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 average avg-energy-green avg-energy-orange avg-energy-purple particle-size toggle-red-state toggle-green-state min-particle-energy max-particle-energy particles-to-add]breed [ particles particle ]breed [ walls wall ]breed [ flashes flash ]breed [ erasers eraser ]breed [ arrowheads arrowhead ]erasers-own [pressure?]flashes-own [birthday]particles-own[ speed mass energy ;; particles info last-collision color-type]walls-own[ energy valve-1? valve-2? pressure? surface-energy]to setup ca reset-ticks set particle-size 1.0 set max-tick-delta 0.02 set particles-to-add 2 set-default-shape flashes "square" set-default-shape walls "wall" set-default-shape erasers "eraser" set-default-shape arrowheads "default" set min-particle-energy 0 set max-particle-energy 10000 ;;(.5 ) * ( max-dist-in-tick-delta / max-tick-delta ) ^ 2 create-erasers 1 [set hidden? true set pressure? true set size 3 set color white] make-box make-particles ask particles [ apply-speed-visualization] set init-avg-speed avg-speed set init-avg-energy avg-energy update-variables do-plottingendto go mouse-action if mouse-interaction = "none - let the particles interact" [ ask particles [ bounce ] ask particles [ move ] ask particles [ check-for-collision ] ask particles with [any? walls-here] [rewind-to-bounce] ask particles with [any? walls-here] [remove-from-walls]] tick-advance tick-delta calculate-tick-delta ask flashes [apply-flash-visualization] ask particles [apply-speed-visualization] update-variables do-plotting displayendto update-variables if any? particles [ set avg-speed mean [speed] of particles set avg-energy mean [energy] of particles ] if any? particles with [color-type = 55] [set avg-energy-green mean [energy] of particles with [color-type = 55]] if any? particles with [color-type = 25] [set avg-energy-orange mean [energy] of particles with [color-type = 25]] if any? particles with [color-type = 115] [set avg-energy-purple mean [energy] of particles with [color-type = 115]]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;WALL INTERACTION;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to toggle-red-wall ifelse toggle-red-state = "closed" [ask walls with [valve-1?] [set hidden? true] set toggle-red-state "open"] [ask walls with [valve-1?] [set hidden? false] set toggle-red-state "closed"]endto toggle-green-wall ifelse toggle-green-state = "closed" [ask walls with [valve-2?] [set hidden? true] set toggle-green-state "open"] [ask walls with [valve-2?] [set hidden? false] set toggle-green-state "closed"]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GAS MOLECULES MOVEMENT;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to bounce ;; particles procedure ;; get the coordinates of the patch we'll be on if we go forward 1 let bounce-patch nobody let bounce-patches nobody let hit-angle 0 let this-patch patch-here let new-px 0 let new-py 0 let visible-wall nobody set bounce-patch min-one-of walls in-cone ((sqrt (2)) / 2) 180 with [myself != this-patch] [distance myself ] if bounce-patch != nobody [ set new-px [pxcor] of bounce-patch set new-py [pycor] of bounce-patch set visible-wall walls-on bounce-patch if any? visible-wall with [not hidden?] [ set hit-angle towards bounce-patch ifelse (hit-angle = 45) or (hit-angle = 225) [set heading (- heading) ] [set heading (180 - heading) ] if show-wall-hits? [ ask patch new-px new-py [ sprout 1 [ set breed flashes set color gray - 2 set birthday ticks ] ] ] ]]endto rewind-to-bounce ;; particles procedure ;; attempts to deal with particle penetration by rewinding the particle path back to a point ;; where it is about to hit a wall ;; the particle path is reversed 49% of the previous tick-delta it made, ;; then particle collision with the wall is detected again. ;; and the particle bounces off the wall using the remaining 51% of the tick-delta. ;; this use of slightly more of the tick-delta for forward motion off the wall, helps ;; insure the particle doesn't get stuck inside the wall on the bounce. let bounce-patch nobody let bounce-patches nobody let hit-angle 0 let this-patch nobody let new-px 0 let new-py 0 let visible-wall nobody bk (speed) * tick-delta * .49 set this-patch patch-here set bounce-patch min-one-of walls in-cone ((sqrt (2)) / 2) 180 with [self != this-patch] [distance myself ] if bounce-patch != nobody [ set new-px [pxcor] of bounce-patch set new-py [pycor] of bounce-patch set visible-wall walls-on bounce-patch if any? visible-wall with [not hidden?] [ set hit-angle towards