Download or read book Characterization of Solitary Waves in Fermi-Pasta-Ulam-Tsingou Systems written by William Falls and published by . This book was released on 2014 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characterization of Solitary Waves in Fermi-Pasta-Ulam-Tsingou systemsby William FallsIt is well known that a velocity perturbation can travel through a mass spring chain withquadratic + quartic interactions as a solitary and antisolitary wave pair. In this thesis wewill characterize traveling waves on a Fermi-Pasta-Ulam-Tsingou (FPUT) chain . We show the existence of solitary wave solutions andcharacterize the solitary wave's width, height and speed. Using the Virial theorem weshow that the FPUT chain be related to an effective Hertzian system . Next we study how solitary waves interact with one another on a FPUT chain. We examine the resulting dynamics and study whether or not solitary waves can break andreform. In addition we study the interacting of solitary waves and anti-solitary waves. We investigate the creation of long lived localized oscillations that can be created fromsolitary wave anti-solitary wave interactions. In recent years, nonlinear wave propagation in 2D structures have also been explored. Inthis thesis we consider the propagation of such a velocity perturbation through systemshaving a 2D "Y" shaped structure where each of the three pieces that make up the "Y"are made of a small mass spring chain. In addition, we consider the case where multiple "Y" shaped structures are used to generate a "tree." Lastly we layout the study of the properties of 2D structures that are not constrained toan explicit shape. We allow these systems to evolve and adapt as energy passes throughthem and study the ultimate shapes they form as a result of external perturbations.