Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Keyword
-
- Conservation Laws (2)
- Approximate Entropy (ApEn) (1)
- Board games (1)
- Cauchy distribution (1)
- Chaotic unimodal quadratic maps (1)
-
- Combinatorial analysis (1)
- Conformal invariants (1)
- Correlation dimension. (1)
- Crystal growth (1)
- Digital electronics (1)
- Engineering design (1)
- Fractal music (1)
- Heart rate variability (HRV) (1)
- High technology industries (1)
- Integrability (1)
- Integrable Systems (1)
- Inverse scattering (1)
- Lax Pair (1)
- Lax pair (1)
- Linear distribution (1)
- Local bifurcation (1)
- Meditation (Chi Yoga and Kundalini) (1)
- Nonlinear dynamics (1)
- Ostrovsky equation. (1)
- Physics (1)
- Physics-Research (1)
- Random walk (1)
- Renormalization group (1)
- Schwarz derivative (1)
- Sierpinski (1)
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Dynamic Systems
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …
Mathematical Methods In Composing Melodies, Thomas Brown
Mathematical Methods In Composing Melodies, Thomas Brown
Undergraduate Theses and Capstone Projects
This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …
Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu
Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu
Articles
The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves.
Analysis Of Heart Rate Variability Signal Using State Space Based Methods, Mihails Tihonciks
Analysis Of Heart Rate Variability Signal Using State Space Based Methods, Mihails Tihonciks
Theses and Dissertations
In this study, we try to determine validity of the several different measures applied to the nonlinear HRV data. There were many studies done using traditional methods of Approximate Entropy, Correlation Dimension, Lyapunov exponents and recurrence plots. While employing some of these methods, we also decided to use Support Vector Machines. This method of analysis is quite new to the world of nonlinear data. We obtained data from five different groups of young healthy adults: spontaneous breathing group (Normal), metronomic breathing group (Metron) and elite athletes (Ironman), as well as two groups of people participating in specific traditional forms of …
Water Waves And Integrability, Rossen Ivanov
Water Waves And Integrability, Rossen Ivanov
Articles
The Euler’s equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler’s equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.
Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov
Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov
Articles
The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion …
Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov
Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov
Articles
Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this ontribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions …