# GasLab Two Gas 3D

### 1 collaborator

Uri Wilensky (Author)

### Tags

gaslab

Tagged by Reuven M. Lerner over 6 years ago

Model group CCL | Visible to everyone | Changeable by group members (CCL)
Model was written in NetLogo 3D 4.1pre7 • Viewed 165 times • Downloaded 12 times • Run 0 times

### WHAT IS IT?

This model is a 2D version of the 3D model Gas Lab Two Gas; it is one in a series of GasLab models. They use the same basic rules for simulating the behavior of gases. Each model integrates different features in order to highlight different aspects of gas behavior.

The basic principle of the models is that gas particles are assumed to have two elementary actions: they move and they collide - either with other particles or with any other objects such as walls.

This model is the simplest gas model in the suite of GasLab models. The particles are moving and colliding with each other with no external constraints, such as gravity or containers. In this model, particles are modeled as perfectly elastic ones with no energy except their kinetic energy -- which is due to their motion. Collisions between particles are elastic. Particles are colored according to their speed -- blue for slow, green for medium, and red for high.

### HOW IT WORKS

The basic principle of all GasLab models is the following algorithm (for more details, see the model "GasLab Gas in a Box"):

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 their surfaces touch. In this model, the time at which any collision is about to occur is measured, and particles move forward until the first pair to collide touch one another. They are collided, and the cycle repeats.

3) The vector of collision for the particles 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, direction and energy.

### HOW TO USE IT

- OPEN: opens the door between the two chambers and allows particles to pas through

- CLOSE: closes the door separating the two chambers

- NUM-MAGENTAS and NUM-CYANS: the number of gas particles of each type.

- COLLIDE?: Turns collisions between particles on and off.

- MAGENTA-INIT-SPEED and CYAN-INIT-SPEED: the initial speed of each type of particle -- particles of the same type start with the same speed.

- MAGENTA-MASS and CYAN-MASS: the mass of each type particle -- particles of the same type have the same mass.

- BOX-SIZE: defines the size of the bounding box

- OPENING-SIZE: define the size of the "door" between the two chambers

As in most NetLogo models, the first step is to press SETUP. It puts in the initial conditions you have set with the sliders. Be sure to wait till the SETUP button stops before pushing GO.

The GO button runs the models again and again. This is a "forever" button.

Monitors:

MAGENTAS IN LEFT CHAMBER, CYANS IN RIGHT CHAMBER, AVERAGE SPEED MAGENTA and CYAN, and AVERAGE ENERGY MAGENTA and CYAN help you track the changes after the "door" has been opened.

Plots:

- Average Speeds: Shows the change in average speed for each type of particle.

- Average Energy: Shows the change in average energy for each type of particle.

Initially, all the particles have the same speed but random directions. Therefore the first histogram plots of speed and energy should show only one column each. As the particles repeatedly collide, they exchange energy and head off in new directions, and the speeds are dispersed -- some particles get faster, some get slower, and the plot will show that change.

### THINGS TO NOTICE

What variables affect how quickly the model reaches a new equilibrium when the wall is removed?

Why does the average speed for each color decrease as the model runs with the wall in place, even though the average energy remains constant?

What happens to the relative energies and speeds of each kind of particle as they intermingle? What effect do the initial speeds and masses have on this relationship?

Does the system reach an equilibrium state?

Do heavier particles tend to have higher or lower speeds when the distribution of energy has reached equilibrium?

Is it reasonable to consider this box "insulated"?

### THINGS TO TRY

Calculate how long the model takes to reach equilibrium with different sizes of windows (holding other parameters constant).

Calculate how long the model takes to reach equilibrium with different particle speeds.

Set the number of cyan particles to zero. This is a model of a gas expanding into a vacuum. This experiment was first done by Joule, using two insulated chambers separated by a valve. He found that the temperature of the gas remained the same when the valve was opened. Why would this be true? Is this model consistent with that observation?

Try some extreme situations, to test your intuitive understanding:

-- masses the same, speeds of the two particles very different

### .

speeds the same, masses very different

### .

a very small number of one kind of particle -- almost, but not quite a vacuum. What happens to those few particles, and how do they affect the other kind?

