD PARTICLES
  new-particles              ;; agentset of particles added via add-particles-middle
  show-dark?                 ;; hides or shows the dark particles in the simulation.
                             ;; see NetLogo features Info tab for full explanation of
                             ;; what dark-particles are and why they are used.
]

breed [ particles particle ]
breed [ flashes flash ]            ;; a breed which is used to mark the spot where a particle just hit the wall


flashes-own [birthday]       ;; flashes only last for a short period and then disappear.
                             ;; their birthday helps us keep track of when they were created and
                             ;; when we need to remove them.

particles-own
[
  speed mass                 ;; particle info
  wall-hits                  ;; # of wall hits during this ticks cycle
  momentum-difference        ;; used to calculate pressure from wall hits
  momentum-instant           ;; used to calculate pressure
  last-collision             ;; keeps track of last particle this particle collided with
  dark-particle?              ;; is this particle visible and interacting with visible particles?
]

to setup
  ca reset-ticks
  set pressure-history [0 0 0]  ;; plotted pressure will be averaged over the past 3 entries
  set show-dark? false
  set-default-shape particles "circle"
  set maxparticles 400
  set tick-delta 0
   ;; starting this at zero means that no particles will move until we've
   ;; calculated vsplit, which we won't even try to do until there are some
   ;; particles.
  set pressure 0
  set particles-to-add 0
  set labels? false

  ;; box has constant size...
  set box-edge (max-pxcor - 1)
   ;;; the delta of the horizontal or vertical surface of
   ;;; the inside of the box must exclude the two patches
   ;; that are the where the perpendicular walls join it,
   ;;; but must also add in the axes as an additional patch
   ;;; example:  a box with an box-edge of 10, is drawn with
   ;;; 19 patches of wall space on the inside of the box
  set delta-horizontal-surface  ( 2 * (box-edge - 1) + 1)
  set delta-vertical-surface  ( 2 * (box-edge - 1) + 1)
  draw-box
  set collisions? true
  make-particles maxparticles
  if labels? [turn-labels-on]

  reset-ticks
end 

to go
  let old-ticks 0

    ask particles [ bounce ]
    ask particles [ move ]
    if collisions? [
    ask particles with [dark-particle? = false]
      [ check-for-collision-regular ]

    ask particles with [dark-particle? = true]
      [ check-for-collision-dark ]
    ]
    set old-ticks ticks
    tick-advance tick-delta
    calculate-instant-pressure

    if floor ticks > floor (ticks - tick-delta) [
       ifelse any? particles with [dark-particle? = false]
          [ set wall-hits-per-particle mean [wall-hits] of particles with [dark-particle? = false] ]
          [ set wall-hits-per-particle 0 ]
       ask particles  [ set wall-hits 0 ]
       calculate-pressure

       update-plots
       ]
    calculate-tick-delta
    ask flashes with [ticks - birthday > 0.4] [
      set pcolor yellow
      die
    ]

    ifelse labels?
      [turn-labels-on]
      [ask turtles [ set label ""]]

   ;; now recolor, since color is based on quantities that may have changed

    if show-speed-as-color? = "red-green-blue" [ask particles  [recolor]]
    if show-speed-as-color? = "purple shades" [ask particles  [recolorshade]]
    if show-speed-as-color? = "one color" [ask particles  [recolornone]]
    if (show-wall-hits? = false) [ ask flashes [ die ]]
    display
end 

to calculate-tick-delta
  ifelse any? particles with [speed > 0]
    [ set tick-delta 1 / (ceiling max [speed] of particles) ]
    [ set tick-delta 1 ]
end 

;;; Pressure is defined as the force per unit area.  In this context,
;;; that means the total momentum per unit time transferred to the walls
;;; by particle hits, divided by the surface area of the walls.  (Here
;;; we're in a two dimensional world, so the "surface area" of the walls
;;; is just their delta.)  Each wall contributes a different amount
;;; to the total pressure in the box, based on the number of collisions, the
;;; direction of each collision, and the delta of the wall.  Conservation of momentum
;;; in hits ensures that the difference in momentum for the particles is equal to and
;;; opposite to that for the wall.  The force on each wall is the rate of change in
;;; momentum imparted to the wall, or the sum of change in momentum for each particle:
;;; F = SUM  [d(mv)/dt] = SUM [m(dv/dt)] = SUM [ ma ], in a direction perpendicular to
;;; the wall surface.  The pressure (P) on a given wall is the force (F) applied to that
;;; wall over its surface area.  The total pressure in the box is sum of each wall's
;;; pressure contribution.

