We find that Coulomb focusing persists even when the Coulomb field is barely noticeable compared with the laser field. Delayed recollisions proliferate in this regime and bring back energy slightly above the 3.17 U_p high-harmonic cutoff, in stark co
ntradiction with the Strong Field Approximation. We investigate the nonlinear-dynamical phase space structures which underlie this dynamics. It is found that the energetic delayed recollisions are organized by a reduced number of periodic orbits and their invariant manifolds.
We revisit the stabilization of ionization of atoms subjected to a superintense laser pulse using nonlinear dynamics. We provide an explanation for the lack of complete ionization at high intensity and for the decrease of the ionization probability a
s intensity is increased. We investigate the role of each part of the laser pulse (ramp-up, plateau, ramp-down) in this process. We emphasize the role of the choice for the ionization criterion, energy versus distance criterion.
The ability to generate complete, or almost complete, chaotic mixing is of great interest in numerous applications, particularly for microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter values at which
complete mixing occurs. The technique is applied to a time periodic, two-dimensional electro-osmotic flow with spatially and temporally varying Helmoltz-Smoluchowski slip boundary conditions. The strategy consists of following the linear stability of some key periodic pathlines in parameter space (i.e., amplitude and frequency of the forcing), particularly through the bifurcation points at which such pathlines become unstable.
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.
The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to w
hich we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.
The design of strategies to generate efficient mixing is crucial for a variety of applications, particularly digital microfluidic devices that use small discrete fluid volumes (droplets) as fluid carriers and microreactors. In recent work, we have pr
esented an approach for the generation and control of mixing inside a translating spherical droplet. This was accomplished by considering Stokes flow within a droplet proceeding downstream to which we have superimposed time dependent (sinusoidal) rotation. The mixing obtained is the result of the stretching and folding of material lines which increase exponentially the surface contact between reagents. The mixing strategy relies on the generation of resonances between the steady and the unsteady part of the flow, which is achieved by tuning the parameters of the periodic rotation. Such resonances, in our system, offer the possibility of controlling both the location and the size of the mixing region within the droplet, which may be useful to manufacture inhomogeneous particles (such as Janus particles). While the period and amplitude of the periodic rotation play a major role, it is shown here by using a triangular function that the particular shape of the rotation (as a function of time) has a minor influence. This finding demonstrates the robustness of the proposed mixing strategy, a crucial point for its experimental realization.
The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles, as in a Free Electron Laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose
a strategy to stabilize the intensity by destabilizing the macro-particle. This strategy involves the study of the linear stability of a specific periodic orbit of a mean-field model. As a control parameter - the amplitude of an external wave - is varied, a bifurcation occur in the system which has drastic effects on the self-consistent dynamics, and in particular, on the macro-particle. We show how to obtain an appropriate tuning of the control parameter which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.
We discuss the influence of periodic orbits on the dissociation of a model diatomic molecule driven by a strong bichromatic laser fields. Through the stability of periodic orbits we analyze the dissociation probability when parameters like the two am
plitudes and the phase lag between the laser fields, are varied. We find that qualitative features of dissociation can be reproduced by considering a small set of short periodic orbits. The good agreement with direct simulations demonstrates the importance of bifurcations of short periodic orbits in the dissociation dynamics of diatomic molecules.
We investigate the multiphoton ionization of hydrogen driven by a strong bichromatic microwave field. In a regime where classical and quantum simulations agree, periodic orbit analysis captures the mechanism: Through the linear stability of periodic
orbits we match qualitatively the variation of experimental ionization rates with control parameters such as the amplitudes of the two modes of the field or their relative phases. Moreover, we discuss an empirical formula which reproduces quantum simulations to a high degree of accuracy. This quantitative agreement shows the mechanism by which short periodic orbits organize the dynamics in multiphoton ionization. We also analyze the effect of longer pulse durations. Finally we compare our results with those based on the peak amplitude rule. Both qualitative and quantitative analyses are implemented for different mode locked fields. In parameter space, the localization of the period doubling and halving allows one to predict the set of parameters (amplitudes and phase lag) where ionization occurs.
Vibrational energy flows unevenly in molecules, repeatedly going back and forth between trapping and roaming. We identify bottlenecks between diffusive and chaotic behavior, and describe generic mechanisms of these transitions, taking the carbonyl su
lphide molecule OCS as a case study. The bottlenecks are found to be lower-dimensional tori; their bifurcations and unstable manifolds govern the transition mechanisms.
