Article
Engineering, Mechanical
Cheng-shi Liu
Summary: We investigated the propagation of acoustic waves in chains of touching beads without precompression using a Fermi-Pasta-Ulam (FPU) chain with a homogeneous fully nonlinear interaction potential. By deriving a new wave equation with a second degree logarithmic nonlinear term and finding its Gaussian solitary wave solution through an integrable factor equation, we showed the existence of Gaussian solitary waves for the second degree logarithmic wave equation in real physical models when the effect of logarithmic nonlinearity is balanced with dispersion.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics
Sergey Kashchenko, Anna Tolbey
Summary: This paper explores irregular solutions of the spatially-distributed Fermi-Pasta-Ulam (FPU) equation, constructing families of special nonlinear systems known as Schrodinger type-quasinormal forms. These systems determine the local behavior of solutions to the original problem as t approaches infinity. The paper also discusses the asymptotics of the main solution of the FPU equation and the interaction of waves moving in opposite directions, as well as the complications arising from perturbing the number of elements in a chain.
Article
Mathematics, Applied
J. H. Li, H. M. Yin, K. S. Chiang, K. W. Chow
Summary: The Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomenon and its dynamics in two-core optical fibers (TCFs) are studied. The cascading mechanism and the transition and saturation of FPUT patterns under different dispersion conditions are investigated. These findings are important for a better understanding of the physics of TCFs and the evaluation of long-distance communication based on multi-core fibers.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Physics, Mathematical
Tomer Goldfriend
Summary: Understanding the interaction between different wave excitations is important for coarse-grained descriptions of many-body systems. We studied the FPUT non-linear chain and showed that it can be modeled as a perturbation of its integrable approximation at short timescales. The separation between trajectories is determined by the interaction between soliton modes and a background of radiative modes. By considering one randomly perturbed soliton-like mode, we explained the power-law profiles observed in previous works.
JOURNAL OF STATISTICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Nkeh Oma Nfor, Serge Bruno Yamgoue, Francois Marie Moukam Kakmeni
Summary: The Hamiltonian of alpha, beta-Fermi Pasta Ulam lattice is considered and the discrete equation of motion is obtained through the Hamilton-Jacobi formalism. The extended Korteweg-de Vries equation is derived and the nonlinear Schrodinger amplitude equation is obtained through the reductive perturbative technique. Numerical simulations show that dark solitons conserve their amplitude and shape after collisions, while bright solitons can be traced in the lattice under certain conditions.
Article
Mechanics
Noel Challamel, Manuel Ferretti, Angelo Luongo
Summary: Analyzed the behavior of a one-dimensional nonlinear elastic chain, known as the Fermi-Pasta-Ulam system, in a static field. The chain consists of elements with a quartic potential and softening nonlinear behavior. When subjected to pure tension, the chain exhibits a multi-degenerate hill-top bifurcation, resulting in several softening branches. The behavior of the springs on each path can either soften or harden, leading to non-unique responses. Bifurcation diagrams illustrate the multitude of bifurcated paths, and their instability is proven. The role of imperfections in modifying equilibrium paths and unfolding degenerate bifurcation is discussed.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2023)
Article
Physics, Fluids & Plasmas
Nathaniel Bohm, Patrick K. Schelling
Summary: This study elucidates the ballistic transport and resonance phenomena in the one-dimensional FPUT model using thermal response functions. The results confirm the existence of periodic oscillations in temperature profiles and demonstrate that resonance involves beats between normal modes. Anharmonic scattering destroys phase coherence, leading to transport towards the diffusive regime. These findings provide new insights into heat transport in low-dimensional systems.
Article
Mathematics, Applied
Dmitry Pelinovsky, Guido Schneider
Summary: This paper investigates a scalar Fermi-Pasta-Ulam (FPU) system on a square two-dimensional lattice. The Kadomtsev-Petviashvili (KP-II) equation is derived using multiple scale expansions, and it accurately describes the dynamics of small-amplitude, slowly varying, unidirectional long waves on the FPU system. The main novelty of this work lies in the utilization of Fourier transform in the analysis of the FPU system in strain variables.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Liangtao Peng, Weicheng Fu, Yong Zhang, Hong Zhao
Summary: This study investigates how the stability of nonlinear modes depends on the perturbation strength and system size, and verifies the same behavior in two different models. The results show that the stability time is inversely proportional to the perturbation strength, and the instability threshold is related to the system size.