to calculate-instant-pressure
  ;; by summing the momentum change for each particle,
  ;; the wall's total momentum change is calculated
  set instant-pressure 15 * sum [momentum-instant] of particles with [dark-particle? = false]
  output-print precision instant-pressure 1
  ask particles
    [ set momentum-instant 0 ]  ;; once the contribution to momentum has been calculated
                                   ;; this value is reset to zero till the next wall hit
end 

to calculate-pressure
  ;; by summing the momentum change for each particle,
  ;; the wall's total momentum change is calculated

  set pressure 15 * sum [momentum-difference] of particles with [dark-particle? = false]
  set pressure-history lput pressure but-first pressure-history

  ask particles
    [ set momentum-difference 0 ]  ;; once the contribution to momentum has been calculated
                                   ;; this value is reset to zero till the next wall hit
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? yellow pcolor or not shade-of? yellow [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 = box-edge)
    [ 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 (dx * 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 = box-edge)
    [ 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 (dy * 2 * mass * speed) / delta-horizontal-surface)
    set momentum-difference momentum-difference + momentum-instant  ]


  if (dark-particle? = false) [
  ask patch new-px new-py
    [ sprout 1 [ ht
                 set breed flashes
                 set birthday ticks
                 set pcolor yellow - 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-regular  ;; particle procedure
  let candidate 0


  ;; Here we impose a rule that collisions only take place when there
  ;; are exactly two particles per patch.  We do this because when the
  ;; student introduces new particles from the side, we want them to
  ;; form a uniform wavefront.
  ;;
  ;; Why do we want a uniform wavefront?  Because it is actually more
  ;; realistic.  (And also because the curriculum uses the uniform
  ;; wavefront to help teach the relationship between particle collisions,
  ;; wall hits, and pressure.)
  ;;
  ;; Why is it realistic to assume a uniform wavefront?  Because in reality,
  ;; whether a collision takes place would depend on the actual headings
  ;; of the particles, not merely on their proximity.  Since the particles
  ;; in the wavefront have identical speeds and near-identical headings,
  ;; in reality they would not collide.  So even though the two-particles
  ;; rule is not itself realistic, it produces a realistic result.  Also,
  ;; unless the number of particles is extremely large, it is very rare
  ;; for three or more particles to land on the same patch (for example,
  ;; with 400 particles it happens less than 1% of the time).  So imposing
  ;; this additional rule should have only a negligible effect on the
  ;; aggregate behavior of the system.
  ;;
  ;; Why does this rule produce a uniform wavefront?  The particles all
  ;; start out on the same patch, which means that without the only-two
  ;; rule, they would all start colliding with each other immediately,
  ;; resulting in much random variation of speeds and headings.  With
  ;; the only-two rule, they are prevented from colliding with each other
  ;; until they have spread out a lot.  (And in fact, if you observe
  ;; the wavefront closely, you will see that it is not completely smooth,
  ;; because some collisions eventually do start occurring when it thins out while fanning.)

  if count other particles-here with [dark-particle? = false] = 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.
    set candidate one-of other particles-here with
      [who < [who] of myself and myself != last-collision and dark-particle? = false]
    ;; 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 

to check-for-collision-dark  ;; particle procedure
  let candidate 0


  ;; Here we impose a rule that collisions only take place when there
  ;; are exactly two particles per patch.  We do this because when the
  ;; student introduces new particles from the side, we want them to
  ;; form a uniform wavefront.
  ;;
  ;; Why do we want a uniform wavefront?  Because it is actually more
  ;; realistic.  (And also because the curriculum uses the uniform
  ;; wavefront to help teach the relationship between particle collisions,
  ;; wall hits, and pressure.)
  ;;
  ;; Why is it realistic to assume a uniform wavefront?  Because in reality,
  ;; whether a collision takes place would depend on the actual headings
  ;; of the particles, not merely on their proximity.  Since the particles
  ;; in the wavefront have identical speeds and near-identical headings,
  ;; in reality they would not collide.  So even though the two-particles
  ;; rule is not itself realistic, it produces a realistic result.  Also,
  ;; unless the number of particles is extremely large, it is very rare
  ;; for three or more particles to land on the same patch (for example,
  ;; with 400 particles it happens less than 1% of the time).  So imposing
  ;; this additional rule should have only a negligible effect on the
  ;; aggregate behavior of the system.
  ;;
  ;; Why does this rule produce a uniform wavefront?  The particles all
  ;; start out on the same patch, which means that without the only-two
  ;; rule, they would all start colliding with each other immediately,
  ;; resulting in much random variation of speeds and headings.  With
  ;; the only-two rule, they are prevented from colliding with each other
  ;; until they have spread out a lot.  (And in fact, if you observe
  ;; the wavefront closely, you will see that it is not completely smooth,
  ;; because some collisions eventually do start occurring when it thins out while fanning.)