Try relating quantitatively the ratio of the equilibrium speeds of both gases after the wall is opened to the ratio of the masses of both gases. How are they related?

### EXTENDING THE MODEL

Monitor pressure in the right and left chambers.

Monitor temperature in the right and left chambers.

Replace the partition wall with a moveable piston, so that the two kinds of particles can push against each other without intermingling. Do they arrive at a different equilibrium then?

Replace the partition wall with a surface that can transmit energy.

Add the histograms of energy and speed distribution (such as found in the "Free Gas" model).

### NETLOGO FEATURES

Notice the use of the histogram primitive.

When making 3D shapes, both sides of a shape must be defined or else one side becomes transparent. We use this feature to create a box with opaque inside walls and fencelike outside walls. For more information about 3d shapes, see the NetLogo User Manual.

### CREDITS AND REFERENCES

This was one of the original Connection Machine StarLogo applications (under the name GPCEE) and is now ported to NetLogo as part of the Participatory Simulations project.

### HOW TO CITE

If you mention this model in an academic publication, we ask that you include these citations for the model itself and for the NetLogo software:

- Wilensky, U. (2007). NetLogo GasLab Two Gas 3D model. http://ccl.northwestern.edu/netlogo/models/GasLabTwoGas3D. 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.

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:

a) this copyright notice is included.

b) this model will not be redistributed for profit without permission from Uri Wilensky. Contact Uri Wilensky for appropriate licenses for redistribution for profit.

This is a 3D version of the 2D model GasLab Two Gas.

