Related papers: Instabilities and relaxation to equilibrium in lon…
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…
In the framework of a recently developed theory for Hamiltonian chaos, which makes use of the formulation of Newtonian dynamics in terms of Riemannian differential geometry, we obtained analytic values of the largest Lyapunov exponent for…
A possibility that in the FPU problem the critical energy for chaos goes to zero with the increase of the number of particles in the chain is discussed. The distribution for long linear waves in this regime is found and an estimate for new…
We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-$\beta$)…
The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of…
By combining results of Mizumachi on the stability of solitons for the Toda lattice with a simple rescaling and a careful control of the KdV limit we give a simple proof that small amplitude, long-wavelength solitary waves in the…
We report numerical evidence of Fermi-Pasta-Ulam-Tsingou (FPUT)-like recurrence in weakly damped, periodically driven alpha-FPUT chains. In narrow regions of driving amplitude and damping, the steady-state energy is exchanged among a few…
We study the transition from integrability to chaos for the three-particle Fermi-Pasta-Ulam- Tsingou (FPUT) model. We can show that both the quartic b-FPUT model ($\alpha$ = 0) and the cubic one ($\beta$ = 0) are integrable by introducing…
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrodinger equation, the modulation instability (MI) of its n = 1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
On-site potentials are ubiquitous in physical systems and strongly influence their heat transport and energy localization. These potentials will inevitably affect the dynamical properties of $q$-breathers (QBs), defined as periodic orbits…
We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…
Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time resonant anomalies…
The cure to the $\ell=1$ Landau-Pomeranchuk (L-P) instabilities in translationally invariant fermions is shown to be a state with an anisotropic gap at the fermi-surface. For higher $\ell$ and for fermions on a lattice, general criteria for…
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…
The Alpha version of the Fermi-Pasta-Ulam problem is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of…
Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the…
$q$-Breathers (QBs) represent a quintessential phenomenon of energy localization, manifesting as stable periodic orbits exponentially localized in normal mode space. Their existence can hinder the thermalization process in nonlinear…
Nonlinear normal mode solutions of the $\beta$-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths.…
Langmuir monolayers are modeled as systems of short chains, which are confined to a planar surface at one end, but free to move within the plane. The phase behavior is calculated in a mean field approximation, which combines the self…