International Young Physicists' Tournament

Problems & Solutions 2014

Sihui Wang, Wenli Gao

• Publisher: WSPC
• Year: 2016
• ISBN:
  9789814740357
• Topic: Biological Sciences
• Subtopic: Science Research & Methodology
• Index: Biological Sciences

International Young Physicists' Tournament (IYPT), is one of the most prestigious international physics contests among high school students. This book is based on the solutions of 2014 IYPT problems. The authors are undergraduate students who participated in the CUPT (Chinese Undergraduate Physics Tournament). It is intended as a college level solution to the challenging open-ended problems. It provides original, quantitative solutions in fulfilling seemingly impossible tasks. This book is not limited to the tasks required by the problems and it is not confined to the models and methods in present literatures. Many of the articles include modification and extension to existing models in references, or derivation and computation based on fundamental physics. This book provides quantitative solutions to practical problems in everyday life.

This is a good reference book for undergraduates, advanced high-school students, physics educators and curious public interested in the intriguing phenomena in daily life.

List of supplementary materials:
More solutions not included in the book:
Solution to problem 4. Ball sound (2 MB)
Solution to problem 13. Rotating saddle (2 MB)
Solution to problem 14. Rubber motor (3 MB)

Others：
Problem 2: Hologram
Video1, IYPT display (16 MB)
Video2, parallax of real objects (1 MB)
Video3, parallax of 'hologram' image (14 MB)

Problem 3: Twisted Rope
Video1, twist process of a silicon gel rope (twisted 8 rounds) (16 MB)
Video2, twist process of a multi-strand rope (twisted 20 rounds) (17 MB)

Problem 6: Bubble crystal
Video 1, the attraction of two bubbles (4 MB)
Video 2, bubble crystal formation (1 MB)
Video 3, vacancy and replacement (1 MB)

Problem 8: Freezing droplets
Video1, freezing of water droplets (10 MB)
Video2, freezing of a paraffin droplet (9 MB)

Problem 10: Coefficient of diffusion
Video1, Diffusion of particles (3 MB)
Source Code, The full set of program we used in experiment (2 MB)

Problem 12: Cold balloon
Video1, sphere.avi:
Change of strain energy density distribution of a spherical balloon. The lower part has a larger deformation so that the temperature increase is larger. The color scale is the same as in Fig. 13. Red indicates larger energy density, blue the smaller one. (17 MB)

Video2, realballoon.avi:
Change of strain energy density distribution of a real balloon. The color scale is the same as in Fig. 15. Red indicates larger energy density and larger temperature increase, blue for smaller change. (17 MB)

Problem 15: Oil Stars
Video1, six-crests.mov: stable faraday waves of six crests (2 MB)
Video2, one-and-two crests.gif: faraday waves of one and two crests (1 MB)
Video3, three-crests.gif: faraday waves of three crests (1 MB)
Video4, four-crests.gif: faraday waves of four crests (1 MB)

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Chapter 1

2014 Problem 1: Invent Yourself

Zexun Lin^*, Wending Zhao^†, Wenli Gao and Huijun Zhou

School of Physics, Nanjing University

In this solution, we rebuild Chua’s chaotic circuit, and investigate its behavior. We have observed several stages of its behavior, like periodical, single attractor and double attractors, both in experiment and simulation. And we apply commonly used methods (Poincaré section, bifurcation) to theoretically investigate its behavior.

1. Introduction

Problem Statement:

It is known that some electrical circuits exhibit chaotic behavior. Build a simple circuit with such a property, and investigate its behavior. (see Fig. 1)

Fig. 1. Sample circuit diagram

1.1. Problem Review

Chaos was first noticed by Edward Norton Lorenz¹ in 1969. Since then chaos and nonlinearity have become one of the most influential discoveries in the 20th century and are said to be of the same importance as relativity and quantum mechanics.

Chaos and nonlinearity are quite common in our daily life. Pendulums, swings in the playground, the population of wildlife, the behavior of cloud and many other such kinds of things, as long as you can imagine, can exhibit chaotic behaviors. In the book² Chaos Making a New Science?, chaos is described as: order masquerading as randomness, revealing that order and regularity can be extracted from randomness, which makes it a little bit easier for people to investigate and describe the complex behaviors of chaotic systems.

Chaotic circuits have provided us an ideal and simple method to study and investigate chaotic behavior. In 1983 Leon O. Chua³ invented a simple electronic circuit to exhibit chaotic behavior, which was commonly known as Chua’s circuit. In this paper, we investigate the chaotic behavior based on Chua’s circuit.

1.2. Definition of Chaos

In contrast to the regularity and simplicity of linear behavior, the complexity and irregularity of chaotic behavior make itself difficult to be understood and described. Some scientists have tried out a lot of different methods and finally struggle out some appropriate methods to illustrate its behavior both in qualitative and quantitative aspects.⁴

The pioneer of chaos, Edward Norton Lorenz, commented that chaos was “deterministic nonperiodic flow”,¹ emphasizing that the nonexistence of periodicity was intrinsic, which he also described as butterfly effect.

From the modern perspective, chaos refers to the phenomenon that the smallest of changes in a system can result in very large differences in that system’s behavior. Still, Edward Lorenz have summarized the theory as follows: When the present determines the future, but the approximate present does not approximately determine the future.⁵ We can conclude that chaos is an intrinsic property of deterministic system and that the long-term behavior is unpredictable since it is critically dependent on initial value.

Furthermore, it is commonly believed that mathematics is the precise language of scientific description. Therefore, a mathematical definition is given as follows (from Devaney⁶):

Setting V as an aggregate, if it fulfills the following three requirements, we say f has chaotic behavior in V:

1. f is extremely sensitive to initial value

2. f is topological transitive

3. f has dense state point in V

2. Circuit Building⁴

2.1. Circuit Diagram

Chua’s circuit was invented in 1983 by Leon O. Chua.³ Its diagram is shown in Fig. 2.

It only consists of one resister, two capacitors, one inductor and one nonlinear component. Due to its convenience for building and the clear illustration of both linear and chaotic behaviors, it is widely used for exhibiting chaotic phenomenon.

Fig. 2. Circuit diagram

Some parameters of our experiment are listed in Table 1:

Table 1. Classic parameters for electronic co...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Epigraph
• Contents
• List of Authors
• 1. 2014 Problem 1: Invent Yourself
• 2. 2014 Problem 2: Hologram
• 3. 2014 Problem 3: Twisted Rope
• 4. 2014 Problem 5: Loaded Hoop
• 5. 2014 Problem 6: Bubble Crystal
• 6. 2014 Problem 7: Pot-in-Pot refrigerator
• 7. 2014 problem 8: Freezing Droplets
• 8. 2014 Problem 10: Coefficient of Diffusion
• 9. 2014 Problem 12: Cold Balloon
• 10. 2014 Problem 15: Oil Stars
• 11. 2014 Problem 16: Magnetic Brakes
• Appendix A: IYPT Problems of 2014
• Appendix B: The Regulations of the International Young Physicists’ Tournament
• Author Index
• Subject Index