Connected Chemistry 5 Temperature 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
  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)
  zero-pressure-count        ;; how many zero entries are in pressure-history
  wall-hits-per-particle     ;; average number of wall hits per particle
  length-horizontal-surface  ;; the size of the wall surfaces that run horizontally - the top and bottom of the box
  length-vertical-surface    ;; the size of the wall surfaces that run vertically - the left and right of the box
  walls                      ;; agentset containing patches that are the walls of the box
  maxparticles
  total-particle-number
  init-avg-speed init-avg-energy  ;; initial averages
  avg-speed avg-energy particle0-speed           ;; current averages
  outside-energy
  min-outside-energy
  max-outside-energy
  temp-increment
  volume
  temperature
  collide?
  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 [ dark-particles dark-particle ]
breed [ flashes flash ]

flashes-own [birthday]

particles-own
[
  speed mass energy          ;; particle info
  wall-hits                  ;; # of wall hits during this clock cycle ("big tick")
  momentum-difference        ;; used to calculate pressure from wall hits
  last-collision
  momentum-instant
]

dark-particles-own
[
  speed mass energy          ;; particle info
  wall-hits                  ;; # of wall hits during this clock cycle ("big tick")
  momentum-difference        ;; used to calculate pressure from wall hits
  last-collision
  momentum-instant
]

to setup
  ca reset-ticks
  set show-dark? false
  set collide? true
   set maxparticles 400
  set temp-increment 7.5
  set min-outside-energy 0
  set max-outside-energy 300
  set-default-shape particles "circle"
  set-default-shape dark-particles "nothing"
  set-default-shape flashes "square"
  set max-tick-delta 0.1073
  ;; box has constant size...
  set box-edge (max-pxcor - 1)
  ;;; the length 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 length-horizontal-surface  ( 2 * (box-edge - 1) + 1)
  set length-vertical-surface  ( 2 * (box-edge - 1) + 1)
  set outside-energy 100
  make-box
  make-particles maxparticles
  set pressure-history [0 0 0]  ;; plotted pressure will be averaged over the past 3 entries
  set zero-pressure-count 0
  update-variables
  set temperature (avg-energy * 6)
  set init-avg-speed avg-speed

  ask particles with [ who = 0 ] [set particle0-speed speed]
  set init-avg-energy avg-energy

  do-plotting
  if speed-as-color? = "red-green-blue" [ ask particles [recolor-banded ] ]
  if speed-as-color? = "purple shades" [ ask particles [recolor-shaded ]]
  if speed-as-color? = "one color" [ ask particles [recolor-none ]]
  if speed-as-color? = "custom color" [ ]
end 

to go
  ask walls
    [ set pcolor box-color ]
  ask particles [ bounce ]
  ask particles [ move ]
  ask dark-particles [ bounce-dark ]
  ask dark-particles [ move ]
  ask particles [ showlabel ]
  if collide?
  [
    ask particles
      [ check-for-collision ]

    ask dark-particles
      [ check-for-collision ]
  ]
  tick-advance tick-delta

  calculate-instant-pressure

  if floor ticks > floor (ticks - tick-delta)
  [
    ifelse any? particles
      [ set wall-hits-per-particle mean [wall-hits] of particles  ]
      [ set wall-hits-per-particle 0 ]
    ask particles
      [ set wall-hits 0 ]
    calculate-pressure
    update-variables
    do-plotting
  ]
  calculate-tick-delta
  ask particles with [ who = 0 ]
    [ set particle0-speed speed ]

  ask flashes with [ticks - birthday > 0.4]
    [ die ]

  if speed-as-color? = "red-green-blue"
    [ ask particles [recolor-banded ] ]
  if speed-as-color? = "blue shades"
    [ ask particles [recolor-shaded ] ]
  if speed-as-color? = "one color"
    [ ask particles [recolor-none ] ]
  set temperature (avg-energy * 6)
  display
end 

to calculate-tick-delta
  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 

;;; 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 length.)  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 length 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-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
  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
  ;; get the coordinates of the patch we'll be on if we go forward 1
  let new-patch patch-ahead 1
  let new-px [pxcor] of new-patch
  let new-py [pycor] of new-patch
  ;; if we're not about to hit a wall, we don't need to do any further checks
  if (abs new-px != box-edge and abs new-py != box-edge)
    [ stop ]
  ;; 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) / length-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) / length-horizontal-surface)
      set momentum-difference momentum-difference + momentum-instant
    ]
  if [heated-wall?] of patch new-px new-py   ;; check if the patch ahead of us is heated
    [ set energy ((energy +  outside-energy ) / 2)
      set speed sqrt (2 * energy / mass )
      recolor-banded
    ]


