Projectile-Shape Dependence of Impact Craters in Loose Granular Media

We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper

The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus

The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in 1 dimension. We find an interesting family of stable periodic orbits and fixed points, and explore bifurcations of those points as we take weaker and weaker dissipation.Comment: 16 pages, 7 figure

Pathogen-host reorganization during Chlamydia invasion revealed by cryo-electron tomography

Invasion of host cells is a key early event during bacterial infection, but the underlying pathogen-host interactions are yet to be fully visualised in three-dimensional detail. We have captured snapshots of the early stages of bacterial-mediated endocytosis in situ by exploiting the small size of chlamydial elementary bodies (EBs) for whole cell cryo-electron tomography. Chlamydiae are obligate intracellular bacteria that infect eukaryotic cells and cause sexually transmitted infections and trachoma, the leading cause of preventable blindness. We demonstrate that Chlamydia trachomatis LGV2 EBs are intrinsically polarised. One pole is characterised by a tubular inner membrane invagination, while the other exhibits asymmetric periplasmic expansion to accommodate an array of type III secretion systems (T3SSs). Strikingly, EBs orient with their T3SS-containing pole facing target cells, enabling the T3SSs to directly contact the cellular plasma membrane. This contact induces enveloping macropinosomes, actin-rich filopodia and phagocytic cups to zipper tightly around the internalising bacteria. Once encapsulated into tight early vacuoles, EB polarity and the T3SSs are lost. Our findings reveal previously undescribed structural transitions in both pathogen and host during the initial steps of chlamydial invasion

Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the $\Lambda$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations.Comment: 7 pages, 3 figure

Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory

This paper is concerned with the long-time dynamics of the nonlinear wave equation in one-space dimension, $$u_{tt} - \delta^2 u_{xx} +V'(u) =0 \qquad x\in [0,1]$$ where $\delta>0$ is a parameter and $V(u)$ is a potential bounded from below and growing at least like $u^2$ as $|u|\to\infty$. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure and when the potential is double-welled, for example when $V(u) = \tfrac14(1-u^2)^2$, there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here we quantify this phenomenon by calculating exactly via Transition State Theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. Numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter $\delta$ in small enough. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger $\delta$, however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency, indicating that successive transitions between the metastable sets are correlated and the coarse-graining to a Markov chain fails

Space - Single Precision Cowell Trajectory Program

Single Precision Cowell Trajectory program - digital computer program for trajectory computatio

SFPRO - Single Precision Cowell Trajectory Processor

Digital computer program for IBM 7094 computer to generate spacecraft tracking station calculation

Projectile-shape dependence of impact craters in loose granular media

We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.Comment: 3 pages, 3 figures; experimen