Biomedical subjects
Publications and source records attributed to F B Rizzato.
In the present analysis we study the broad-band triplet interaction in regimes of large amplitudes. Linear response theories associated with nonlinear arguments are used to show that even though coherence of high-frequency modes is lost as one first encounters chaotic regimes, it can be restored as field amplitudes grow further. We discuss implications of the feature for fixed-phase interactions.
We study soliton stability under the action of strong external perturbations. Limits on the weak perturbation approach are established with the help of average Lagrangian methods and full simulations. We found that for the same relative perturbation, larger amplitude solitons develop instability earlier than weaker amplitude solitons.
We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.
We extend a previous study [R. Pakter and F. B. Rizzato, Phys. Rev. Lett. 87, 044801 (2001)] and investigate the nonlinear dynamics of periodically focused intense particle beams. We show that (i) the scenario as the focusing field increases is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as believed so far, but the existence of successive regions of stability interrupted by gaps where periodic solutions are either unstable or simply do not exist; (ii) the beam can be focused to tighter radii using stable matched solutions found for focusing field strengths greater than the previous threshold. A comprehensive analysis is carried out as a function of the relevant parameters of the system. Self-consistent simulations validate the findings. The gaps are of crucial importance because they must be avoided if the goal is beam confinement with matched solutions; we develop an analytical model to determine the gap structure, which agrees well with computer simulations.
We analyze typical time scales resulting from the coupled dynamics of high- and low-frequency wave components in solitary solutions of the Zakharov equations. Linear stability analysis around the solitary modes suggests that adiabatic regimes may be obtained in the limit of high- and low-field intensities where the disparity of eigenfrequencies is large. Full simulations, however, reveal that adiabaticity arising from oscillatory motion can in fact be observed only over relatively short periods of time prior to noticeable radiation emission.
A stability analysis of periodically focused intense particle beams based on the beam envelope equation is performed. We show that (i) the scenario, as the focusing field increases, is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as generally believed, but the existence of successive regions of stability interrupted by gaps of instability; (ii) the beam can be focused to tighter radii using new stable matched solutions found for focusing field strengths greater than the previous threshold. Self-consistent simulations validate the findings.
In this paper we examine the coupling of two wave triplets sharing two common modes. The analysis is performed in the solitonic sector of the parameter space where uncoupled solutions departing from linearly unstable homogeneous initial conditions evolve into a collection of regularly interspersed, spatiotemporally localized spikes. The uncoupled system is integrable, but coupling destroys integrability. As coupling grows, energy transfer to smaller spatial scales does appear and becomes faster not only in linearly unstable, but also in linearly stable cases. Chaos in low-dimensional subsystems appears to be responsible for the transfer. We perform a series of numerical tests to verify this idea.
In this paper we introduce and examine a generalization of the complex Ginzburg-Landau equation (CGLE) where the self-interaction contained in the cubic term is replaced by a coupling involving the original field and a low-frequency one. New instabilities arise and a radically new asymptotic dynamical behavior emerges displaying defect turbulence over wide regions of the parameter space.