  ask patch new-px new-py
    [ sprout 1
      [ set breed flashes
        set color 11 ;;pcolor-of 11
        if (color < 10)
          [ set color 10 ]
        set birthday ticks
      ]
    ]
end 
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

to bounce-dark  ;; particle procedure
  ;; get the coordinates of the patch we'll be on if we go forward 1
  let new-patch patch-ahead 1
  let new-px [pxcor] of new-patch
  let new-py [pycor] of new-patch
  ;; if we're not about to hit a wall, we don't need to do any further checks
  if (abs new-px != box-edge and abs new-py != box-edge)
    [stop]
  ;; 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) / length-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) / length-horizontal-surface)
      set momentum-difference momentum-difference + momentum-instant
    ]
  if [heated-wall?] of patch new-px new-py   ;; check if the patch ahead of us is heated
    [ set energy ((energy +  outside-energy ) / 2)
      set speed sqrt (2 * energy / mass )
      recolor-banded
    ]
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.  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.)
  let others-here nobody

  ifelse breed = particles
    [ set others-here other particles-here ]
    [ set others-here other dark-particles-here ]

  if count others-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 others-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
  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 ^ 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
;;;
;;; visualization procedures
;;;
end 

to update-variables
  set avg-speed  mean [speed] of particles
  set avg-energy mean [energy] of particles
end 



;

to cool-walls
  ifelse ( outside-energy > 20 )
    [ set outside-energy outside-energy - temp-increment ]
    [ set outside-energy 0 ]
  if (outside-energy = 0)
    [ user-message "You are currently trying to cool the walls of the container below absolute zero (OK or -273C).  Absolute zero is the lowest theoretical temperature for all matter in the universe and has never been achieved in a real-world laboratory"]
end 

to heat-walls
  set outside-energy outside-energy + temp-increment
    if (outside-energy > 300)
      [ set outside-energy 300
        user-message "You have reached the maximum allowable temperature for the walls of the container in this model."
      ]
end 

;;
;;; visualization procedures
;;;

to showlabel
 ifelse labels?
   [ set label who
     set label-color white
     if (who = 0) [set label-color (orange + 1)]
   ]
   [ set label "" ]
end 

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

to recolor-shaded
  ifelse speed < 27
    [ set color 111 + speed / 3 ]
    [ set color 119.999 ]
end 

to recolor-none
  set color green - 1
end 

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

;;;
;;; reporters
;;;



;; reports color of box according to temperature and position
;; if only one side is heated, the other walls will be yellow

to-report box-color
  ifelse heated-wall?
    [ report scale-color red outside-energy -60 340 ]
    [ report yellow ]
end 

;; reports true if there is a heated wall at the given location

to-report heated-wall?
  if (( abs pxcor = box-edge) and (abs pycor <= box-edge)) or
     ((abs pycor = box-edge) and (abs pxcor <= box-edge))
    [ report true ]
  report false
end 

;;;
;;; drawing procedures
;;;

;; draws the box

to make-box
  set walls patches with [ ((abs pxcor = box-edge) and (abs pycor <= box-edge)) or
                           ((abs pycor = box-edge) and (abs pxcor <= box-edge)) ]
  ask walls
    [ set pcolor box-color ]
end 

;; creates initial particles

to make-particles  [n]
  create-particles number
    [ setup-particle
      if speed-as-color? = "red-green-blue" [ recolor-banded ]
      if speed-as-color? = "blue shades" [ recolor-shaded ]
      if speed-as-color? = "one color" [ recolor-none ]
    ]

  create-dark-particles ( n - number )
    [ setup-particle
      set color red
      if show-dark? [set shape "default"]
    ]

  set total-particle-number number

  calculate-tick-delta
end 

to setup-particle  ;; particle procedure
  set speed random-float 20
  set mass 1.0
  set energy (0.5 * mass * speed * speed)
  set last-collision nobody
  set wall-hits 0
  set momentum-difference 0
  random-position
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 


;;; plotting procedures

to do-plotting
  set-current-plot "Pressure vs. Time"
  plotxy ticks (mean pressure-history)

  set-current-plot "Gas Temp. vs. Time"
  plotxy ticks avg-energy * 6

  set-current-plot "Average Speed vs. Time"
  plotxy ticks avg-speed
end 

to calculate-instant-pressure
  ;; by summing the momentum change for each particle,
  ;; the wall's total momentum change is calculated
  set instant-pressure 15 * 30 * sum [momentum-instant] of particles
  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 


; Copyright 2005 Uri Wilensky.
; See Info tab for full copyright and license.