Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Conservation Laws (2)
- Board games (1)
- Combinatorial analysis (1)
- Conformal invariants (1)
- Crystal growth (1)
-
- Digital electronics (1)
- Engineering design (1)
- High technology industries (1)
- Integrability (1)
- Integrable Systems (1)
- Inverse scattering (1)
- Journal articles (1)
- Lax Pair (1)
- Lax pair (1)
- Local bifurcation (1)
- Ostrovsky equation. (1)
- Physics (1)
- Physics-Research (1)
- Renormalization group (1)
- Schwarz derivative (1)
- Solitons (1)
- Solitons. (1)
- System design (1)
- Virasoro algebra (1)
- Publication Type
Articles 1 - 6 of 6
Full-Text Articles in Mathematics
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 …
Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun
Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun
Xiao-Jun Yang
The dynamic feature of high buildings is discussed in the present study with the application of ANSYS，the large finite element analysis software，aimed at the analysis of dynamic response of high buildings．Based on the case of a 15一story-building，a model of beam and shell 3-D finite element structure is built and the frequency of structure and the mode of vibration are computed in the study；furthermore，the structural dynamic response is discussed under different seismic waves with the use of the history analysis method．The results show that the more intense the seismic wave is，the bigger is the dynamic response of the buildings．The information can …
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 …
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.
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.
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 …