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The Fermi–Pasta–Ulam–Tsingou (FPUT) problem addresses fundamental questions in statistical physics, and attempts to understand the origin of recurrences in the system have led to many great advances in nonlinear dynamics and mathematical physics. In this work, we revisit the problem and study quasiperiodic recurrences in the weakly nonlinear α -FPUT system in more detail. We aim to reconstruct the quasiperiodic behavior observed in the original paper from the canonical transformation used to remove the three-wave interactions, which is necessary before applying the wave turbulence formalism. We expect the construction to match the observed quasiperiodicity if we are in the weakly nonlinear regime. Surprisingly, in our work, we find that this is not always the case and in particular, the recurrences observed in the original paper cannot be constructed by our method. We attribute this disagreement to the presence of small denominators in the canonical transformation used to remove the three-wave interactions before arriving at the starting point of wave turbulence. We also show that these small denominators are present even in the weakly nonlinear regime, and they become more significant as the system size is increased. We also discuss our results in the context of the problem of equilibration in the α -FPUT system and point out some mathematical challenges when the wave turbulence formalism is applied to explain thermalization in the α -FPUT problem. We argue that certain aspects of the α -FPUT system such as thermalization in the thermodynamic limit and the cause of quasiperiodicity are not clear, and that they require further mathematical and numerical studies. [ABSTRACT FROM AUTHOR]

An introduction to articles in the issue is presented on topics including the electrodissolution of p-type silicon, numeral simulations of a reaction-diffusion-convection model that shows an active coupling between oscillatory chemical kinetics and the viscously-driven instability, and the exothermic autocatalytic reaction of chlorite and thiourea.

2023-JC-YB-071, 2022JQ-010), Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 22JP053), Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSQ037), NSFC of China (Grant No. 41975040), and the Taishan Industrial Experts Program. This work was supported by the National Key R&D Program of China under Grant No. 2021ZD0201300, the Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (Program Nos. This article was originally published online on 17 July 2023 with an error in the Acknowledgment section. [Extracted from the article]

The nonlinear science community experienced a painful loss with the sudden death of our colleague and friend, Professor Tito Arecchi. Tito Arecchi was a pioneer of nonlinear optics and laser physics, as well as nonlinear dynamics. The Arecchi-Bonifacio equations are universally used to describe the dynamics of a single mode laser. [Extracted from the article]

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the wellestablished theory of equilibrium statistical mechanics. [ABSTRACT FROM AUTHOR]