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We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U (x) under the influence of a time-periodic space-homogeneous external field E(t). This nonintegrable system allows for both quasiperiodic and chaotic solutions in time. If the field is neither symmetric E(t + t 0) = E(−t + t 0) for any t 0 nor antisymmetric(More)
A theoretical study of linear wave scattering by time-periodic spatially localized excitations (discrete breathers) is presented. A peculiar effect of total reflection occurs due to a Fano resonance when a localized state originating from closed channels resonates with the open channel. For the discrete nonlinear Schrödinger chain, we give an analytical(More)
The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit, each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain(More)
We study the scattering of solitons in the nonlinear Schrödinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The analytical predictions are tested numerically in regimes characterized by various time scales. Special attention is paid(More)
We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamilto-nian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the(More)
A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric(More)
Vulnerabilities related to weak passwords are a pressing global economic and security issue. We report a novel, simple, and effective approach to address the weak-password problem. Building upon chaotic dynamics, criticality at phase transitions, CAPTCHA recognition, and computational round-off errors, we design an algorithm that strengthens the security of(More)