# Brownian Motion

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globals [ ;; time to next collision tick-delta ;; distance from the center to the walls box-edge ;; first and second particle colliding. particle1 particle2 ;; list of collisions times [[time particle1 particle2] ...] collisions big-particle-size big-particle-mass small-particle-size small-particle-mass ] breed [particles particle] particles-own [ speed mass energy ] ;;;;;;;;;;;;;;;;;;;;;; SETUP PROCEDURES ;;;;;;;;;;;;;;;;;;;;;;;;; to setup clear-all set-default-shape particles "circle" set box-edge max-pxcor ask patches with [(abs pxcor = box-edge or abs pycor = box-edge)] [ set pcolor yellow ] set small-particle-mass 2 * initial-total-energy / number-of-particles set big-particle-mass mass-ratio * small-particle-mass set small-particle-size 1 set big-particle-size 5 make-particles set particle1 nobody set particle2 nobody set collisions [] reset-ticks ask particles [ check-for-wall-collision ] ask particles [ check-for-particle-collision ] end to make-particles ;; ;; Create one big particle at the center create-particles 1 [ set speed 0 set size big-particle-size set mass big-particle-mass set energy (mass * speed ^ 2) / 2 set color yellow setxy 0 0 ] create-particles number-of-particles [ set speed 1 set size 1 set mass small-particle-mass set energy (mass * speed ^ 2) / 2 set color green while [overlapping?] [position-randomly] ] end to-report overlapping? report any? other particles in-radius small-particle-size or distance patch 0 0 <= (small-particle-size + big-particle-size) / 2 end to position-randomly ;; particle procedure ;; place particle at random inside the box setxy one-of [1 -1] * random-float (box-edge - 0.5 - size / 2) one-of [1 -1] * random-float (box-edge - 0.5 - size / 2) end ;;;;;;;;;;;;;;;;;; GO PROCEDURES ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go ;; advance time to next collision tick-delta ;; and set the colliding particles particle1 and particle2 choose-next-collision ask particles [ jump (speed * tick-delta) ] perform-next-collision tick-advance tick-delta recalculate-particles-that-just-collided end to choose-next-collision ;; if collisions = [] [ stop ] ;; pick the shortes time of projected collision let this-next first collisions foreach collisions [a -> if first a < first this-next [set this-next a] ] let dt item 0 this-next ;; if the next collision is more than 1 tick only advance 1 tick set tick-delta (dt - ticks) if tick-delta > 1 [ set tick-delta 1 set particle1 nobody set particle2 nobody stop ] set particle1 item 1 this-next set particle2 item 2 this-next end to perform-next-collision ;; if particle1 = nobody [ stop ] if is-string? particle2 [ if particle2 = "left wall" or particle2 = "right wall" [ ask particle1 [ set heading (- heading) ] stop ] if particle2 = "top wall" or particle2 = "bottom wall" [ ask particle1 [ set heading (180 - heading) ] stop ] ] ask particle1 [ collide-with particle2 ] end to collide-with [ other-particle ] ;; let mass2 [mass] of other-particle let speed2 [speed] of other-particle let heading2 [heading] of other-particle let theta towards other-particle ;; convert velocity to components along theta and perpendicular to theta let v1-tangent (speed * cos (theta - heading)) let v1-perpendicular (speed * sin (theta - heading)) let v2-tangent (speed2 * cos (theta - heading2)) let v2-perpendicular (speed2 * sin (theta - heading2)) ;; compute the velocity of the center of mass along theta let vcm (((mass * v1-tangent) + (mass2 * v2-tangent)) / (mass + mass2)) ;; new velocities after the collision along direction of theta set v1-tangent (2 * vcm - v1-tangent) set