Physics 123 Physics Made Easy: Ideas, Recipes, Creative Playfulness

1
Physics 123Physics Made Easy Ideas, Recipes,
Creative Playfulness

• Alfred Hubler
• Center for Complex Systems Research
• I like chaos

http//server10.how-why.com/blog
2

• Todays topics reflections on the lab
• Scientific Method
• Uncertainties, Reproducibility, and Testing of a
  Hypothesis

3
Scientific Method Context A belief system- What
is true? 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. Reproducible Data same
experiment produces same results at a different
time, at a different location measured by
different people (record keeping is
important) Observation sensation of a human
sense Scientific Model math, logic, computer
program Hypothesis formulation of scientific
models which predict observations. Testing
Prediction Observation?
Discussion Other belief system include faith,
intuition, traditions. Scientific method works
well for simple systems. ?
4

• Uncertainty, Reproducibility, and Testing of a
  Hypothesis
• Sources of uncertainty
• -Uncertainty in the design of the experiment,
  -i.e. when is the cup of macaroni really full,
  are all macaroni of the same kind, etc.
• -Uncertainty in the measurement, -i.e. did the
  experimenter miscount?
• Chaos, -i.e. high sensitivity to noise, history,
  context ?
• Bottom line Uncertainty is OK. Reproducible data
  have an error bar.
• Testing Hypothesis is correct, if model
  prediction is within the error bar.

5
Growth of Fractal Networks Chaos
needle electrode sprays charge over oil surface
20 kV
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 D1.6 mm particles sit on the bottom of
the dish
6
Phenomenology Overview

12 cm
stage I strand formation
t0s
10s
5m 13s
14m 7s

14m 14s
14m 41s
15m 28s
77m 27s
stage II boundary connection
stage III geometric expansion
stationary state
7
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.
8
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.
9
Qualitative effects of initial distribution
Slightly different initial condition produces
very different number of trees gtchaos
10
?
Can we predict the structure of the emerging
transportation network?
11
Predicting the Fractal Transporatation Network
Left Initial condition, Right Emergent
transporation network
12
Todays topics reflections on the
lab 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.