Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

Three-axis attitude determination via Kalman filtering of magnetometer data

A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system

The Spatial Distribution of the Galactic First Stars II: SPH Approach

We use cosmological, chemo-dynamical, smoothed particle hydrodynamical simulations of Milky-Way-analogue galaxies to find the expected present-day distributions of both metal-free stars that formed from primordial gas and the oldest star populations. We find that metal-free stars continue to form until z~4 in halos that are chemically isolated and located far away from the biggest progenitor of the final system. As a result, if the Population III initial mass function allows stars with low enough mass to survive until z=0 (< 0.8 Msol), they would be distributed throughout the Galactic halo. On the other hand, the oldest stars form in halos that collapsed close to the highest density peak of the final system, and at z=0 they are located preferentially in the central region of the Galaxy, i.e., in the bulge. According to our models, these trends are not sensitive to the merger histories of the disk galaxies or the implementation of supernova feedback. Furthermore, these full hydrodynamics results are consistent with our N-body results in Paper I, and lend further weight to the conclusion that surveys of low-metallicity stars in the Galactic halo can be used to directly constrain the properties of primordial stars. In particular, they suggest that the current lack of detections of metal-free stars implies that their lifetimes were shorter than a Hubble time, placing constraints on the metal-free initial mass function.Comment: Accepted by ApJ. Emulate ApJ styl

The Emergence of the Thick Disk in a CDM Universe II: Colors and Abundance Patterns

The recently emerging conviction that thick disks are prevalent in disk galaxies, and their seemingly ubiquitous old ages, means that the formation of the thick disk, perhaps more than any other component, holds the key to unravelling the evolution of the Milky Way, and indeed all disk galaxies. In Paper I, we proposed that the thick disk was formed in an epoch of gas rich mergers, at high redshift. This hypothesis was based on comparing N-body/SPH simulations to a variety of Galactic and extragalactic observations, including stellar kinematics, ages and chemical properties.Here examine our thick disk formation scenario in light of the most recent observations of extragalactic thick disks. In agreement, our simulted thick disks are old and relatively metal rich, with V-I colors that do not vary significantly with distance from the plane. Further, we show that our proposal results in an enhancement of alpha-elements in thick disk stars as compared with thin disk stars, consistent with observations of the relevant populations of the Milky Way. We also find that our scenario naturally leads to the formation of an old metal weak stellar halo population with high alpha-element abundances.Comment: submitted to Ap

Influence of single-neutron stripping on near-barrier ⁶He+²⁰⁸Pb and ⁸He+²⁰⁸Pb elastic scattering

The influence of single-neutron stripping on the near-barrier elastic scattering angular distributions for the 6,8He+208Pb systems is investigated through coupled reaction channels (CRC) calculations fitting recently published data to explore the differences in the absorptive potential found in the scattering of these two neutron-rich nuclei. The inclusion of the coupling reduces the elastic cross section in the Coulomb-nuclear interference region for 8He scattering, whereas for 6He its major impact is on the large-angle elastic scattering. The real and imaginary dynamic polarization potentials are obtained by inverting the CRC elastic scattering S-matrix elements. These show that the main absorptive features occur between 11 and 12 fm for both projectiles, while the attractive features are separated by about 1 fm, with their main structures occurring at 10.5 fm for 6He and 11.5 fm for 8He

Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point-particle of mass $\mu$ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius r_p(t) satisfies r_p(t)> 5M at all times.Comment: revtex4, 24 pages, 23 figures, 3 tables, submitted to PR

Multi-neutron transfer in 8^{8}He induced reactions near the Coulomb barrier

The measured inclusive $^6$He and $^4$He production cross sections of G. Marqu{\'i}nez-Dur{\'a}n {\em et al.}, Phys.\ Rev.\ C {\bf 98}, 034615 (2018) are reexamined and the conclusions concerning the relative importance of 1n and 2n transfer to the production of $^6$He arising from the interaction of a 22 MeV $^8$He beam with a $^{208}$Pb target revised. A consideration of the kinematics of the 2n-stripping reaction when compared with the measured $^6$He total energy versus angle spectrum places strict limits on the allowed excitation energy of the $^{210}$Pb residual, so constraining distorted wave Born approximation calculations that the contribution of the 2n stripping process to the inclusive $^6$He production can only be relatively small. It is therefore concluded that the dominant $^6$He production mechanism must be 1n stripping followed by decay of the $^7$He ejectile. Based on this result we present strong arguments in favor of direct, one step four-neutron (4n) stripping as the main mechanism for $^4$He production.Comment: 7 pages, 2 figure

Do Lognormal Column-Density Distributions in Molecular Clouds Imply Supersonic Turbulence?

Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed clouds. We calculate and present the column-density distributions of three clouds, modeled with very different techniques, none of which is dominated by supersonic turbulence. The first star-forming cloud is simulated using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only by thermal-pressure forces, drives the evolution. The second cloud is magnetically subcritical with subsonic turbulence, simulated using nonideal MHD; in this case the evolution is due to gravitationally-driven ambipolar diffusion. The third cloud is isothermal, self-gravitating, and has a smooth density distribution analytically approximated with a uniform inner region and an r^-2 profile at larger radii. We show that in all three cases the column-density distributions are lognormal. Power-law tails develop only at late times (or, in the case of the smooth analytic profile, for strongly centrally concentrated configurations), when gravity dominates all opposing forces. It therefore follows that lognormal column-density distributions are generic features of diverse model clouds, and should not be interpreted as being a consequence of supersonic turbulence.Comment: 6 pages, 6 figures, accepted for publication in MNRA