CHAOS OF A DRIPPING FAUCET Dan Allan and

CHAOS… OF A DRIPPING FAUCET Dan Allan and Adam Bublitz

CHAOS Dripping faucet is nonlinear dynamic system Drop influences initial conditions of faucet Affects next drop Therefore, increasing flow rate causes bifurcations Leads to chaos

OUR SET-UP Water bucket acts as reservoir Flow to dropper on stand Through He. Ne laser Blocks beam aimed at detector Lab. View writes data

RECONSTRUCTION, PHASE 1 Previous lab disrepair Hoses leaked…very close to our electronics Bought new hoses and fixtures Rearranged Computers and water are now as far apart as possible Cleaned the equipment Assembled a new set-up

MISSING DATA Problem with our Lab. View program Dropped seconds of data randomly Default Clock Rate Changing clock speed of waveform minimizes data “drops” Dove into the Lab. View code for experiment 700 Clock Rate Cannot eliminate completely or resolution suffers 100 Clock Rate

RECONSTRUCTION, PHASE 2 Consequence of trying to fix missed data rewrote the Lab. View vi Old Code count each smallest increment of time (1/1000 sec) the laser was blocked only write to file after certain number of samples not commented and hard to understand New Code commented much shorter writes differences of time (only important data)

Old Code New Code

DATA ANALYSIS: SOURCES OF ERROR Computer lag results in missed drops Not every drop passes through the laser beam Also had a problem with the drop rate “jumping” discretely (shown below) thought to be most probably caused by our changing pressure in our reservoir

DROPPER A (1. 9 MM) 7. 51 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

DROPPER A (1. 9 MM) 15. 56 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

DROPPER A (1. 9 MM) 21. 41 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

DROPPER B (0. 45 MM) 6. 21 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

DROPPER B (0. 45 MM) 9. 47 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

DROPPER B (0. 45 MM) 11. 10 DROPS/SEC The “Spectrum” of Drop Frequency # Drops Time(sec) Logistic Map: Comparing Successive Drops Time(sec) Time(ms)

Dropper A (1. 9 mm) Dropper B (0. 45 mm)

SUGGESTIONS FOR FUTURE GROUPS Take time to understand flow of our Lab. View code We finally stopped the leaks on the second bucket You can now have constant pressure in your reservoir Find a way to make the laser, detector, and dropper stay aligned Now that everything works well, take many data sets: varying water flow and dropper diameter