Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System

We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.Comment: To appear in the 2003 December issue of the Smarandache Notions Journa

Magnetic Field Effects on the Head Structure of Protostellar Jets

We present the results of 3-D SPMHD numerical simulations of supermagnetosonic, overdense, radiatively cooling jets. Two initial magnetic configurations are considered: (i) a helical and (ii) a longitudinal field. We find that magnetic fields have important effects on the dynamics and structure of radiative cooling jets, especially at the head. The presence of a helical field suppresses the formation of the clumpy structure which is found to develop at the head of purely hydrodynamical jets. On the other hand, a cooling jet embedded in a longitudinal magnetic field retains clumpy morphology at its head. This fragmented structure resembles the knotty pattern commonly observed in HH objects behind the bow shocks of HH jets. This suggests that a strong (equipartition) helical magnetic field configuration is ruled out at the jet head. Therefore, if strong magnetic fields are present, they are probably predominantly longitudinal in those regions. In both magnetic configurations, we find that the confining pressure of the cocoon is able to excite short-wavelength MHD K-H pinch modes that drive low-amplitude internal shocks along the beam. These shocks are not strong however, and it likely that they could only play a secondary role in the formation of the bright knots observed in HH jets.Comment: 14 pages, 2 Gif figures, uses aasms4.sty. Also available on the web page http://www.iagusp.usp.br/preprints/preprint.html. To appear in The Astrophysical Journal Letter

Ultra-High-Energy Cosmic Ray Acceleration by Magnetic Reconnection in Newborn Accretion Induced Collapse Pulsars

We here investigate the possibility that the ultra-high energy cosmic ray (UHECR) events observed above the GZK limit are mostly protons accelerated in reconnection sites just above the magnetosphere of newborn millisecond pulsars which are originated by accretion induced collapse (AIC). We show that AIC-pulsars with surface magnetic fields $10^{12} G < B_{\star} \lesssim 10^{15}$ G and spin periods $1 ms \lesssim P_{\star} < 60 ms$, are able to accelerate particles to energies $\geq 10^{20}$ eV. Because the expected rate of AIC sources in our Galaxy is very small (\sim 10^{-5} yr^{-1}), the corresponding contribution to the flux of UHECRs is neglegible, and the total flux is given by the integrated contribution from AIC sources produced by the distribution of galaxies located within the distance which is unaffected by the GZK cutoff ($\sim 50$ Mpc). We find that the reconnection efficiency factor needs to be $\xi \gtrsim 0.1$ in order to reproduce the observed flux of UHECRs.Comment: Latex file, 16 pages, 2 figures, replaced with revised version accepted for publication in the ApJ letter

Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Galactic Outflows and the pollution of the Galactic Environment by Supernovae

We here explore the effects of the SN explosions into the environment of star-forming galaxies like the Milky Way. Successive randomly distributed and clustered SNe explosions cause the formation of hot superbubbles that drive either fountains or galactic winds above the galactic disk, depending on the amount and concentration of energy that is injected by the SNe. In a galactic fountain, the ejected gas is re-captured by the gravitational potential and falls back onto the disk. From 3D nonequilibrium radiative cooling hydrodynamical simulations of these fountains, we find that they may reach altitudes up to about 5 kpc in the halo and thus allow for the formation of the so called intermediate-velocity-clouds (IVCs) which are often observed in the halos of disk galaxies. The high-velocity-clouds that are also observed but at higher altitudes (of up to 12 kpc) require another mechanism to explain their production. We argue that they could be formed either by the capture of gas from the intergalactic medium and/or by the action of magnetic fields that are carried to the halo with the gas in the fountains. Due to angular momentum losses to the halo, we find that the fountain material falls back to smaller radii and is not largely spread over the galactic disk. Instead, the SNe ejecta fall nearby the region where the fountain was produced, a result which is consistent with recent chemical models of the galaxy. The fall back material leads to the formation of new generations of molecular clouds and to supersonic turbulence feedback in the disk.Comment: 10 pages, 5 figures; paper of invited talk for the Procs. of the 2007 WISER Workshop (World Space Environment Forum), Alexandria, Egypt, October 2007, Spa. Sci. Rev

Features of collisionless turbulence in the intracluster medium from simulated Faraday Rotation maps

Observations of the intracluster medium (ICM) in galaxy clusters suggest for the presence of turbulence and the magnetic fields existence has been proved through observations of Faraday Rotation and synchrotron emission. The ICM is also known to be filled by a rarefied weakly collisional plasma. In this work we study the possible signatures left on Faraday Rotation maps by collisionless instabilities. For this purpose we use a numerical approach to investigate the dynamics of the turbulence in collisionless plasmas based on an magnetohydrodynamical (MHD) formalism taking into account different levels of pressure anisotropy. We consider models covering the sub/super-Alfv\'enic and trans/supersonic regimes, one of them representing the fiducial conditions corresponding to the ICM. From the simulated models we compute Faraday Rotation maps and analyze several statistical indicators in order to characterize the magnetic field structure and compare the results obtained with the collisionless model to those obtained using standard collisional MHD framework. We find that important imprints of the pressure anisotropy prevails in the magnetic field and also manifest in the associated Faraday Rotation maps which evidence smaller correlation lengths in the collisionless MHD case. These points are remarkably noticeable for the case mimicking the conditions prevailing in ICM. Nevertheless, in this study we have neglected the decrease of pressure anisotropy due to the feedback of the instabilities that naturally arise in collisionless plasmas at small scales. This decrease may not affect the statistical imprint differences described above, but should be examined elsewhere.Comment: 24 pages, 15 figures, MNRAS accepte

Particle Acceleration in Turbulence and Weakly Stochastic Reconnection

Fast particles are accelerated in astrophysical environments by a variety of processes. Acceleration in reconnection sites has attracted the attention of researchers recently. In this letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in previous work (de Gouveia Dal Pino & Lazarian, 2005) and demonstrated numerically in Kowal, de Gouveia Dal Pino & Lazarian (2011). When turbulence is included within the current sheet, the acceleration rate, which depends on the reconnection rate, is highly enhanced. This is because reconnection in the presence of turbulence becomes fast and independent of resistivity (Lazarian & Vishniac, 1999; Kowal et al., 2009) and allows the formation of a thick volume filled with multiple simultaneously reconnecting magnetic fluxes. Charged particles trapped within this volume suffer several head-on scatterings with the contracting magnetic fluctuations, which significantly increase the acceleration rate and results in a first-order Fermi process. For comparison, we also tested acceleration in MHD turbulence, where particles suffer collisions with approaching and receding magnetic irregularities, resulting in a reduced acceleration rate. We argue that the dominant acceleration mechanism approaches a second order Fermi process in this case.Comment: 6 pages, 1 figur