Pseudo-rotations of the open annulus

In this paper, we study pseudo-rotations of the open annulus, \emph{i.e.} conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular that, for every pseudo-rotation $h$ of angle $\rho$, the rigid rotation of angle $\rho$ is in the closure of the conjugacy class of $h$. We also prove that pseudo-rotations are not persistent in $C^r$ topology for any $r\geq 0$.Comment: 25 page

Some fossil ginkgophytes and a possible vojnovskyalean element from the Glossopteris flora of Vereeniging, Transvaal

Main articleA short historical review is given of previously described sites where plant fossils occur in Lower Karroo beds at Vereeniging in the Southern Transvaal. Reference is made to the importance of these sites because of the outstanding discoveries made here in the past. Some new material from the same sites is described and several unusual elements in the Glossopteris flora of Vereeniging are recorded for the first time. Leaves of a plant not previously recorded from Gondwanaland are provisionally described under the term cf. Nephropsis on account of a strong resemblance to leaves of the Russian Permian genus Nephropsis Zalessky. The remaining specimens in the assemblage are tentatively placed in the genera Ginkgoites Seward and Psygmophyllum Schimper respectively. Owing to the paucity of material, type numbers are assigned in certain cases, instead of specific names. Specific identification is attempted, however, in the case of four of the specimens, which are provisionally assigned to Psygmophyllum kidstoni Seward.Non

On some "northern" elements in the Lower Gondwana flora of Vereeniging, Transvaal

Main articleA small assemblage of plant elements from the Lower Permian of Vereeniging, in the southern Transvaal, is described here. The assemblage is constituted of form-genera normally only found in the palaeo floristic regions of the northern hemisphere. The genera concerned are: Pecopteris (Asterotheca), Cladophlebis, Sphenophyllum and Psygmophyllum. The intermingling of these "Northern" elements with the Glossopteris flora of Vereeniging serves to illustrate the mixed nature of this flora. Reference is made to similar mixed Gondwana floras elsewhere in Africa and also in South America.Non

Strain versus stress in a model granular material: a Devil's staircase

The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitudes, the dependence of the resulting strain on stress direction is a Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered throughout text, very close to published pape

A Model for Granular Texture with Steric Exclusion

We propose a new method to characterize the geometrical texture of a granular packing at the particle scale including the steric hindrance effect. This method is based on the assumption of a maximum disorder (entropy) compatible both with strain-induced anisotropy of the contact network and steric exclusions. We show that the predicted statistics for the local configurations is in a fairly agreement with our numerical data.Comment: 9 pages, 5 figure

Scattering by a toroidal coil

In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with a long-range magnetic potential associated to a magnetic field supported inside a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix $S(\lambda)$. We prove that the essential spectrum of $S(\lambda)$ is an interval of the unit circle depending only on the magnetic flux $\phi$ across the section of $\mathbb{T}$. Additionally we show that, in contrast to the Aharonov-Bohm potential in ${\mathbb{R}}^2$, the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.Comment: LaTeX2e 17 pages, 1 figur

Optical brain imaging using a semi-transparent organic light-emitting diode

We report optical brain imaging using a semi-transparent organic light-emitting diode (OLED) based on the orange light-emitting polymer (LEP) Livilux PDO-124. The OLED serves as a compact, extended light source which is capable of uniformly illuminating the cortical surface when placed across a burr hole in the skull. Since all layers of the OLED are substantially transparent to photons with energies below the optical gap of the LEP, light emitted or reflected by the cortical surface may be efficiently transmitted through the OLED and into the objective lens of a low magnification microscope ('macroscope'). The OLED may be placed close to the cortical surface, providing efficient coupling of incident light into the brain cavity; furthermore, the macroscope may be placed close to the upper surface of the OLED, enabling efficient collection of reflected/emitted light from the cortical surface. Hence the use of a semi-transparent OLED simplifies the optical setup, while at the same time maintaining high sensitivity. The OLED is applied here to one of the most demanding forms of optical brain imaging, namely extrinsic optical imaging involving a voltage sensitive dye (VSD). Specifically, we carry out functional imaging of the primary visual cortex (V1) of a rat, using the voltage sensitive dye RH-1691 as a reporter. Imaging through the OLED light-source, we are able to resolve small (~ 0.1 %) changes in the fluorescence intensity of the dye due to changes in the neuronal membrane potential following a visual stimulus. Results are obtained on a single trial basis -- i.e. without averaging over multiple measurements -- with a time-resolution of ten milliseconds