Liquid Difusion - Bifocal Modeling Curriculum
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globals [ tick-delta ;; how much we advance the tick counter this time through max-tick-delta ;; the largest tick-delta is allowed to be drop-counter limit mouse-up? bored so-so excited something-cool found-error experiments left-temperature right-temperature temperature ] breed [ erasers eraser ] breed [ walls wall ] breed [ particles particle ] particles-own [ speed mass energy ;; particle info last-collision first-time ] walls-own [ energy valve-1? valve-2? pressure? surface-energy ] to setup ;; clear all ca set limit 50 create-erasers 1 [set hidden? true set size 3 set color white] ;; import the bitmap ask patches [set pcolor white] ;;import-pcolors "becker.png" draw-beaker ask patches with [pycor < 70 and pycor > -80 and pxcor > 20 and pxcor < 59][set pcolor white] ;; set-default-shape particles "circle" ;; initialize drop counter set drop-counter 10000 ;; set max-tick-delta 0.1073 ;; make-particles-within-box set experiments "add ink" reset-ticks set left-temperature mean [speed] of particles with [xcor < 0] set right-temperature mean [speed] of particles with [xcor > 0] set temperature mean [speed] of particles end ;; creates initial particles to make-particles-within-box create-particles 500 [ setup-particle random-position ] calculate-tick-delta end to calculate-tick-delta ;; tick-delta is calculated in such way that even the fastest ;; particle will jump at most 1 patch length in a tick. As ;; particles jump (speed * tick-delta) at every tick, making ;; tick length the inverse of the speed of the fastest particle ;; (1/max speed) assures that. Having each particle advance at most ;; one patch-length is necessary for it not to "jump over" a wall ;; or another particle. 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 to setup-particle ;; particle procedure set speed temperatura-inicial set mass 3 set energy (.5 * mass * speed * speed) set color cyan set size 4 set first-time 1 ; was 0 set last-collision nobody end ;; place particle at random location inside the box. to random-position ;; particle procedure setxy (-72 + random-float (142)) -77 + random-float (120) set heading random-float 360 end to draw-beaker ask patches with [pxcor = -74 and (pycor >= -90 and pycor <= 80)] [set pcolor 0] ask patches with [pxcor = 73 and (pycor >= -90 and pycor <= 80)] [set pcolor 0] ask patches with [pycor = -90 and (pxcor >= -74 and pxcor <= 73)] [set pcolor 0] end ;; step the model to go mouseme ifelse mouse-up? != false [ if mouse-down? and drop-counter > 0 and experiments = "add ink" and mouse-ycor < 70 and mouse-xcor > -60 and mouse-xcor < 40[ set mouse-up? false drop-ink set drop-counter drop-counter - 1 ] if mouse-down? and experiments = "draw wall" [ ask patch round mouse-xcor round mouse-ycor [ set pcolor grey ask neighbors [set pcolor grey ask neighbors [set pcolor grey]] ] ] if mouse-down? and experiments = "heat up water" [ set mouse-up? false drop-hot-water ] if mouse-down? and experiments = "cool down water" [ set mouse-up? false drop-cold-water ] ] [ if not mouse-down? [ set mouse-up? true ] ] ask particles [ bounce ] ask particles [ move ] ask particles [ check-for-collision ] set left-temperature mean [speed] of particles with [xcor < 0] set right-temperature mean [speed] of particles with [xcor > 0] set temperature mean [speed] of particles tick-advance tick-delta calculate-tick-delta display end to bounce ;; particle procedure ;; get the coordinates of the patch we will be on if we go forward 1 if [pcolor ] of patch-here != white [die ask one-of particles with [color = cyan][hatch 1 [setup-particle] ]] let new-patch patch-ahead 1 let new-px [pxcor] of new-patch let new-py [pycor] of new-patch ifelse [pcolor] of new-patch = white and new-py < limit [ ;; if we're not about to hit a wall, we don't need to do any further checks stop ] [ ;; a drop has to fall if (color = blue and ycor >= limit)[stop] ;; if hitting the top or bottom, reflect heading