No abstract

We present the detailed dynamics of the particles in the -Fermi-Pasta-Ulam-Tsingou (FPUT) chain after the initiation of a localized nonlinear excitation (LNE) by squeezing a central bond in the monodispersed chain at time t = 0 while all other particles remain in their original relaxed positions. In the absence of phonons in the system, the LNE appears to initiate its relaxation process by symmetrically emitting two very weak solitary waves. The next stage involves the spreading of the LNE and the formation of nonsolitary wave-like objects to broaden the excitation region until a stage is reached when many weak solitary wave-like objects can be emitted as the system begins its journey to quasi-equilibrium and then to equilibrium. In addition to being of fundamental interest, these systems may be realized using cantilever systems and could well hold the key to constructing the next generation of broadband energy harvesting systems.

PACS 05.90.+m-Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems PACS 05.45.-a-Nonlinear dynamics and chaos PACS 05.70.Ln-Nonequilibrium and irreversible thermodynamics Abstract-We develop new analytic descriptions for solitary waves (SWs) and SW-like objects in the non-integrable and strongly nonlinear β-Fermi-Pasta-Ulam-Tsingou (β-FPUT) system for various strengths of the harmonic term in the potential. We then show that that the collision of identical solitary waves in the decorated β-FPUT chain can lead to the formation of one or more long-lived localized nonlinear excitations (LNEs), thereby suggesting that these systems allow engineering of preferential energy distribution over extended times.

In this paper, we expand upon our recent studies of an agent-based model of a battle between an intelligent army and an insurgent army to explore the role of modifying strategy according to the state of the battle (adaptive strategy) on battle outcomes. This model leads to surprising complexity and rich possibilities in battle outcomes, especially in battles between two well-matched sides. We contend that the use of adaptive strategies may be e↵ective in winning battles.