Stable retrograde orbits around the triple system 2001 SN263

The NEA 2001 SN263 is the target of the ASTER MISSION - First Brazilian Deep Space Mission. Araujo et al. (2012), characterized the stable regions around the components of the triple system for the planar and prograde cases. Knowing that the retrograde orbits are expected to be more stable, here we present a complementary study. We now considered particles orbiting the components of the system, in the internal and external regions, with relative inclinations between $90^{\circ}< I \leqslant180^{\circ}$, i.e., particles with retrograde orbits. Our goal is to characterize the stable regions of the system for retrograde orbits, and then detach a preferred region to place the space probe. For a space mission, the most interesting regions would be those that are unstable for the prograde cases, but stable for the retrograde cases. Such configuration provide a stable region to place the mission probe with a relative retrograde orbit, and, at the same time, guarantees a region free of debris since they are expected to have prograde orbits. We found that in fact the internal and external stable regions significantly increase when compared to the prograde case. For particles with $e=0$ and $I=180^{\circ}$, we found that nearly the whole region around Alpha and Beta remain stable. We then identified three internal regions and one external region that are very interesting to place the space probe. We present the stable regions found for the retrograde case and a discussion on those preferred regions. We also discuss the effects of resonances of the particles with Beta and Gamma, and the role of the Kozai mechanism in this scenario. These results help us understand and characterize the stability of the triple system 2001 SN263 when retrograde orbits are considered, and provide important parameters to the design of the ASTER mission.Comment: 11 pages, 8 figures. Accepted for publication in MNRAS - 2015 March 1

Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur

Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum

Consider the family of Schr\"odinger operators (and also its Dirac version) on $\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ $$H^W_{\omega,S}=\Delta + \lambda F(S^n\omega) + W, \quad \omega\in\Omega,$$ where $S$ is a transformation on (compact metric) $\Omega$, $F$ a real Lipschitz function and $W$ a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that $H^W_{\omega,S}$ presents quasi-ballistic dynamics for $\omega$ in a dense $G_{\delta}$ set. Applications include potentials generated by rotations of the torus with analytic condition on $F$, doubling map, Axiom A dynamical systems and the Anderson model. If $W$ is a rank one perturbation, examples of $H^W_{\omega,S}$ with quasi-ballistic dynamics and point spectrum are also presented.Comment: 17 pages; to appear in Journal of Differential Equation

Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excluding some very specific ones) the Bernoulli Dirac system is localized, independently of the mass.Comment: 9 pages, no figures - J. Physics A: Math. Ge

Dynamical Lower Bounds for 1D Dirac Operators

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass.Comment: 18 pages; to appear in Math.

Empowering Rural Citizen Journalism Via Web 2.0 Technologies

Once acquainted with the modern information and communication tools made available with the advent of the Internet, five Brazilian rural communities participating in a pilot project to develop a self-sustaining telecenter model, engaged in citizen journalism using inexpensive digital video cameras. Community members used Web 2.0 collaborative tools to post short videos on the telecenter portal. The 95 video blogs published between September 2006 and May 2008 recorded various aspects of community life,including religious celebrations,oral history arts and crafts traditions,folklore,and envirnmental concerns. This study evaluates the impact of video blogging in these communities