bounce-patch ifelse (hit-angle = 45) or (hit-angle = 225) [set heading (- heading) ] [set heading (180 - heading) ] if show-wall-hits? [ ask patch new-px new-py [ sprout 1 [ set breed flashes set color gray - 2 set birthday ticks ] ] ] ]] fd (speed) * tick-delta * .51endto move ;; particles procedure if patch-ahead (speed * tick-delta) != patch-here [ set last-collision nobody ] jump (speed * tick-delta)end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GAS MOLECULES COLLISIONS;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;from GasLabto calculate-tick-delta ;; tick-delta is calculated in such way that even the fastest ;; particles will jump at most 1 patch delta in a ticks tick. As ;; particles jump (speed * tick-delta) at every ticks tick, making ;; tick delta the inverse of the speed of the fastest particles ;; (1/max speed) assures that. Having each particles advance at most ; one patch-delta is necessary for it not to "jump over" a wall ; or another particles. 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 ]endto check-for-collision ;; particles 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 particles 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 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 collisions eventually do start occurring when it thins out while fanning.) if count other particles-here in-radius 1 = 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 particles. ;; 2. they must not be the same particles 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 particles.;;;; THIS IS THE HEART OF THE particles 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-particles, 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 particles centers;; (call it theta).;; 2. Convert the representation of the velocity of each particles 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 particles.;; 5. Perform final cleanup and update derived quantities.to collide-with [ other-particles ] ;; particles procedure ;;; PHASE 1: initial setup ;; for convenience, grab quantities from other-particles let mass2 [mass] of other-particles let speed2 [speed] of other-particles let heading2 [heading] of other-particles ;; 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-particles 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 particles 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 particles 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-particles [ 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)) ] ]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; mouse interaction procedures;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to mouse-action let snap-xcor 0 let snap-ycor 0 let orig-xcor 0 let orig-ycor 0 let eraser-window-walls nobody let eraser-window-particles nobody ifelse mouse-down? [ set orig-xcor mouse-xcor set orig-ycor mouse-ycor set snap-xcor round orig-xcor set snap-ycor round orig-ycor ask patches with [pxcor = snap-xcor and pycor = snap-ycor] [ set eraser-window-walls walls-on neighbors set eraser-window-walls eraser-window-walls with [not pressure?] set eraser-window-particles particles-on neighbors if mouse-interaction = "draw basic wall" [ ask walls-here [die] sprout 1 [ set breed walls set color gray initialize-this-wall ] ] if mouse-interaction = "draw red removable wall" [ set toggle-red-state "open" toggle-red-wall ask walls-here [die] sprout 1 [ set breed walls set color red initialize-this-wall set valve-1? true ] ] if mouse-interaction = "draw green removable wall" [ set toggle-green-state "open" toggle-green-wall ask walls-here [die] sprout 1 [ set breed walls set color 55 initialize-this-wall set valve-2? true ] ] if mouse-interaction = "big eraser" [ ask erasers [ set hidden? false set shape "eraser" setxy orig-xcor orig-ycor ] ask eraser-window-walls [die] ask eraser-window-particles [die] ] if mouse-interaction = "add purple particles" or mouse-interaction = "add green particles" or mouse-interaction = "add orange particles" [ ask erasers [ set hidden? false set shape "spray paint" setxy orig-xcor orig-ycor ] sprout particles-to-add [ set breed particles setup-particles jump random-float 2 if mouse-interaction = "add purple particles" [set color-type 115 color-particle-and-link] if mouse-interaction = "add orange particles" [set color-type 25 color-particle-and-link] if mouse-interaction = "add green particles" [set color-type 55 color-particle-and-link] apply-speed-visualization ] ] if mouse-interaction = "paint particles purple" or mouse-interaction = "paint