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Ricardo Chacon

Publications and source records attributed to Ricardo Chacon.

9 recordsLinked to original sources
arXiv2010

Criticality-induced universality in ratchets

Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chacón, J. Phys. A \textbf{40}, F413 (2007)], i.e., the existence of a universal force waveform which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be \textit{unique} for both temporal and spatial biharmonic forces, and general (\textit{non}-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize \textit{any} application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.

nlin.CD↗
arXiv2009

Universal scaling laws of chaotic escape in dissipative multistable systems subjected to autoresonant excitations

A theory concerning the emergence and control of chaotic escape from a potential well by means of autoresonant excitations is presented in the context of generic, dissipative, and multistable systems. Universal scaling laws relating both the onset and lifetime of transient chaos with the parameters of autoresonant excitations are derived theoretically using vibrational mechanics, Melnikov analysis, and energy-based autoresonance theory. Numerical experiments show that these scaling laws are robust against both the presence of noise and re-shaping.

nlin.CD↗
arXiv2006

Homoclinic Signatures of Dynamical Localization

It is demonstrated that the oscillations in the width of the momentum distribution of atoms moving in a phase-modulated standing light field, as a function of the modulation amplitude, are correlated with the variation of the chaotic layer width in energy of an underlying effective pendulum. The maximum effect of dynamical localization and the nearly perfect delocalization are associated with the maxima and minima, respectively, of the chaotic layer width. It is also demonstrated that kinetic energy is conserved as an almost adiabatic invariant at the minima of the chaotic layer width, and that the system is accurately described by delta-kicked rotors at the zeros of the Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and Lyapunov exponents confirm all the theoretical predictions.

nlin.CD↗
arXiv2006

General exact theory of autoresonance in nonautonomous systems

A general exact theory of autoresonance (self-sustained resonance) in both dissipative and Hamiltonian nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. The theory is applied to Duffing oscillators to obtain exact analytical expressions for autoresonance excitations and solutions which explain all the phenomenological and approximate results arising from the previous approach to autoresonance phenomena.

physics.acc-ph↗
arXiv2005

On the ratchet effect

While the dependence of the directed transport on each of the ratchet-controlling parameters has been individually investigated experimentally, theoretically, and numerically, there is still no general criterion to apply to the whole set of these parameters to optimally control directed transport in general systems. We report that, to optimally enhance directed transport, there exists a universal force waveform which can be understood as the result of two competing fundamental mechanisms: the increase of the degree of breaking of symmetries and the decrease of the force impulse. We demonstrate that this universal waveform explains all the previous experimental, theoretical, and numerical results for a great diversity of systems, including motor enzymes.

physics.class-ph↗
arXiv2004

Melnikov method approach to control of homoclinic and heteroclinic chaos by weak harmonic excitations

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative, oscillator systems by weak harmonic excitations is presented, including diverse applications such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains, and chaotic charged particles in the field of an electrostatic wave packet.

nlin.CD↗
arXiv2004

Dissipative dynamics of a charged particle in the field of three plane waves: chaos and control

The chaotic dissipative dynamics of a charged particle in the field of three plane waves is theoretically (Melnikov's method) and numerically (Lyapunov exponents) investigated. In particular, the effectiveness of one of such waves in controlling the chaotic dynamics induced by the remaining two waves is theoretically predicted and numerically confirmed. Two mechanisms underlying the chaos-suppression scenario are identified. One mechanism requires chaos-inducing and chaos-suppressing waves to have both commensurate wavelengths and commensurate relative (with respect to the remaining third wave) phase velocities, while the other mechanism allows the chaotic dynamics to be tamed when such quantities are incommensurate. The present findings may be directly applied to several important problems in plasma physics, including that of the chaos-induced destruction of magnetic surfaces in tokamaks.

nlin.CD↗