CHAOS OF A DRIPPING FAUCET Dan Allan and Adam Bublitz C HAOS Dripping faucet is nonlinear dynamic system Drop influences initial conditions of faucet Affects next drop Therefore, increasing flow rate causes bifurcations Leads to chaos O UR S ET - UP Water bucket acts as reservoir Flow to dropper on stand Through HeNe laser Blocks beam aimed at detector LabView writes data R ECONSTRUCTION, P HASE 1 Previous lab disrepair Hoses leakedvery 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 LabView program Dropped seconds of data randomly Changing clock speed of waveform minimizes data drops Dove into the LabView code for experiment Cannot eliminate completely or resolution suffers Default Clock Rate 700 Clock Rate 100 Clock Rate R ECONSTRUCTION, P HASE 2 Consequence of trying to fix missed data rewrote the LabView 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 Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency Time(ms)Time(sec) # Drops Time(sec) DROPPER A (1.9 mm) DROPS/SEC Time(ms)Time(sec) # Drops Time(sec) Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency DROPPER A (1.9 mm) DROPS/SEC Time(ms)Time(sec) # Drops Time(sec) Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency DROPPER B (0.45 mm) 6.21 DROPS/SEC Time(ms)Time(sec) # Drops Time(sec) Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency DROPPER B (0.45 mm) 9.47 DROPS/SEC Time(ms)Time(sec) # Drops Time(sec) Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency DROPPER B (0.45 mm) DROPS/SEC Time(ms)Time(sec) # Drops Time(sec) Logistic Map: Comparing Successive Drops The Spectrum of Drop Frequency Dropper A (1.9 mm)Dropper B (0.45 mm) SUGGESTIONS FOR FUTURE GROUPS Take time to understand flow of our LabView 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