particles orange" or mouse-interaction = "paint particles green" [ ask erasers [ set hidden? false set shape "spray paint" setxy orig-xcor orig-ycor ] ask eraser-window-particles [ if mouse-interaction = "paint particles purple" [set color-type 115 color-particle-and-link] if mouse-interaction = "paint particles orange" [set color-type 25 color-particle-and-link] if mouse-interaction = "paint particles green" [set color-type 55 color-particle-and-link] apply-speed-visualization ] ] if mouse-interaction = "speed up particles" [ ask erasers [ set hidden? false set shape "spray paint" setxy orig-xcor orig-ycor ] ask eraser-window-particles [ set energy (energy * 1.1) set energy limited-particle-energy set speed speed-from-energy apply-speed-visualization ] ] if mouse-interaction = "slow down particles" [ ask erasers [ set hidden? false set shape "spray paint" setxy orig-xcor orig-ycor ] ask eraser-window-particles [ set energy (energy / 1.1) set energy limited-particle-energy set speed speed-from-energy apply-speed-visualization ] ] ] ask particles with [any? walls-here] [remove-from-walls] ;; deal with any walls drawn on top of particles ] [ask erasers [set hidden? true]]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; particle speed and flash visualization procedures;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to apply-flash-visualization set size (size * .95) if (ticks - birthday > 0.4) [ die ]endto apply-speed-visualization if visualize-speed? = "arrows" [ scale-arrowheads] if visualize-speed? = "different shades" [ recolorshade ] if visualize-speed? = "none" [ recolornone ]endto color-particle-and-link let this-link my-out-links let this-color-type color-type set color this-color-type ask this-link [set color this-color-type]endto scale-arrowheads let this-xcor xcor let this-ycor ycor let this-speed speed let this-heading heading let this-arrowhead out-link-neighbors let this-link my-out-links ask this-link [set hidden? false] ask this-arrowhead [ set xcor this-xcor set ycor this-ycor set heading this-heading fd .5 + this-speed / 3 ]endto recolorshade let this-link my-out-links ask this-link [set hidden? true] ifelse speed < 27 [ set color color-type - 3 + speed / 3 ] [ set color color-type + 4.999 ]endto recolornone let this-link my-out-links ask this-link [set hidden? true] set color color-typeend;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; initialization procedures;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to make-box ask patches with [(pycor = min-pycor or pycor = max-pycor or pxcor = min-pxcor or pxcor = max-pxcor) ] [ sprout 1 [set breed walls set color yellow initialize-this-wall set pressure? true] ]endto initialize-this-wall set valve-1? false set valve-2? false set pressure? falseendto make-particles create-particles initial-#-particles [ setup-particles random-position ]endto setup-particles ;; particles procedure set shape "circle" set size particle-size set energy initial-gas-temperature set color-type 115 set color color-type set mass (10) ;; atomic masses of oxygen atoms hatch 1 [set breed arrowheads set hidden? true create-link-from myself [tie]] set speed speed-from-energy set last-collision nobodyend;; Place particles at random, but they must not be placed on top of wall atoms.;; This procedure takes into account the fact that wall molecules could have two possible arrangements,;; i.e. high-surface area ot low-surface area.to random-position ;; particles procedure let open-patches nobody let open-patch nobody set open-patches patches with [not any? turtles-here and pxcor != max-pxcor and pxcor != min-pxcor and pycor != min-pycor and pycor != max-pycor] set open-patch one-of open-patches ;; Reuven added the following "if" so that we can get through setup without a runtime error. if open-patch = nobody [ user-message "No open patches found. Exiting." stop ] setxy ([pxcor] of open-patch) ([pycor] of open-patch)end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; wall penetration error handling procedure;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; if particles actually end up within the wall;;to remove-from-walls let this-wall walls-here with [not hidden?] if count this-wall != 0 [ let available-patches patches with [not any? walls-here] let closest-patch nobody if (any? available-patches) [ set closest-patch min-one-of available-patches [distance myself] set heading towards closest-patch setxy ([pxcor] of closest-patch) ([pycor] of