On the formation time scale and core masses of gas giant planets

Numerical simulations show that the migration of growing planetary cores may be dominated by turbulent fluctuations in the protoplanetary disk, rather than by any mean property of the flow. We quantify the impact of this stochastic core migration on the formation time scale and core mass of giant planets at the onset of runaway gas accretion. For standard Solar Nebula conditions, the formation of Jupiter can be accelerated by almost an order of magnitude if the growing core executes a random walk with an amplitude of a few tenths of an au. A modestly reduced surface density of planetesimals allows Jupiter to form within 10 Myr, with an initial core mass below 10 Earth masses, in better agreement with observational constraints. For extrasolar planetary systems, the results suggest that core accretion could form massive planets in disks with lower metallicities, and shorter lifetimes, than the Solar Nebula.Comment: ApJL, in pres

Magnetically modulated accretion in T Tauri stars

We examine how accretion on to T Tauri stars may be modulated by a time-dependent `magnetic gate' where the inner edge of the accretion disc is disrupted by a varying stellar field. We show that magnetic field variations on time-scales shorter than 10^5 yr can modulate the accretion flow, thus providing a possible mechanism both for the marked photometric variability of T Tauri stars and for the possible conversion of T Tauri stars between classical and weak line status. We thus suggest that archival data relating to the spectrophotometric variability of T Tauri stars may provide an indirect record of magnetic activity cycles in low-mass pre-main-sequence stars.Comment: LaTeX file (requires mn.sty), 4 pages, no figures or tables. To appear in MNRAS

Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation

We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion equation. It was shown numerically that this model can exhibit quasi-one-dimensional constant speed travelling wave solutions. We present an analytic study of the existence and uniqueness problem for constant speed travelling wave solutions. We find that such solutions exist only for speeds greater than some threshold speed giving minimum speed waves which have a sharp profile. For speeds greater than this minimum speed the waves are smooth. We also characterise the dependence of the wave profile on the decay of the front of the initial perturbation in bacterial density. An investigation of the partial differential equation problem establishes,via a global existence and uniqueness argument, that these waves are the only long time solutions supported by the problem. Numerical solutions of the partial differential equation problem are presented and they confirm the results of the analysis

Civil Procedure in the Province of Quebec

Address of Hon. J. Armitage Ewing, K. C., of the Montreal, Canada, Bar, at the Annual Meeting of the Indiana State Bar Association, September 16, 1938

Modeling chemotaxis reveals the role of reversed phosphotransfer and a bi-functional kinase-phosphatase

Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY6, aided by its specific phosphatase, the bifunctional kinase CheA3, acts as a phosphate sink for the other RRs; and (2) a phosphorelay pathway involving CheB2 connects the cytoplasmic cluster kinase CheA3 with the polar localised kinase CheA2, and allows CheA3-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA3 to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources

Civil Procedure in the Province of Quebec

Address of Hon. J. Armitage Ewing, K. C., of the Montreal, Canada, Bar, at the Annual Meeting of the Indiana State Bar Association, September 16, 1938

Astrometric signatures of self-gravitating protoplanetary discs

We use high resolution numerical simulations to study whether gravitational instabilities within circumstellar discs can produce astrometrically detectable motion of the central star. For discs with masses of M_disc = 0.1 M_star, which are permanantly stable against fragmentation, we find that the magnitude of the astrometric signal depends upon the efficiency of disc cooling. Short cooling times produce prominent filamentary spiral structures in the disc, and lead to stellar motions that are potentially observable with future high precision astrometric experiments. For a disc that is marginally unstable within radii of \~10 au, we estimate astrometric displacements of 10-100 microarcsec on decade timescales for a star at a distance of 100 pc. The predicted displacement is suppressed by a factor of several in more stable discs in which the cooling time exceeds the local dynamical time by an order of magnitude. We find that the largest contribution comes from material in the outer regions of the disc and hence, in the most pessimistic scenario, the stellar motions caused by the disc could confuse astrometric searches for low mass planets orbiting at large radii. They are, however, unlikely to present any complications in searches for embedded planets orbiting at small radii, relative to the disc size, or Jupiter mass planets or greater orbiting at large radii.Comment: 6 pages, 9 figures, accepted for publication in MNRA

Measurement of the topological surface state optical conductance in bulk-insulating Sn-doped Bi1.1_{1.1}Sb0.9_{0.9}Te2_2S single crystals

Topological surface states have been extensively observed via optics in thin films of topological insulators. However, in typical thick single crystals of these materials, bulk states are dominant and it is difficult for optics to verify the existence of topological surface states definitively. In this work, we studied the charge dynamics of the newly formulated bulk-insulating Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_2$S crystal by using time-domain terahertz spectroscopy. This compound shows much better insulating behavior than any other bulk-insulating topological insulators reported previously. The transmission can be enhanced an amount which is 5$\%$ of the zero-field transmission by applying magnetic field to 7 T, an effect which we believe is due to the suppression of topological surface states. This suppression is essentially independent of the thicknesses of the samples, showing the two-dimensional nature of the transport. The suppression of surface states in field allows us to use the crystal slab itself as a reference sample to extract the surface conductance, mobility, charge density and scattering rate. Our measurements set the stage for the investigation of phenomena out of the semi-classical regime, such as the topological magneto-electric effect.Comment: 5 pages, 3 figures, submitted in Augus