Physics 123 Physics Made Easy: Ideas, Recipes, Creative Playfulness Alfred Hubler Center for Complex Systems Research “I like chaos”

Todays topics: - Scientific Method - Uncertainties, Reproducibility, and Testing of a Hypothesis

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 unitsNo unitsbad unitsinconsistent 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.counting errorsexperimental 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=0s10s5m 13s14m 7s 14m 14s14m 41s15m 28s77m 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

Can we predict the structure of the emerging transportation network? ?

Predicting the Fractal Transporatation Network Left: Initial condition, Right: Emergent transporation network

Today’s topics: Scientific Method Idea : Use observations to predict the future Definition: 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 Testing Hypothesis is correct, if model prediction is within the error bar.