Chaos… of a dripping fauce University of Rochester混沌……一滴水的水龍頭羅切斯特大學(xué)

1、chaoschaosof a of a dripping dripping faucetfaucetdan allan dan allan and and adam bublitzadam bublitzchaosdripping faucet is nonlinear dynamic systemdrop influences initial conditions of faucet affects next droptherefore, increasing flow rate causes bifurcationsleads to chaosour set-upwater bucket

2、acts as reservoirflow to dropper on standthrough hene laserblocks beam aimed at detectorlabview writes datareconstruction, phase 1previous lab disrepairhoses leakedvery close to our electronicsbought new hoses and fixturesrearrangedcomputers and water are now as far apart as possiblecleaned the equi

3、pmentassembled a new set-upmissing dataproblem with our labview programdropped seconds of data randomlychanging clock speed of waveform minimizes data “drops”dove into the labview code for experimentcannot eliminate completely or resolution suffersdefault clock rate700 clock rate100 clock raterecons

4、truction, phase 2consequence of trying to fix missed datarewrote the labview vi old codecount each smallest increment of time (1/1000 sec) the laser was blockedonly write to file after certain number of samplesnot commented and hard to understandnew codecommentedmuch shorterwrites differences of tim

5、e (only important data)old codenew codedata analysis: sources of errorcomputer lag results in missed dropsnot every drop passes through the laser beamalso had a problem with the drop rate “jumping” discretely (shown below)thought to be most probably caused by our changing pressure in our reservoirdr

6、opper a (1.9 mm)7.51 drops/seclogistic map: comparing logistic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum” of drop frequencyfrequencytime(ms)time(sec)# dropstime(sec)dropper a (1.9 mm)15.56 drops/sectime(ms)time(sec)# dropstime(sec)logistic map: comparing log

7、istic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum” of drop frequencyfrequencydropper a (1.9 mm)21.41 drops/sectime(ms)time(sec)# dropstime(sec)logistic map: comparing logistic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum”

8、 of drop frequencyfrequencydropper b (0.45 mm)6.21 drops/sectime(ms)time(sec)# dropstime(sec)logistic map: comparing logistic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum” of drop frequencyfrequencydropper b (0.45 mm)9.47 drops/sectime(ms)time(sec)# dropstime(s

9、ec)logistic map: comparing logistic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum” of drop frequencyfrequencydropper b (0.45 mm)11.10 drops/sectime(ms)time(sec)# dropstime(sec)logistic map: comparing logistic map: comparing successive dropssuccessive dropsthe “spectrum” of drop the “spectrum” of drop frequencyfrequencydropper a (1.9 mm)dropper b (0.45 mm)suggestions for future groupstake time to understand flow of our labview codewe finally stopped the leaks on the second bucketyou can now have constant pressure in your reservoir