  if count other particles-here with [dark-particle? = true] = 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.
    set candidate one-of other particles-here with
      [who < [who] of myself and myself != last-collision and dark-particle? = true]
    ;; 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
  let mass2 0
  let speed2 0
  let heading2 0
  let theta 0
  let v1t 0
  let v1l 0
  let v2t 0
  let v2l 0
  let vcm 0




  ;;; PHASE 1: initial setup

  ;; for convenience, grab some quantities from other-particle
  set mass2 [mass] of other-particle
  set speed2 [speed] of other-particle
  set 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.
  set 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
  set v1t (speed * cos (theta - heading))
  set v1l (speed * sin (theta - heading))

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



  ;;; PHASE 3: manipulate vectors to implement collision

  ;; compute the velocity of the system's center of mass along theta
  set 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 * v1t) + (v1l * v1l))
  ;; 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))
    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
end 

;;;
;;; drawing procedures
;;;

;; draws the box

to draw-box
  ask patches with [ ((abs pxcor = box-edge) and (abs pycor <= box-edge)) or
                     ((abs pycor = box-edge) and (abs pxcor <= box-edge)) ]
    [ set pcolor yellow ]
  ask patches with [pycor = 0 and pxcor < (1 - box-edge)]
  [
    set pcolor yellow - 5  ;; trick the bounce code so particles don't go into the inlet
    ask patch-at 0  1 [ set pcolor yellow ]
    ask patch-at 0 -1 [ set pcolor yellow ]
  ]
end 


;;;
;;; particle setup and addition procedures
;;;

;; creates initial particles

to make-particles [number]
  create-particles number
  [
    setup-particle
    set speed random-float 20
    random-position
    set color red
  ]

  set total-particle-number initial-number

  ask particles with [who < initial-number]
    [
      set shape "circle"
      set dark-particle? false
       if show-speed-as-color? = "red-green-blue" [ recolor ]
      if show-speed-as-color? = "purple shades" [ recolorshade ]
      if show-speed-as-color? = "one color" [ recolornone ]
    ]

  calculate-tick-delta
end 


;; adds particles from the left (the valve from a pump)

to add-particles-side

       set particles-to-add number-to-add
  ifelse ((particles-to-add + total-particle-number ) > maxparticles)
    [user-message (word "The maximum number of particles allowed in this model is " maxparticles ".  You can not add " number-to-add
     " more particles to the " (count particles with [dark-particle? = false]) " you already have in the model")]
    [
      if particles-to-add > 0 [

       ask particles with [who < (total-particle-number + particles-to-add) and who >= total-particle-number]
        [ set dark-particle? false
          set shape "circle"
          setxy (- box-edge) 0
          set heading 90 ;; east
          rt 45 - random-float 90
          set speed 10
          if show-speed-as-color? = "red-green-blue" [ recolor ]
          if show-speed-as-color? = "purple shades" [ recolorshade ]
          if show-speed-as-color? = "one color" [ recolornone ]
        ]
      set total-particle-number (total-particle-number + particles-to-add)
      set particles-to-add 0

      calculate-tick-delta
      ]
     ]
end 

to setup-particle  ;; particle procedure
  set speed 10
  set mass 1.0
  set last-collision nobody
  set wall-hits 0
  set momentum-difference 0
  set dark-particle? true
  ifelse show-dark?
    [set shape "default"]
    [set shape "nothing" set color green]
end 


;; place particle at random location inside the box.

to random-position ;; particle procedure
  setxy ((1 - box-edge) + random-float ((2 * box-edge) - 2))
        ((1 - box-edge) + random-float ((2 * box-edge) - 2))
end 


;;;
;;; visualization procedures
;;;

to recolor  ;; particle procedure
  ifelse speed < (0.5 * 10)
  [
    set color blue
  ]
  [
    ifelse speed > (1.5 * 10)
      [ set color red ]
      [ set color green ]
  ]
end 

to recolorshade
  ifelse speed < 27
  [ set color 111 + speed / 3 ]
  [ set color 119.999 ]
end 

to recolornone
  set color green - 1
end 

to turn-labels-on
 ;; [ask turtles [ set label who set label-color orange + 3 ]]
end 


; Copyright 2004 Uri Wilensky.
; See Info tab for full copyright and license.