NEW JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Matteo Gallone, Antonio Ponno, Bob Rink
Summary: This paper investigates the higher order expansion and dynamics approximation of quasi unidirectional waves in the FPUT chain. It reveals that the dynamics to second order is governed by a combination of the first two nontrivial equations in the KdV hierarchy, while to third order a specific parameter condition needs to be satisfied. The results suggest why the FPUT paradox persists for longer than expected and how a breakdown of integrability may lead to system thermalization.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Mathematics
Kazuyuki Yoshimura, Yusuke Doi
Summary: The research demonstrates the existence of discrete breathers in nonlinear lattices under specific conditions, including odd symmetric, even symmetric, and multi-pulse discrete breathers. These breathers can be located separately on the lattice and are applicable to various types of interaction potentials.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
H. M. Yin, Q. Pan, K. W. Chow
Summary: This study investigates the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon for the Ablowitz-Ladik equation through analytical and computational approaches, as well as data-driven machine learning techniques to predict doubly periodic solutions in different regimes. The results show agreement between neural network predictions, numerical simulations, and analytical solutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Peter J. Olver, Ari Stern
Summary: This study investigates the dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi-Pasta-Ulam-Tsingou systems. The results show that under certain conditions, the solutions exhibit fractal profiles at irrational times and quantised profiles at rational times.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
H. M. Yin, K. W. Chow
Summary: Breathers, modulation instability, and recurrence phenomena are studied in the derivative nonlinear Schrodinger equation with second order dispersion, cubic nonlinearity, and self-steepening effect. Numerical simulations and theoretical analysis reveal the significant role of self-steepening effect in the dynamics and chaotic behavior of Fourier coefficients.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Physics, Multidisciplinary
Zheng Zhou, Li Jin-Hua, Ma You-Qiao, Ren Hai-Dong
Summary: In this work, the effects of perturbation amplitude and perturbation frequency on the Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence phenomenon are explored numerically. The results show that perturbation amplitude significantly affects the number of FPUT cycles, while perturbation frequency has relatively minor effects on the FPUT cycles. Moreover, large perturbation amplitudes result in irregular FPUT patterns and large perturbation frequencies lead to fewer high-order sidebands.
ACTA PHYSICA SINICA
(2022)
Editorial Material
Physics, Multidisciplinary
Marco Baiesi, Alberto Rosso, Thomas Speck
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2018)
Article
Physics, Multidisciplinary
Ivan Di Terlizzi, Marco Baiesi
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2019)
Article
Multidisciplinary Sciences
Marco Baiesi, Enzo Orlandini, Flavio Seno, Antonio Trovato
SCIENTIFIC REPORTS
(2019)
Article
Physics, Multidisciplinary
Gianluca Teza, Stefano Iubini, Marco Baiesi, Attilio L. Stella, Carlo Vanderzande
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2020)
Article
Biochemistry & Molecular Biology
Federico Norbiato, Flavio Seno, Antonio Trovato, Marco Baiesi
INTERNATIONAL JOURNAL OF MOLECULAR SCIENCES
(2020)
Article
Physics, Multidisciplinary
Ivan Di Terlizzi, Marco Baiesi
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Mathematical
Ivan Di Terlizzi, Felix Ritort, Marco Baiesi
JOURNAL OF STATISTICAL PHYSICS
(2020)
Article
Physics, Multidisciplinary
Giacomo Barzon, Karan Kabbur Hanumanthappa Manjunatha, Wolfgang Rugel, Enzo Orlandini, Marco Baiesi
Summary: In many countries, there has been a deceleration in the time evolution of COVID-19 even before lockdowns, possibly due to increased social awareness. The susceptible-hidden-infected-recovered model introduced by Barnes explains this phenomenon.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Chemistry, Physical
Marco Baiesi, Stefano Iubini, Enzo Orlandini
Summary: A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process, with subtle end-recombination dynamics that may not be easily detected in rheology experiments. The relaxation time scale is exponential and related to the free energy of an end cap and branching free energy.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Chemistry, Physical
Anna Braghetto, Enzo Orlandini, Marco Baiesi
Summary: Explainable and interpretable unsupervised machine learning helps to understand the underlying structure of data. An ensemble analysis of machine learning models is introduced to consolidate their interpretation. The application of this method reveals unexpected properties of amino acids and protein secondary structure.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Physics, Fluids & Plasmas
Gianmaria Falasco, Eli Barkai, Marco Baiesi
Summary: The research extends the virial theorem to nonequilibrium conditions for Langevin dynamics and has important experimental applications.
Correction
Physics, Multidisciplinary
Marco Baiesi, Carlo Burigana, Livia Conti, Gianmaria Falasco, Christian Maes, Lamberto Rondoni, Tiziana Trombetti
PHYSICAL REVIEW RESEARCH
(2020)
Article
Physics, Multidisciplinary
Marco Baiesi, Carlo Burigana, Livia Conti, Gianmaria Falasco, Christian Maes, Lamberto Rondoni, Tiziana Trombetti
PHYSICAL REVIEW RESEARCH
(2020)
Article
Chemistry, Physical
Stefano Iubini, Marco Baiesi, Enzo Orlandini
Article
Physics, Multidisciplinary
Marco Baiesi, Christian Maes
JOURNAL OF PHYSICS COMMUNICATIONS
(2018)