Click to Run Model

```globals
[
tick-delta                         ;; how much we advance the tick counter this time through
min-tick-delta                     ;; the smallest tick-delta is allowed to be
init-avg-speed init-avg-energy     ;; initial averages
collision-times                    ;; a list that of times of pending collisions

;; averages from the end of the last tick
avg-speed avg-energy
avg-speed-magenta
avg-speed-cyan
avg-energy-magenta
avg-energy-cyan

open?                              ;; is there an opening in the divider?
]

breed [ dividers divider ]
breed [ walls wall ]

breed [ particles particle ]
particles-own
[
vx vy vz                   ;; velocities rel axes
speed mass energy          ;; particle info
collision-time             ;; to determine when collision is
collision-with             ;; to determine who the collision is with
last-collision             ;; so they don't collide with one another many times
]

to setup
clear-all
;; the wall shape is a custom 3D shape contained in "wall.txt"
set-default-shape particles "circle"
set-default-shape walls "wall"
set tick-delta .01
set min-tick-delta .0000001
make-box
make-particles
update-variables
set init-avg-speed avg-speed
set init-avg-energy avg-energy
set open? false
set avg-speed-cyan mean [speed] of turtles with [color = cyan]
set avg-speed-magenta mean [speed] of turtles with [color = magenta]
set avg-energy-cyan mean [energy] of turtles with [color = cyan]
set avg-energy-magenta mean [ energy ] of turtles with [color = magenta]
do-plotting
end

to go
set collision-times [] ;; empty this out for new input
[
set collision-time tick-delta
set collision-with nobody
if collide? [
detect-collisions
detect-wall-collisions
]
]
set collision-times sort collision-times

ifelse first collision-times < tick-delta   ;; if something will collide before the tick
[
ask particles [ jump speed * first collision-times ] ; most particles to first collision
tick-advance first collision-times ;; now, collide all the particles that are ready
ask particles with [ collision-time = first collision-times ]
[
ifelse is-particle? collision-with
[
if collision-with > self [ ;; so that we don't collide the same particles twice
collide collision-with
set last-collision collision-with
ask collision-with [ set last-collision myself ]
]
]
[ wall-collide collision-with ]
]
]
[
ask particles [ jump speed * tick-delta ]
]

if last-collision != nobody and is-particle? last-collision
[
if distance last-collision > ( ( ( [size] of last-collision ) / 2 ) + ( size / 2 ) ) * 1.1
[ set last-collision nobody ]
]
]

if floor ticks > floor (ticks - tick-delta)
[ update-variables ]

set avg-speed-cyan mean [speed] of turtles with [color = cyan]
set avg-speed-magenta mean [speed] of turtles with [color = magenta]
set avg-energy-cyan mean [energy] of turtles with [color = cyan]
set avg-energy-magenta mean [energy] of turtles with [color = magenta]

do-plotting
display
end

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

;;;
;;; distance and collision procedures
;;;

to detect-collisions ;; particle procedure

;; detect-collisions is a particle procedure that determines the time it takes to the collision between
;; two particles (if one exists).  It solves for the time by representing the equations of motion for
;; distance, velocity, and time in a quadratic equation of the vector components of the relative velocities
;; and changes in position between the two particles and solves for the time until the next collision

let my-x-speed x-velocity heading pitch speed
let my-y-speed y-velocity heading pitch speed
let my-z-speed z-velocity pitch speed

ask other particles with [self != [last-collision] of myself]
[
let dpx 0
let dpy 0
let dpz 0

;; since our world is wrapped, we can't just use calcs like xcor - my-x. Instead, we take the smallest
;; of either the wrapped or unwrapped distance for each dimension

set dpx xcor - [xcor] of myself
set dpy ycor - [ycor] of myself
set dpz zcor - [zcor] of myself

let x-speed x-velocity heading pitch speed  ;; speed of other particle in the x direction
let y-speed y-velocity heading pitch speed  ;; speed of other particle in the y direction
let z-speed z-velocity pitch speed          ;; speed of other particle in the z direction

