Collisions and close encounters involving massive main-sequence stars

We study close encounters involving massive main sequence stars and the evolution of the exotic products of these encounters as common--envelope systems or possible hypernova progenitors. We show that parabolic encounters between low-- and high--mass stars and between two high--mass stars with small periastrons result in mergers on timescales of a few tens of stellar freefall times (a few tens of hours). We show that such mergers of unevolved low--mass stars with evolved high--mass stars result in little mass loss ($\sim0.01$ M$_{\odot}$) and can deliver sufficient fresh hydrogen to the core of the collision product to allow the collision product to burn for several million years. We find that grazing encounters enter a common--envelope phase which may expel the envelope of the merger product. The deposition of energy in the envelopes of our merger products causes them to swell by factors of $\sim100$. If these remnants exist in very densely-populated environments ($n\gtrsim10^{7}$ pc$^{-3}$), they will suffer further collisions which may drive off their envelopes, leaving behind hard binaries. We show that the products of collisions have cores rotating sufficiently rapidly to make them candidate hypernova/gamma--ray burst progenitors and that $\sim0.1$ of massive stars may suffer collisions, sufficient for such events to contribute significantly to the observed rates of hypernovae and gamma--ray bursts.Comment: 15 pages, 13 figures, LaTeX, to appear in MNRAS (in press

Percolation games, probabilistic cellular automata, and the hard-core model

Let each site of the square lattice $\mathbb{Z}^2$ be independently assigned one of three states: a \textit{trap} with probability $p$, a \textit{target} with probability $q$, and \textit{open} with probability $1-p-q$, where $0<p+q<1$. Consider the following game: a token starts at the origin, and two players take turns to move, where a move consists of moving the token from its current site $x$ to either $x+(0,1)$ or $x+(1,0)$. A player who moves the token to a trap loses the game immediately, while a player who moves the token to a target wins the game immediately. Is there positive probability that the game is \emph{drawn} with best play -- i.e.\ that neither player can force a win? This is equivalent to the question of ergodicity of a certain family of elementary one-dimensional probabilistic cellular automata (PCA). These automata have been studied in the contexts of enumeration of directed lattice animals, the golden-mean subshift, and the hard-core model, and their ergodicity has been noted as an open problem by several authors. We prove that these PCA are ergodic, and correspondingly that the game on $\mathbb{Z}^2$ has no draws. On the other hand, we prove that certain analogous games \emph{do} exhibit draws for suitable parameter values on various directed graphs in higher dimensions, including an oriented version of the even sublattice of $\mathbb{Z}^d$ in all $d\geq3$. This is proved via a dimension reduction to a hard-core lattice gas in dimension $d-1$. We show that draws occur whenever the corresponding hard-core model has multiple Gibbs distributions. We conjecture that draws occur also on the standard oriented lattice $\mathbb{Z}^d$ for $d\geq 3$, but here our method encounters a fundamental obstacle.Comment: 35 page

Structural Analysis and Performance-Based Validation of a Composite Wing Spar

Electric-motor powered aircraft possess the ability to operate with efficient energy delivery, but lack the operational range of internal combustion engine powered aircraft. This range limitation requires the use of high aspect ratio, thin-chord wings to minimize aerodynamic drag losses, which results in highly loaded composite spar structures. High aspect ratio wings are required to increase mission durations for a NASA-developed experimental multi-rotor electric powered aircraft denoted as the Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) or X-57. This paper examines the structural performance of the composite main wing spars to validate spar strength using ply-based laminate finite element methods. Geometric scaling of a main spar test-section was initially proposed for proof-testing but sacrificed stability. Ply-based structures modeling with local structural features was implemented as a risk-reduction methodology. Ply-based modeling was selected to augment the conventional building block approach to reduce risk, and leverage a performance-based approval processes encouraged in Federal Aviation Administration (FAA) design guidance. Therefore, ply-based laminate modeling of the full-scale main spar and forward spar shear-web attachments were subsequently undertaken to determine load path complexity with predicted flight loads. Ply-based modeling included stress concentrations and interlaminate behavior at interface locations that can be obscured in traditional finite element sizing models. Analysis of the wing spar laminate ply-based models compared with bearing test coupon performance was used to reduce future wing assembly proof-testing burden and facilitate performance-based flight hardware safety for the X-57 experimental aircraft

The Jammed Phase of the Biham-Middleton-Levine Traffic Model

Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each North-facing car moves one unit North if there is a vacant site for it to move into. At even time steps, East-facing cars move East in the same way. We prove that when p is sufficiently close to 1 traffic is jammed, in the sense that no car moves infinitely many times. The result extends to several variant settings, including a model with cars moving at random times, and higher dimensions.Comment: 15 pages, 5 figures; revised journal versio