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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
1/4
1/8
1/12
1/16
1/24
1/32
1/x
1
2
4
8
12
16
24
32
Numb
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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 initial values for X and Y, solve Uedas equations.
(ii
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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 them hasnt recently run into the earth, but there have
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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, solve the equations for the pendulum
with the initial
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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 population as a function of generation.
1. The population sho
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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 ) = " # (0) sin& t)
l % l (
a
2
A linear pendulum (l = 1
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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 Feigenbaum thought about turbulence in liquids and gase
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 random. A main difference between a chaotic system and a
ra
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: Divide a line segment into 5 segments of equal length as sh
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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 Feigenbaum
2. Who was a young physicist at Los Alamos in
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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 the parameter, l, solve the equations for the
pendulum