let dvx x-speed - my-x-speed ;; relative speed difference between particles in the x direction
let dvy y-speed - my-y-speed ;; relative speed difference between particles in the y direction
let dvz z-speed - my-z-speed ;; relative speed difference between particles in the z direction

let sum-r ([size] of myself / 2) + (size / 2) ;; sum of both particle radii

let p-squared   ((dpx * dpx) + (dpy * dpy) + (dpz * dpz)) - (sum-r ^ 2)   ;; p-squared represents difference of the
;; square of the radii and the square
;; of the initial positions

let pv 2 * ((dpx * dvx) + (dpy * dvy) + (dpz * dvz))  ;;the vector product of the position times the velocity
let v-squared (dvx * dvx) + (dvy * dvy) + (dvz * dvz) ;; the square of the difference in speeds
;; represented as the sum of the squares of the x-component
;; and y-component of relative speeds between the two particles

;; p-squared, pv, and v-squared are coefficients in the quadratic equation shown above that
;; represents how distance between the particles and relative velocity are related to the time,
;; t, at which they will next collide (or when their edges will just be touching)

let D1 pv ^ 2 -  (4 * v-squared * p-squared)

let time-to-collision  -1

if D1 >= 0
[ set time-to-collision (- pv - sqrt D1) / (2 * v-squared) ]

if time-to-collision < tick-delta and time-to-collision > min-tick-delta
[
set collision-with myself
set collision-time time-to-collision
set collision-times lput time-to-collision collision-times
]
if time-to-collision < min-tick-delta and time-to-collision > 0
[
set collision-with myself
set collision-time min-tick-delta
set collision-times lput min-tick-delta collision-times
]
]
end

to detect-wall-collisions ;; particle procedure
update-component-vectors
let my-vx vx * tick-delta
let my-vy vy * tick-delta
let my-vz vz * tick-delta

detect-wall-collision "xy"
( wall-max-pzcor - ( size / 2 ) )
( wall-min-pzcor + ( size / 2 ) )
zcor
my-vz
detect-wall-collision "yz"
( wall-max-pxcor - ( size / 2 ) )
( wall-min-pxcor + ( size / 2 ) )
xcor
my-vx
detect-wall-collision "xz"
( wall-max-pycor - ( size / 2 ) )
( wall-min-pycor + ( size / 2 ) )
ycor
my-vy
detect-divider-collision

if collision-time < min-tick-delta [
set collision-time min-tick-delta
]
set collision-times lput collision-time collision-times
end

;; detect-wall-collision plane of wall, wall cor, wall cor, cor of particle, speed of particle

to detect-wall-collision [ plane max-wall min-wall cor cor-speed ] ;; particle procedure
if ( cor + cor-speed ) > max-wall or
( cor + cor-speed ) < min-wall
[
let distance-to-wall abs( max-wall - cor )
let time-fraction ( distance-to-wall / cor-speed )
if ( time-fraction * tick-delta ) < collision-time and last-collision != plane
[
set collision-time time-fraction * tick-delta
set collision-with plane
]
]
end

to detect-divider-collision ;; particle procedure
let my-vx vx * tick-delta
if xcor > 0 and my-vx < 0 and ( xcor + my-vx ) < (size / 2)
[
let distance-to-wall xcor - (size / 2)
let time-fraction distance-to-wall / my-vx
if ( time-fraction * tick-delta ) < collision-time and last-collision != "divider"
[
;; where particle will be once it hits divider
let future-ycor ycor + ( vy * time-fraction * tick-delta )
let future-zcor zcor + ( vz * time-fraction * tick-delta )
if not ( ( abs( future-ycor ) <= ( wall-max-pycor * opening-size / 100 ) and
abs( future-zcor ) <= ( wall-max-pzcor * opening-size / 100 ) ) and
open? )
[
set collision-time time-fraction * tick-delta
set collision-with "divider"
]
]
]
if xcor < 0 and my-vx > 0 and ( xcor + my-vx ) > (- size / 2)
[
let distance-to-wall abs( xcor + (size / 2) )
let time-fraction distance-to-wall / my-vx
if ( time-fraction * tick-delta ) < collision-time and last-collision != "divider"
[
let future-ycor ycor + ( vy * time-fraction * tick-delta ) ;; where particle will be once it hits divider
let future-zcor zcor + ( vz * time-fraction * tick-delta )
if not ( ( abs( future-ycor ) <= ( wall-max-pycor * opening-size / 100 ) and
abs( future-zcor ) <= ( wall-max-pzcor * opening-size / 100 ) ) and
open? )
[
set collision-time time-fraction * tick-delta
set collision-with "divider"
]
]
]
end

to collide [ particle2 ] ;; particle procedure
update-component-vectors

;; find heading and pitch from the center of particle1 to the center of particle2