closest-patch) ] ]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GRAPHS;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to do-plotting set-current-plot "Temperature of gases" if any? particles with [color-type = 55] [ set-current-plot-pen "green" plotxy ticks avg-energy-green ] if any? particles with [color-type = 25] [ set-current-plot-pen "orange" plotxy ticks avg-energy-orange ] if any? particles with [color-type = 115] [ set-current-plot-pen "purple" plotxy ticks avg-energy-purple ]end;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;REPORTERS;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;to-report speed-from-energy report sqrt (2 * energy / mass)endto-report energy-from-speed report (mass * speed * speed / 2)endto-report limited-particle-energy let limited-energy energy if limited-energy > max-particle-energy [set limited-energy max-particle-energy] if limited-energy < min-particle-energy [set limited-energy min-particle-energy] report limited-energyend; Copyright 2006 Uri Wilensky.; See Info tab for full copyright and license.@#$#@#$#@GRAPHICS-WINDOW32010726437161612.01101110001-1616-1616111ticks30.0BUTTON901016543go/stopgoT1TOBSERVERNILNILNILNIL1BUTTON10108543NILsetupNIL1TOBSERVERNILNILNILNIL1SLIDER104531578initial-#-particlesinitial-#-particles0100611NILHORIZONTALSLIDER1080315113initial-gas-temperatureinitial-gas-temperature150025011NILHORIZONTALPLOT10200315422Temperature of gasestimetemp.0.010.00.0200.0truetrue"" ""PENS"orange" 1.0 0 -955883 true "" """purple" 1.0 0 -8630108 true "" """green" 1.0 0 -10899396 true "" ""CHOOSER165115315160mouse-interactionmouse-interaction"none - let the particles interact" "draw basic wall" "draw red removable wall" "draw green removable wall" "big eraser" "slow down particles" "speed up particles" "paint particles purple" "paint particles green" "paint particles orange" "add green particles" "add purple particles" "add orange particles"7BUTTON165165315198remove/replace green walltoggle-green-wallNIL1TOBSERVERNILNILNILNIL1SWITCH1701031443show-wall-hits?show-wall-hits?01-1000BUTTON10165160198remove/replace red walltoggle-red-wallNIL1TOBSERVERNILNILNILNIL1CHOOSER10115160160visualize-speed?visualize-speed?"none" "different shades" "arrows"1@#$#@#$#@## WHAT IS IT?This model supports a drawing style interface for "sketching" up representations of new systems to explore related to gas behavior and gas particles. This model is part of the "Connected Chemistry" curriculum http://ccl.northwestern.edu/curriculum/ConnectedChemistry/ which explores the behavior of gases.Most of the models in the Connected Chemistry curriculum use the same basic rules for simulating the behavior of gases. Each model highlights different features of how gas behavior is related to gas particle behavior.In all of the models, gas particles are assumed to move and to collide, both with each other and with objects such as walls.In this model, particles can be added, color coded, and sped up or slowed down, by drawing with the mouse cursor in the WORLD & VIEW. Also, additional types of removable and replaceable walls can be added to the WORLD.This model enables students to draw a model of a real world system and then test that model. A wide range of real world systems can be modeled with this simple interface (e.g. diffusion of perfume from an uncapped container, hot gas mixed with a cold gas, mixtures of gases).## HOW IT WORKSThe particles are modeled as hard balls with no internal energy except that which is due to their motion. Collisions between particles are elastic. Collisions with the wall are not.The exact way two particles collide is as follows:1. A particle moves in a straight line without changing its speed, unless it collides with another particle or bounces off the wall.2. Two particles "collide" if they find themselves on the same patch. In this model, two turtles are aimed so that they will collide at the origin.3. An angle of collision for the particles is chosen, as if they were two solid balls that hit, and this angle describes the direction of the line connecting their centers.4. The particles exchange momentum and energy only along this line, conforming to the conservation of momentum and energy for elastic collisions.5. Each particle is assigned its new speed, heading and energy.As the walls of the box are heated, the sides of the walls will change color from a deep red (cool) to a bright red, to pink to a pale pink white (hot). The walls contain a constant heat value throughout the simulation.The exact way particles gain energy from the walls of the box is as follows:1. Particles check their state of energy (kinetic).2. They hit or bounce off the wall.3. They find wall energy and set their new energy to be the average of their old kinetic energy and the wall energy.4. They change their speed and direction after the wall hit.