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Physics 123Physics Made Easy: Ideas, Recipes,
Creative Playfulness
Alfred Hubler
Center for Complex Systems Research“I like chaos”
http://server17.how-why.com/blog
Scientific Method
Context: A belief system- “What is true?”
Scientific method: Use past to predict the future.
Discussion: -Other belief system include faith, intuition, traditions.
-Scientific method works well for simple systems.
Uncertainty, Reproducibility, and Testing of a Hypothesis
Sources of uncertainty:-No units, bad units, inconsistent units-Uncertainty in the design of the experiment, -i.e. when is the cup of macaroni really full, are all cups of the same kind, etc.-Uncertainty in the measurement, -i.e. counting errors; experimental resolution.-Noise, or other irregular, unknown forces are important, -i.e. in a coin flip: high sensitivity to noise, history, context = chaos
Bottom line: Uncertainty is OK. Measurements are reproducible if they agree with the error bars (bad units => large error bars).
Testing: Hypothesis is correct, if the model prediction matches the experiment within the error bar, but good science = small error bars
Growth of Fractal Networks: Chaos
20 kV
needle electrode sprays charge over oil surface
air gap between needle electrode and oil surface approx. 5 cm
ring electrode forms boundary of dish
has a radius of 12 cm
oil height is approximately 3 mm, enough to cover the particles
castor oil is used: high viscosity, low ohmic heating, biodegradable
particles are non-magnetic stainless steel, diameter D=1.6 mm
particles sit on the bottom of the dish
Phenomenology Overview
12 cm
t=0s 10s 5m 13s 14m 7s
14m 14s 14m 41s 15m 28s 77m 27s
stage I:strand
formation
stage II:boundary
connection stage III: geometric expansion
stationary state
Adjacency defines topological species of each particle
Termini = particles touching only one other particle
Branching points = particles touching three or more other particles
Trunks = particles touching only two other particles
Particles become termini or three-fold branch points in stage III. In addition there are a few loners (less than 1%). Loners are not connected to any other particle. There are no closed
loops in stage III.
Relative number of each species is reprodicible: 22% termini, 22% branching points
Graphs show how the number of termini, T, and branching points, B, scale with the total number of particles in the tree.
Qualitative effects of initial distribution
Slightly different initial condition produces very different number of trees =>chaos
Predicting the Fractal Transporatation Network
Left: Initial condition, Right: Emergent transporation network
Today’s topics:
Scientific MethodIdea: Use observations to predict the futureDefinition: A scientific method consists of the collection of reproducible data through observation , and the formulation and testing of scientific models which predict these observations.
Uncertainties Design Flaws, Measurement Uncertainty, Chaos
TestingHypothesis is correct, if model prediction is within the error bar.