We show interaction between high- and low-frequency modes in periodic $\alpha$-FPU chains with alternating large masses. The treatment discusses the difficult case where number of particles $N=2p$ involves $p$ prime. A key role is played by identifying symmetric invariant manifolds, thus reducing dimension problems drastically, a Mathematica programme focused on these systems. could explicitly ...

The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This ‘Birkhoff-Gustavson normal form’ retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a...

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, C. R. Acad. Sci., Ser. I: Math, 332, 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very...

By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrödinger equation, the modulation instability (MI) of its n=1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked step with the n=1 mode. This fundamental insight, the enslavement of all higher modes to the n=1 mode, explains t...

Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly anharmonic interaction potentials are described by the generalized Korteweg-de Vries (KdV) equation. Justification of the small-amplitude approximation is usually performed on the time scale, for which dynamics of the KdV equation is defined. We show how to extend justification analysis on longer time intervals provided dyn...

Manufacturing and environmental variability lead to timing errors in computing systems that are typically corrected by error detection and correction mechanisms at the circuit level. The cost and speed of recovery can be improved by memoization-based optimization methods that exploit spatial or temporal parallelisms in suitable computing fabrics such as general-purpose graphics processing units...