A Dynamical Systems Approach to Schwarzschild Null Geodesics

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum Lc corresponds to the unstable circular orbit at r=3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r=0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the limit as L goes to infinity, as described in Schwarzschild coordinates, these geodesics begin at r=0, flow along t=constant lines, turn around at r=2M, then continue to r=0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.Comment: 14 pages, 3 Figure

Multiphoton Ionization of Nitrobenzene in Non-Aqueous Solutions: Characterization of the Cation and Ion-Molecule Chemistry

The phenoxy cation has been generated in polar and nonpolar solutions by multiphoton ionization of nitrobenzene using nanosecond pulses of 266 nm and 355 nm light. The ions have been characterized by pulsed conductivity (ion mobility) measurements and transient absorption spectroscopy. The involvement of the phenoxy ion in ion-molecule chemistry with either neutral solute or solvent molecules has also been observed and the photochemical products and quantum yields of the ion-molecule products are presented and compared with the neutral photochemistry results

Chaotic exchange of solid material between planetary systems: implications for lithopanspermia

We examine a low energy mechanism for the transfer of meteoroids between two planetary systems embedded in a star cluster using quasi-parabolic orbits of minimal energy. Using Monte Carlo simulations, we find that the exchange of meteoroids could have been significantly more efficient than previously estimated. Our study is relevant to astrobiology as it addresses whether life on Earth could have been transferred to other planetary systems in the solar system's birth cluster and whether life on Earth could have been transferred here from beyond the solar system. In the solar system, the timescale over which solid material was delivered to the region from where it could be transferred via this mechanism likely extended to several hundred million years (as indicated by the 3.8-4.0 Ga epoch of the Late Heavy Bombardment). This timescale could have overlapped with the lifetime of the Solar birth cluster (~100-500 Myr). Therefore, we conclude that lithopanspermia is an open possibility if life had an early start. Adopting parameters from the minimum mass solar nebula, considering a range of planetesimal size distributions derived from observations of asteroids and Kuiper Belt Objects and theoretical coagulation models, and taking into account Oort Cloud formation models, the expected number of bodies with mass > 10 kg that could have been transferred between the Sun and its nearest cluster neighbor could be of the order of 1E14-3E16, with transfer timescales of 10s Myr. We estimate that of the order of 3E8 x l(km) could potentially be life-bearing, where l(km) is the depth of the Earth crust in km that was ejected as the result of the early bombardment.Comment: Accepted by Astrobiology. Submitted: Sep. 21, 2011. Accepted: May 2, 2012. 39 pages. 21 figures. arXiv admin note: substantial text overlap with arXiv:0808.326

Uv Multiphoton Induced Chemistry of Nitrobenzene in Solution

The technique of Multiphoton Induced Chemistry (MPIC) has been employed to initiate ion-molecule chemistry of organic molecules in solution. We report one of the first examples of the use of liquid phase multiphoton ionization (MPI) to prepare organic cations, which then react with the solvent in ionmolecule processes. The products obtained in this chemical sequence are significantly different from those observed in conventional or multiphoton-induced neutral chemistry in the same solvent. The particular example explored in this work is the reactivity of the nitrobenzene cation in methanol solvent. Products of the ion-molecule chemistry, detected by gas chromatography/mass spectrometry, are phenol and benzyl alcohol. These products depend upon the square of the laser intensity. It is shown by ionization current measurements in a conductance cell, that ionic species are produced as precursors to the observed products. The implications of this application of MPI are briefly discussed. A preliminary report on the unimolecular chemistry of the highly excited neutral molecule is also included. The product of this channel is nitrosobenzene. It is shown, in this case, that the reactive state is most likely a highly vibrationally excited ground state molecule, not the lowest triplet level invoked in conventional photochemistry

On the Regularizability of the Big Bang Singularity

The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, $w$. We prove that for $w >1$ it is regularizable only for $w$ satisfying relative prime number conditions, and for $w \leq 1$ it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an invariant manifold. The relationship of this result to other cosmological models is briefly discussed.Comment: 22 pages, 0 figure

Where Did The Moon Come From?