let tpitch towards-pitch particle2

;; use these to determine the x, y, z components of theta
let tx x-velocity theading tpitch 1
let ty y-velocity theading tpitch 1
let tz z-velocity tpitch 1

;; find the speed of particle1 in the direction of n
let particle1-to-theta orth-projection vx vy vz tx ty tz

;; express particle1's movement along theta in terms of xyz
let x1-to-theta particle1-to-theta * tx
let y1-to-theta particle1-to-theta * ty
let z1-to-theta particle1-to-theta * tz

;; now we can find the x, y and z components of the particle's velocity that
;; aren't in the direction of theta by subtracting the x, y, and z
;; components of the velocity in the direction of theta from the components
;; of the overall velocity of the particle
let x1-opp-theta vx - x1-to-theta
let y1-opp-theta vy - y1-to-theta
let z1-opp-theta vz - z1-to-theta

;; do the same for particle2
let particle2-to-theta orth-projection [vx] of particle2 [vy] of particle2 [vz] of particle2 tx ty tz

let x2-to-theta particle2-to-theta * tx
let y2-to-theta particle2-to-theta * ty
let z2-to-theta particle2-to-theta * tz

let x2-opp-theta [vx] of particle2 - x2-to-theta
let y2-opp-theta [vy] of particle2 - y2-to-theta
let z2-opp-theta [vz] of particle2 - z2-to-theta

;; calculate the velocity of the center of mass along theta
let vcm ( ( mass * particle1-to-theta ) + ( [mass] of particle2 * particle2-to-theta ) )
/ ( mass + [mass] of particle2 )

;; switch momentums along theta
set particle1-to-theta 2 * vcm - particle1-to-theta
set particle2-to-theta 2 * vcm - particle2-to-theta

;; determine the x, y, z components of each particle's new velocities
;; in the direction of theta
set x1-to-theta particle1-to-theta * tx
set y1-to-theta particle1-to-theta * ty
set z1-to-theta particle1-to-theta * tz

set x2-to-theta particle2-to-theta * tx
set y2-to-theta particle2-to-theta * ty
set z2-to-theta particle2-to-theta * tz

;; now, we add the new velocities along theta to the unchanged velocities
;; opposite theta to determine the new heading, pitch, and speed of each particle
set vx x1-to-theta + x1-opp-theta
set vy y1-to-theta + y1-opp-theta
set vz z1-to-theta + z1-opp-theta
set pitch vpitch vx vy vz
set speed vspeed vx vy vz
set energy 0.5 * mass * speed ^ 2

set vx x2-to-theta + x2-opp-theta
set vy y2-to-theta + y2-opp-theta
set vz z2-to-theta + z2-opp-theta
set pitch vpitch vx vy vz
set speed vspeed vx vy vz
set energy 0.5 * mass * speed ^ 2
]
end

to open-middle
if opening-size = 20 [
ask dividers [ set shape "opening20" ]
]
if opening-size = 40 [
ask dividers [ set shape "opening40" ]
]
if opening-size = 60 [
ask dividers [ set shape "opening60" ]
]
if opening-size = 80 [
ask dividers [ set shape "opening80" ]
]
if opening-size = 100 [
]
set open? true
end

to close-middle
ask dividers [ set shape "flash" ]
set open? false
end

to wall-collide [ collision-wall ] ;; particle procedure
update-component-vectors

ifelse collision-wall = "yz"
[
][
ifelse collision-wall = "xz"
[
][
ifelse collision-wall = "xy"
[
set pitch vpitch vx vy ( - vz )
]
[
] ] ]
end

;;;
;;; drawing procedures
;;;

;; creates box

to make-box
create-walls 1 [ ;; bottom wall
set zcor wall-min-pzcor
]
create-walls 1 [ ;; top wall
set pitch 180
set zcor wall-max-pzcor
]
create-walls 1 [ ;; upper wall
set pitch 90
set ycor wall-max-pycor
]
create-walls 1 [ ;; lower wall
set pitch -90
set ycor wall-min-pycor
]
create-walls 1 [ ;; right wall
set roll -90
set xcor wall-max-pxcor
]
create-walls 1 [ ;; left wall
set roll 90
set xcor wall-min-pxcor
]
create-dividers 1 [ ;; center wall
set color grey
set roll 90
set xcor 0
set shape "flash"
set size box-width
]
set color grey + random 3
set size box-width
set shape "wall"
]
end

;; creates initial particles

to make-particles
create-particles num-magentas
[
setup-particle magenta-init-speed magenta-mass magenta
random-position "left-half"
]
create-particles num-cyans
[
setup-particle cyan-init-speed cyan-mass cyan
random-position "right-half"
]
check-initial-positions 0
check-center-divider
end

to setup-particle [ my-speed my-mass my-color ] ;; particle procedure
set speed my-speed
set mass my-mass
set energy 0.5 * mass * (speed ^ 2)
set color my-color
set size mass ^ 0.33
end

;; makes sure particles aren't overlapped at setup

