A Metrizable Topology on the Contracting Boundary of a Group

The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the contracting boundary. When the space is the Cayley graph of a finitely generated group we show that our new topology is metrizable.Comment: v1: 26 pages, 3 figures; v2: 44 pages, 6 figures, additional results; v3: 46 pages, 7 figures, minor change

Simulating AIA observations of a flux rope ejection

Extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. Observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. These observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. To this end we aim to produce synthesised AIA observations from simluations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. We sythesise observations of AIA in the channels at 304 A, 171 A, 335 A, and 94 A. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 A and 171 A channels with a high density core. The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

Nonlinear force-free field modelling of solar coronal jets in theoretical configurations

Coronal jets occur frequently on the Sun, and may contribute significantly to the solar wind. With the suite of instruments available now, we can observe these phenomena in greater detail than ever before. Modeling and simulations can assist further in understanding the dynamic processes involved, but previous studies tend to consider only one mechanism (e.g. emergence or rotation) for the origin of the jet. In this study we model a series of idealised archetypal jet configurations and follow the evolution of the coronal magnetic field. This is a step towards understanding these idealised situations before considering their observational counterparts. Several simple situations are set up for the evolution of the photospheric magnetic field: a single parasitic polarity rotating or moving in a circular path; as well as opposite polarity pairs involved in flyby (shearing), cancellation or emergence; all in the presence of a uniform, open background magnetic field. The coronal magnetic field is evolved in time using a magnetofrictional relaxation method. While magnetofriction cannot accurately reproduce the dynamics of an eruptive phase, the structure of the coronal magnetic field, as well as the build up of electric currents and free magnetic energy are instructive. Certain configurations and motions produce a flux rope and allow the significant build up of free energy, reminiscent of the progenitors of so-called blowout jets, whereas other, simpler configurations are more comparable to the standard jet model. The next stage is a comparison with observed coronal jet structures and their corresponding photospheric evolution

Stellar Differential Rotation and Coronal Timescales

We investigate the timescales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the geometric mean of the lap time and the surface diffusion timescale. In contrast, the lifetime of flux ropes are proportional to the lap time. With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than two days. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae

Correlation length and negative phase velocity in isotropic dielectric-magnetic materials

A composite material comprising randomly distributed spherical particles of two different isotropic dielectric-magnetic materials is homogenized using the second-order strong-property-fluctuation theory in the long-wavelength approximation. Whereas neither of the two constituent materials by itself supports planewave propagation with negative phase velocity (NPV), the homogenized composite material (HCM) can. The propensity of the HCM to support NPV propagation is sensitive to the distributional statistics of the constituent material particles, as characterized by a two--point covariance function and its associated correlation length. The scope for NPV propagation diminishes as the correlation length increases