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PHY206 In-class Lab#6
The box-counting dimension
In class, we have estimated the box-counting dimensions for a few geometrical objects.
For the wave, I got the following data:
Scale factor
x
1
1/2
1
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PHY206 Homework#6
Answers in bold
1. Use the mathematica notebook, Ueda(4-12).nb, to explore the Ueda attractor
First, initialize the notebook.
(i) Set the end time to be 100.
(ii) Using the default
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PHY206 Homework#1:Answers
Answers in bold
I. Determinism and predictability
Asteroids go around the sun just as the planets do and some of them sometimes cross the
earths orbit. Fortunately, none of
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PHY206 Homework#3: solutions
Answers in bold
I. Use the mathematica notebook, DampedForcedPendulum(2/27).nb, to explore
the damped forced pendulum.
(ii) Using the default settings for the parameters
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PHY206 Homework#4
Answers in bold
Use the mathematica notebook, Logistic(3-4).nb, to explore the logistic equation.
Make sure to initialize the notebook first.
(i) Choose r = 0.8 and plot the popula
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The pendulum and gravity
1. Measuring
pendulum
g
using
The linear pendulum
d
d
g
! = " and
!=" #
dt
dt
l
Initial conditions:
! (0) " 0 and ! (0) = 0
" g%
! (t ) = ! (0) cos$ t '
# l &
g $ g'
! (t )
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PHY206 Reading Quiz#1
1. In 1974, Mitchell Feigenbaum was working at _ National Laboratory.
(a) Argonne
(d) Los Alamos
(b) Lawrence Berkeley
(e) Pacific Northwest
(c) Lawrence Livermore
2. Mitchell
PHY206 In-class Lab#1: Random walks versus chaotic walks
The main goal of this lab
Because a chaotic system evolves in time following a specific deterministic rule, its
behavior is not completely rand
PHY206 In-class Lab#5: Exploring fractals
1. A modified Cantor set
By applying the following construction rule over and over again, we can create a
fractal object similar to the Cantor set.
Rule: Divi
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PHY206 Reading Quiz#19
1. Who introduced the renormalization group theory to the study of phase transitions?
(a) Peter Carruthers
(d) James Yorke
(b) Edward Lorenz
(e) Kenneth Wilson
(c) Mitchell Fe
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PHY206 Homework#2: solutions
Answers in bold
I. Use the mathematica notebook, PlanePendulum(2/21).nb, to explore the plane
pendulum.
First, initialize the notebook.
(i) Using the default setting for