Physics 123Physics Made Easy: Ideas, Recipes,

Creative Playfulness

Alfred Hubler

Center for Complex Systems Research“I like chaos”

http://server17.how-why.com/blog

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 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

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 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.