v2-tangent (2 * vcm - v2-tangent) ;; convert back to normal speed and heading set speed sqrt (v1-tangent ^ 2 + v1-perpendicular ^ 2) set energy kinetic-energy if v1-perpendicular != 0 or v1-tangent != 0 [ set heading (theta - (atan v1-perpendicular v1-tangent)) ] ask other-particle [ set speed sqrt(v2-tangent ^ 2 + v2-perpendicular ^ 2) set energy kinetic-energy if v2-perpendicular != 0 or v2-tangent != 0 [ set heading (theta - (atan v2-perpendicular v2-tangent)) ] ] end to recalculate-particles-that-just-collided ;; Remove from the list collisions of particles that we're done ifelse is-turtle? particle2 [ set collisions filter [ a -> item 1 a != particle1 and item 2 a != particle1 and item 1 a != particle2 and item 2 a != particle2 ] collisions ask particle2 [ check-for-wall-collision ] ask particle2 [ check-for-particle-collision ] ][ ;; particle2 is a wall. Filter out particle1 of the list set collisions filter [ a -> item 1 a != particle1 and item 2 a != particle1 ] collisions ] if particle1 != nobody [ ask particle1 [ check-for-wall-collision ] ask particle1 [ check-for-particle-collision ] ] ;; make sure we fileter out particles1 and particle2 set collisions filter [ a -> item 1 a != particle1 or item 2 a != particle2 ] collisions ;; done set particle1 nobody set particle2 nobody end to check-for-wall-collision ;; determines when a particle will hit a wall ;; first along the horizontal direction let vx (speed * dx) if vx != 0 [ ;; how long to hit the right wall let t-right (box-edge - 0.5 - xcor - (size / 2)) / vx if t-right > 0 [assign-colliding-wall t-right "right wall"] ;; how long to hit the left wall let t-left ((- box-edge) + 0.5 - xcor + (size / 2)) / vx if t-left > 0 [assign-colliding-wall t-left "left wall"] ] ;; Now along the vertical direction let vy (speed * dy) if vy != 0 [ ;; how long to hit the top wall let t-top (box-edge - 0.5 - ycor - (size / 2)) / vy if t-top > 0 [assign-colliding-wall t-top "top wall"] ;; how long to hit the bottom wall let t-bottom ((- box-edge) + 0.5 - ycor + (size / 2)) / vy if t-bottom > 0 [assign-colliding-wall t-bottom "bottom wall"] ] end to assign-colliding-wall [time-to-collision wall] ;; store the time to collision, self (the particle) and the wall ;; add clock to time-to-collision let colliding-pair (list (time-to-collision + ticks) self wall) set collisions fput colliding-pair collisions end to check-for-particle-collision ;; let my-x xcor let my-y ycor let my-particle-size size let my-x-speed speed * dx let my-y-speed speed * dy ask other particles [ let dpx (xcor - my-x) ;; relative distance along x direction let dpy (ycor - my-y) let x-speed (speed * dx) let y-speed (speed * dy) let dvx (x-speed - my-x-speed) ;; relative speed difference let dvy (y-speed - my-y-speed) let sum-radii (((my-particle-size) / 2) + (([size] of self) / 2)) let p-squared (dpx ^ 2 + dpy ^ 2 - sum-radii ^ 2) let pv ( 2 * ((dpx * dvx) + (dpy * dvy))) let v-squared ( dvx ^ 2 + dvy ^ 2) let determinant pv ^ 2 - (4 * v-squared * p-squared) let time-to-collision -1 if determinant > 0 [ set time-to-collision ( - pv - sqrt determinant) / (2 * v-squared) ] if time-to-collision > 0 [ set collisions fput (list (time-to-collision + ticks) self myself) collisions ] ] end to-report kinetic-energy report (mass * speed ^ 2) / 2 end

There is only one version of this model, created about 1 year ago by Jesus Marcano.

## Attached files

File | Type | Description | Last updated | |
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Brownian Motion.png | preview | Preview for 'Brownian Motion' | about 1 year ago, by Jesus Marcano | Download |

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