## HOW TO USE ITButtons:SETUP - sets up the initial conditions set on the sliders.GO/STOP - runs and stops the model.MOUSE INTERACTION - when this is set to "none - let the particles interact" the particles will move and interact with each other and the surroundings. When set to any other value you can then click in the WORLD & VIEW to paint, erase, color, or add various objects and properties.Sliders:INITIAL-#-PARTICLES - sets the number of gas particles in the box when the simulation starts.INITIAL-GAS-TEMPERATURE sets the initial temperature of the gas.Switches:SHOW-WALL-HITS? turn visualization of when particles hits the walls (as flashes) on or offChoosers:VISUALIZE-SPEED? allows you to visualize particle speeds. For example, selecting "arrows", creates a representation of each particle velocity using a scalar arrow. Selecting "shades" creates representation of each particle speed using a brighter (faster) or darker (slower) shade of the particle's color.MOUSE-INTERACTION sets the type interaction the user can do with the mouse in the WORLD & VIEW. Possible settings include:"none - let the particles interact" - particles move about"draw basic wall" - adds a gray wall under the mouse cursor"draw red removable wall" - adds a red wall under the mouse cursor which can be alternatively removed and replaced (like a valve) using the REMOVE/REPLACE RED WALL."draw green removable wall" - adds a green wall under the mouse cursor which can be alternatively removed and replaced (like a valve) using the REMOVE/REPLACE GREEN WALL."big eraser" - erases all objects (except the yellow box boundary walls) under the mouse cursor."slow down particles" - increase the current speed of the particles by 10%."speed up particles" - reduces the current speed of the particles by 10%."paint particles green" - recolors the particles under the mouse cursor green (other settings include orange and purple)"add green particles" - adds a couple of new particles under the mouse cursor (other settings include orange and purple)Plots:- 1: TEMPERATURE OF GASES VS. TIME: plots the temperature of the different gases in the model, as indicated by their color (orange particles, green particles, and purple particles)## THINGS TO NOTICEThe mouse interaction can be used while the model is running as well as when it is stopped.## THINGS TO TRYCreate a model of how odors move throughout a room. Why do some people smell the odor before others? Does the layout of furniture, large objects, and walls in the room effect the movement of the odor? How about the temperature of the air in the room?Create a model of diffusion of a perfume from a closed container. How would you represent the different gases (the perfume and the surrounding air)? What shape will the container be? How will you model a removable cap or lid?Create a model of room filled with cold air and a different room filled with warm air. How will represent these different rooms of air? What could you add to show what happens when they mix?Create a model of heat transfer that shows what happens to the energy of one very fast moving gas particle when it hits a bunch of very slow moving gas particles. What does this show happening to the energy of the initial gas particles?## RELATED MODELSSee GasLab ModelsSee other Connected Chemistry models.## CREDITS AND REFERENCESThis model is part of the Connected Chemistry curriculum. See http://ccl.northwestern.edu/curriculum/chemistry.We would like to thank Sharona Levy and Michael Novak for their substantial contributions to this model.## HOW TO CITEIf you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:* Wilensky, U. (2006). NetLogo Connected Chemistry 8 Gas Particle Sandbox model. http://ccl.northwestern.edu/netlogo/models/ConnectedChemistry8GasParticleSandbox. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.To cite the Connected Chemistry curriculum as a whole, please use: Wilensky, U., Levy, S. T., & Novak, M. (2004). Connected Chemistry curriculum. http://ccl.northwestern.edu/curriculum/chemistry. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.## COPYRIGHT AND LICENSECopyright 2006 Uri Wilensky.This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.Commercial licenses are also available. 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