Time-frequency analysis of chaotic systems

We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also called instantaneous frequencies, enable us to analyze the phase space structures. In particular, this method detects resonance trappings and transitions and allows a characterization of the notion of weak and strong chaos. We illustrate the method with the trajectories of the standard map and the hydrogen atom in crossed magnetic and elliptically polarized microwave fields.Comment: 36 pages, 18 figure

Double-ionization mechanisms of magnesium driven by electron impact

We study double ionization of Mg by electron impact through the vantage point of classical mechanics. We consider all electron-electron correlations in a Coulomb four-body problem, where three electrons belong to the atom and the fourth electron causes the impact ionization. From our model we compute the double-ionization probability of Mg for impact energies from 15 to 125 eV. Double ionization occurs through eight double-ionization mechanisms, which we classify into four categories: inner shell capture, direct, delay, and ionized inner shell mechanisms. We show that delay and ionized inner shell mechanisms require electron-electron correlations among the four electrons, and are responsible for the second increase in the double-ionization probability. Furthermore, we show that our theoretical prediction about the relative prominence of certain double-ionization mechanisms is in agreement with experimental results on the relative prominence of non-first- over first-order mechanisms

Guiding-center motion for electrons in strong laser fields

We consider the dynamics of electrons in combined strong laser and Coulomb fields. Under a timescale separation condition, we reduce this dynamics to a guiding-center framework. More precisely, we derive a hierarchy of models for the guiding-center dynamics based on averaging over the fast motion of the electron using Lie transforms. The reduced models we obtain describe well the different ionization channels, in particular, the conditions under which an electron is rescattered by the ionic core or is directly ionized. The comparison between these models highlights the models which are best suited for a qualitative and quantitative agreement with the parent dynamics

Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

The Transition State in a Noisy Environment

Transition State Theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a time-dependent dividing surface free of such recrossings in the presence of noise. The no-recrossing limit of Transition State Theory thus becomes generally available for the description of reactions in a fluctuating environment

Mechanism of delayed double ionization in a strong laser field

When intense laser pulses release correlated electrons, the time delay between the ionizations may last more than one laser cycle. We show that this "Recollision-Excitation with Subsequent Ionization" pathway originates from the inner electron being promoted to a sticky region by a recollision where it is trapped for a long time before ionizing. We identify the mechanism which regulates this region, and predict oscillations in the double ionization yield with laser intensity

Renormalization group approach to vibrational energy transfer in protein

Renormalization group method is applied to the study of vibrational energy transfer in protein molecule. An effective Lagrangian and associated equations of motion to describe the resonant energy transfer are analyzed in terms of the first-order perturbative renormalization group theory that has been developed as a unified tool for global asymptotic analysis. After the elimination of singular terms associated with the Fermi resonance, amplitude equations to describe the slow dynamics of vibrational energy transfer are derived, which recover the result obtained by a technique developed in nonlinear optics [S.J. Lade, Y.S. Kivshar, Phys. Lett. A 372 (2008) 1077].Comment: 11 page

A Low Profile Wideband Log Periodic Microstrip Antenna Design for C-Band Applications

In this study, a wideband low profile microstrip antenna design for C-band applications is presented. The proposed antenna consists of a monopol log periodic patch in the equilateral triangular dimensions with the microstrip line fed and a rectangular ground plane. The antenna has 9×19.8 mm2 overall size, thickness of 1.6 mm and 4.3 dielectric constant. According to the simulation results, the proposed antenna has a very wide bandwidth while operating in the frequency band of 4.25-7.95 GHz and 5 GHz resonance frequency. The proposed antenna was also prototyped on FR4 substrate with the 0.02 tangent loss and the measurement results were quite similar by the simulated results

Bottlenecks to vibrational energy flow in OCS: Structures and mechanisms

Finding the causes for the nonstatistical vibrational energy relaxation in the planar carbonyl sulfide (OCS) molecule is a longstanding problem in chemical physics: Not only is the relaxation incomplete long past the predicted statistical relaxation time, but it also consists of a sequence of abrupt transitions between long-lived regions of localized energy modes. We report on the phase space bottlenecks responsible for this slow and uneven vibrational energy flow in this Hamiltonian system with three degrees of freedom. They belong to a particular class of two-dimensional invariant tori which are organized around elliptic periodic orbits. We relate the trapping and transition mechanisms with the linear stability of these structures.Comment: 13 pages, 13 figure