around y axis if (ycor < new-py - 1 or ycor > new-py - 1) [ set heading (180 - heading) ;if first-time = 0 [set first-time 1] set speed speed ; if color = blue and first-time <= 5 [ ; set speed 0.0001 ; set first-time first-time + 1 ; ] ] ;; if hitting the left or right, reflect heading around x axis if (xcor <= new-px - 1 or xcor >= new-px - 1) [ set heading (360 - heading) ] ] end to factor-gravity ;; turtle procedure let gravity 0 ifelse color = cyan [set gravity 0.01 ][set gravity .01 ] let vx (dx * speed) let vy (dy * speed) - (gravity * tick-delta) ;; fixed gravity now is 3.5 was set speed sqrt ((vy ^ 2) + (vx ^ 2)) set heading atan vx vy end to move ;; particle procedure ;; In other GasLab models, we use "jump speed * tick-delta" to move the ;; turtle the right distance along its current heading. In this ;; model, though, the particles are affected by gravity as well, so we ;; need to offset the turtle vertically by an additional amount. The ;; easiest way to do this is to use "setxy" instead of "jump". ;; Trigonometry tells us that "jump speed * tick-delta" is equivalent to: ;; setxy (xcor + dx * speed * tick-delta) ;; (ycor + dy * speed * tick-delta) ;; so to take gravity into account we just need to alter ycor ;; by an additional amount given by the classical physics equation: ;; y(t) = 0.5*a*t^2 + v*t + y(t-1) ;; but taking tick-delta into account, since tick-delta is a multiplier of t. let xcorr (xcor + dx * speed * tick-delta) if xcorr <= -117 or xcorr >= 116 [set xcorr xcor] let gravity 0 ifelse color = cyan [set gravity 0.01 ][set gravity .01 ] ;; let ycorr (ycor + dy * speed * tick-delta - gravity * (0.5 * tick-delta * tick-delta)) ifelse color = cyan [ ] [ ;if ycorr >= limit [set ycorr ycor - 1] ] if ycorr > 75 [die] setxy xcorr ycorr factor-gravity end to drop-ink ;Turtle procedure for releasing a drop onto the pond ask patch round mouse-xcor round mouse-ycor [ sprout-particles 30 [ set heading -180 setxy round mouse-xcor + random 20 round mouse-ycor + random 10 set speed temperatura-inicial set mass 1 set energy (.5 * mass * speed * speed) set color blue set size 4 set first-time 0 set last-collision nobody ] ] end to drop-cold-water ask patch round mouse-xcor round mouse-ycor [ ask particles in-radius 20 [ set speed 1 ] ] end to drop-hot-water ask patch round mouse-xcor round mouse-ycor [ ask particles in-radius 20 [ set speed 150 ] ] end to check-for-collision ;; particle procedure let where (patch-set patch-at -1 1 patch-at 0 1 patch-at 1 1 patch-at -1 -1 patch-at 1 0 patch-at 0 0) let enemies other particles-on where if count enemies = 1 ;; modified to be realistic, was = 1 [ let candidate one-of enemies with [who < [who] of myself and myself != last-collision] 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 ;;; PHASE 1: initial setup ;; for convenience, grab some quantities from other-particle let mass2 [mass] of other-particle let speed2 [speed] of other-particle let 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. 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-particle 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 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 * speed) ;; 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 ;; no recoloring in our case end to mouseme ask erasers [ if mouse-inside? [setxy mouse-xcor mouse-ycor] if mouse-inside? [ if experiments = "draw wall" [ set shape "square" set color grey set size 6 ] if experiments = "add ink" [ set shape "none" set color blue set size 6 ] ; set shape "none" if experiments = "cool down water" [ set shape "circle 3" set color blue set size 40 ] if experiments = "heat up water" [ set shape "circle 3" set color red set size 40 ] ] set hidden? not mouse-inside? ] end
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Liquid Difusion - Bifocal Modeling Curriculum.png | preview | Preview for 'Liquid Difusion - Bifocal Modeling Curriculum' | almost 6 years ago, by Paulo Blikstein | Download |
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