Bifurcations leading to stochasticity in a cyclotron-maser system

This paper is concerned with the orbital dynamics of electrons in a cyclotron maser [CO Chen, Phys. Rev. A 46,6654 (1992)] with modulated maser fields. Amplitude modulation is a natural result of wave-particle energy exchanges, and for typical system parameters, the nonlinear bifurcations of periodic orbits are investigated as the modulation level increases. Attention is focused on primary stable orbits exhibiting the same periodicity as the modulation for low modulational levels. This interest is related to the fact that the destruction of these orbits is generally associated with considerable spread of chaos over the phase space. It is found that two groups of such orbits do exist, each group located in a particular region of the phase space. As the modulation level grows, the overall behavior can be classified as a function of the modulation frequency. If this frequency is large there are two orbits in the group; one undergoes an infinite cascade of period doubling bifurcations and the other simply collapses with neighboring unstable orbits. If the frequency is small the number of orbits is larger; the collapsing orbit is still present and some of the others may fail to undergo the period doubling cascade

An outlier-resistant κ\kappa-generalized approach for robust physical parameter estimation

In this work we propose a robust methodology to mitigate the undesirable effects caused by outliers to generate reliable physical models. In this way, we formulate the inverse problems theory in the context of Kaniadakis statistical mechanics (or $\kappa$-statistics), in which the classical approach is a particular case. In this regard, the errors are assumed to be distributed according to a finite-variance $\kappa$-generalized Gaussian distribution. Based on the probabilistic maximum-likelihood method we derive a $\kappa$-objective function associated with the finite-variance $\kappa$-Gaussian distribution. To demonstrate our proposal's outlier-resistance, we analyze the robustness properties of the $\kappa$-objective function with help of the so-called influence function. In this regard, we discuss the role of the entropic index ($\kappa$) associated with the Kaniadakis $\kappa$-entropy in the effectiveness in inferring physical parameters by using strongly noisy data. In this way, we consider a classical geophysical data-inverse problem in two realistic circumstances, in which the first one refers to study the sensibility of our proposal to uncertainties in the input parameters, and the second is devoted to the inversion of a seismic data set contaminated by outliers. The results reveal an optimum $\kappa$-value at the limit $\kappa \rightarrow 2/3$, which is related to the best results.Comment: 37 pages, 23 figure

Improving regular acceleration in the nonlinear interaction of particles and waves

In this work one studies the effects arising from the inclusion of a stationary extraordinary mode in the resonant interaction of magnetized particles and perpendicularly propagating electrostatic waves. It is found that for a stationary mode frequency of the order of the Larmor frequency and with a suitably chosen amplitude, one is able to suppress the resonance which drives the weakly relativistic dynamics into chaos. Improved regular acceleration of initially low energy particles is thus attained. Analytical estimates of the optimal stationary mode amplitude is presented. A detailed study of the topological effects due to resonance suppression based on bifurcation analysis is performed. The main results are verified with the help of single particle numerical simulations

Improving regular acceleration in the nonlinear interaction of particles and waves

In this work one studies the effects arising from the inclusion of a stationary extraordinary mode in the resonant interaction of magnetized particles and perpendicularly propagating electrostatic waves. It is found that for a stationary mode frequency of the order of the Larmor frequency and with a suitably chosen amplitude, one is able to suppress the resonance which drives the weakly relativistic dynamics into chaos. Improved regular acceleration of initially low energy particles is thus attained. Analytical estimates of the optimal stationary mode amplitude is presented. A detailed study of the topological effects due to resonance suppression based on bifurcation analysis is performed. The main results are verified with the help of single particle numerical simulations

Manifold reconnection in chaotic regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand enhanced diffusion in phase space in terms of relatively smooth rearrangements of stable and unstable manifolds of unstable fixed points

Manifold reconnection in chaotic regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand enhanced diffusion in phase space in terms of relatively smooth rearrangements of stable and unstable manifolds of unstable fixed points

Resonant islands without separatrix chaos

An alternative type of Hamiltonian nonlinear resonant island is analyzed. In the usual case where the resonant island is pendulumlike, chains bifurcated out of the central elliptic point undergo infinite cascades of period-doubling bifurcations as they approach the island boundary. In the present case we find that those chains undergo either period doubling or inverse saddle-node bifurcations, depending on the strength of perturbing terms. In the saddle-node case we show that just after a reconnection process, external chains cross the island boundary to collapse against the bifurcated internal chains

Nonextensive Gutenberg–Richter law and the connection between earthquakes and marsquakes

The physical analysis of earthquakes is essential for the exploration of the interior structure of a region. Nowadays, the statistics of earthquakes’ occurrence are dominated by the Gutenberg–Richter (GR) law. Here, we report evidence of the similarity between earthquakes and marsquakes by using the generalized GR law in the context of Tsallis nonextensive statistical mechanics. We analyze the Martian quakes that were recorded by the InSight’s seismometer in the Elysium Planitia region, Mars, from January 2019 to December 2019, which corresponds to the first year of geophysical observations by Nasa’s InSight mission. The results show evidence for the similarity between the triggering mechanism of earthquakes and marsquakes. They also reveal the fractal nature of the Martian geological faults

Particle acceleration by large-amplitude waves revisited

We reconsider the problem of particle acceleration by large-amplitude electromagnetic waves. We make use of a fully relativistic Hamiltonian formalism to show that, as opposed to nonelativistic results obtained by Kuo and Lee, acceleration in unmagnetized systems is severely arrested when the phase velocity of the electromagnetic mode approaches the speed of light. For subluminal waves, however, acceleration is shown to be still effective