The current standard theory of the origin of the Moon is that the Earth was hit by a giant impactor the size of Mars causing ejection of iron poor impactor mantle debris that coalesced to form the Moon. But where did this Mars-sized impactor come from? Isotopic evidence suggests that it came from 1AU radius in the solar nebula and computer simulations are consistent with it approaching Earth on a zero-energy parabolic trajectory. But how could such a large object form in the disk of planetesimals at 1AU without colliding with the Earth early-on before having a chance to grow large or before its or the Earth's iron core had formed? We propose that the giant impactor could have formed in a stable orbit among debris at the Earth's Lagrange point $L_4$ (or $L_5$). We show such a configuration is stable, even for a Mars-sized impactor. It could grow gradually by accretion at $L_4$ (or $L_5$), but eventually gravitational interactions with other growing planetesimals could kick it out into a chaotic creeping orbit which we show would likely cause it to hit the Earth on a zero-energy parabolic trajectory. This paper argues that this scenario is possible and should be further studied.Comment: 64 pages, 27 figures, accepted for publication in A

Modeling the Pinning of Au and Ni Clusters on Graphite

The pinning of size-selected AuN and NiN clusters on graphite, for N=7–100, is investigated by means of molecular dynamics simulations and the results are compared to experiment and previous work with Ag clusters. Ab initio calculations of the binding of the metal adatom and dimers on a graphite surface are used to parametrize the potentials used in the simulations. The clusters are projected normally towards a graphite surface and the value of the energy at which pinning first occurs, EP, is determined. Pinning is shown to occur when a surface defect, made by the cluster interaction, is first produced. The simulations give a good agreement with the experimentally determined pinning energy thresholds and the heights of the clusters on the surface. The gold clusters are shown to be flatter and more spread out than the nickel clusters which are more compact

Gold Adatoms and Dimers on Relaxed Graphite Surfaces

The interaction of deposited gold adatoms and dimers with multilayer relaxed graphite surfaces is investigated through a density functional approach with numerical orbitals and a relativistic core pseudopotential. The energy landscape for a gold adatom along [110] agrees with scanning tunneling microscopy observations including the preferred β binding site for adatoms and the mobility difference between silver and gold adatoms. Deposited particles are shown to induce surface deformation and polarization. Static relaxation and dynamic simulations indicate that the energetically preferred binding orientation for a gold dimer is normal rather than parallel to the graphite surface. The dimer response to a simulated scanning tunneling microscopy tip is investigated by molecular dynamics simulations

Vapor Deposited Cr-doped ZnS Thin Films: Towards Optically Pumped Mid-Infrared Waveguide Lasers

Compact, affordable mid-IR lasers require the development of gain materials in waveguide form. We report on the high vacuum deposition of Cr:ZnS films with concentration ranging from 1018-1020 dopants/cm3 . At low concentrations, films display well-isolated absorption associated with substitutional Cr2+ ions in the lattice. Spatial modulation of the dopant concentration suppresses the absorption associated with this substitution. Lateral crystallite sizes less than 30 nm are associated with the lowest substrate temperatures (\u3c50 °C) used during deposition, and waveguide losses as low as 8dB/cm are observed. These materials are promising candidates as gain media for fabrication of waveguide mid-IR lasers

A study of low-energy transfer orbits to the Moon: towards an operational optimization technique

In the Earth-Moon system, low-energy orbits are transfer trajectories from the earth to a circumlunar orbit that require less propellant consumption when compared to the traditional methods. In this work we use a Monte Carlo approach to study a great number of such transfer orbits over a wide range of initial conditions. We make statistical and operational considerations on the resulting data, leading to the description of a reliable way of finding "optimal" mission orbits with the tools of multi-objective optimization