to check-initial-positions [iterations]
let check-again? false
[
if particle-overlap?
[
ifelse color = cyan
[ random-position "right-half" ]
[ random-position "left-half" ]
set check-again? true
]
]
ifelse iterations < 50
[
if check-again?
[ check-initial-positions iterations + 1 ]
]
[
beep
user-message "Not enough room for all these particles!"
]
end

;; makes sure particles don't go through center wall at setup

to check-center-divider
let check-again? false
[
if abs( xcor ) < ( size / 2 )
[
ifelse color = cyan
[ random-position "right-half" ]
[ random-position "left-half" ]
set check-again? true
]
]
if check-again?
[
check-initial-positions 0
check-center-divider
]
end

to-report particle-overlap? ;; particle procedure
report any? other particles with [ distance myself <= ((size + [size] of myself) / 2 ) ]
end

;; place particle at random location inside the box.

to random-position [ side ] ;; particle procedure
ifelse side = "left-half" [
setxyz ( random-float ( ( box-width / 2 ) - 2 ) +
( wall-min-pxcor + 1 ) )
( random-float ( box-height - 2 ) +
( wall-min-pycor + 1 ) )
( random-float ( box-depth - 2 ) +
( wall-min-pzcor + 1 ) )
] [
setxyz ( random-float ( ( box-width / 2 ) - 2 ) +
( 1 ) )
( random-float ( box-height - 2 ) +
( wall-min-pycor + 1 ) )
( random-float ( box-depth - 2 ) +
( wall-min-pzcor + 1 ) )
]
tilt-up asin (1.0 - random-float 2.0)
roll-right random-float 360
update-component-vectors
set pitch vpitch vx vy vz
end

;;;
;;; math procedures
;;;

;; consider the desired box-size

to-report box-width
report ( world-width - 1 ) * ( box-size / 100 )
end

to-report box-height
report ( world-height - 1 ) * ( box-size / 100 )
end

to-report box-depth
report ( world-depth - 1 ) * ( box-size / 100 )
end

to-report wall-max-pxcor
report max-pxcor * ( box-size / 100 )
end

to-report wall-max-pycor
report max-pycor * ( box-size / 100 )
end

to-report wall-max-pzcor
report max-pzcor * ( box-size / 100 )
end

to-report wall-min-pxcor
report min-pxcor * ( box-size / 100 )
end

to-report wall-min-pycor
report min-pycor * ( box-size / 100 )
end

to-report wall-min-pzcor
report min-pzcor * ( box-size / 100 )
end

;; makes sure that the values stored in vx, vy, vz actually reflect
;; the appropriate heading, pitch, speed

to update-component-vectors ;; particle procedure
set vx x-velocity heading pitch speed
set vy y-velocity heading pitch speed
set vz z-velocity pitch speed
end

;; reports velocity of a vector at a given angle and pitch
;; in the direction of x.

to-report x-velocity [ vector-angle vector-pitch vector-speed ]
report sin( vector-angle ) * abs( cos( vector-pitch ) ) * vector-speed
end

;; reports velocity of a vector at a given angle and pitch
;; in the direction of y.

to-report y-velocity [ vector-angle vector-pitch vector-speed ]
report cos( vector-angle ) * abs( cos( vector-pitch ) ) * vector-speed
end

;; reports velocity of a vector at a given angle and pitch
;; in the direction of z.

to-report z-velocity [ vector-pitch vector-speed ]
report sin( vector-pitch ) * vector-speed
end

;; reports speed of a vector given xyz coords

to-report vspeed [ x y z ]
report sqrt( x ^ 2 + y ^ 2 + z ^ 2 )
end

;; reports xt heading of a vector given xyz coords

to-report vheading [ x y z ]
report atan x y
end

;; reports pitch of a vector given xyz coords

to-report vpitch [ x y z ]
report asin ( z / ( vspeed x y z ) )
end

;; called by orthprojection

to-report dot-product [ x1 y1 z1 x2 y2 z2 ]
report ( x1 * x2 ) + ( y1 * y2 ) + ( z1 * z2 )
end

;; component of 1 in the direction of 2 (Note order)

to-report orth-projection [ x1 y1 z1 x2 y2 z2 ]
let dproduct dot-product x1 y1 z1 x2 y2 z2
let speed-of-2 vspeed x2 y2 z2
;; if speed is 0 then there's no projection anyway
ifelse speed-of-2 > 0
[ report dproduct / speed-of-2 ]
[ report 0 ]
end

;;;
;;; plotting procedures
;;;

to do-plotting
set-current-plot "Average Speeds"
set-current-plot-pen "cyan"
plotxy ticks avg-speed-cyan
set-current-plot-pen "magenta"
plotxy ticks avg-speed-magenta

set-current-plot "Average Energies"
set-current-plot-pen "cyan"
plotxy ticks avg-energy-cyan
set-current-plot-pen "magenta"
plotxy ticks avg-energy-magenta
end

; The full copyright notice is in the Information tab.
```

There are 3 versions of this model.