Real rank boundaries and loci of forms

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of $\mathbb P^n\times \mathbb P^1$. Finally, in connection with real rank boundaries, we give a new interpretation of the $2\times n \times n$ hyperdeterminant.Comment: 17 p

Surface structure on abandoned upland blanket peatland tracks

Temporary permissions are often granted for track use on peatlands. However, even when peatland track designs attempt to minimise environmental impacts via use of mesh systems, such linear disturbances may have persistent impacts. We evaluated the surface peatland structure of five abandoned tracks (four with a mesh surface, one unsurfaced) with varying past usage frequencies, at an upland site in northern England. Simplification of the surface nanotopography was found on all tracks compared to surrounding control areas, with increased micro-erosion patterns in rutted areas, and invasive species on some treatments. The frequency of previous usage was not found to be a significant factor controlling nano-topographic loss. Edge effects and hillslope position were influential in places, but these effects were not consistent across treatments. Nano-topographic recovery was found to be inhibited when track usage commenced within a short time frame after track construction. Mesh tracks appear to create a spatial constraint leading to poor development of plants and a reduced ability to form characteristic structures which are integral to mire function

Blanket bogs exhibit significant alterations to physical properties as a result of temporary track removal or abandonment

Temporarily consented tracks made from high-density polyethylene (HDPE) mesh have been used to mitigate both the physical and ecological impacts on peatlands from low-frequency vehicle usage. However, the impacts of mesh track removal or abandonment at the end of the consented period remain poorly understood. Over a 2-year period, we studied replicate sections of abandoned mesh track which, at the start of the experiment, had been unused for approximately 5 years, on a UK blanket bog. Some sections were removed (using two treatment methods – vegetation mown and unprepared), whereas others were left in situ. Metrics were compared both between treatments and to undisturbed reference areas. Significant differences in surface soil moisture were found between abandoned and removed tracks depending on season. Control areas had higher volumetric soil moisture than track locations. Compaction was significantly higher across all track locations in comparison to controls (p < 0.001), but rarefaction was not recorded post-removal, suggesting long-term deformation. Overland flow events were recorded in rut sections for a mean of 16% of the time, compared to <1% in control areas. Sediment traps on the tracks collected 0.406 kg compared to 0.0048 kg from the control traps, equating to a per trap value of 7.3 g from track samplers and 0.17 g from control samplers. Erosion and desiccation features occurred on both removed and abandoned track sections. Both abandonment and removal of mesh tracks have a wide range of impacts on the physical properties of peatlands, suggesting that only where access is a necessity should such a track be installed

Technical Note: New methodology for measuring viscosities in small volumes characteristic of environmental chamber particle samples

Herein, a method for the determination of viscosities of small sample volumes is introduced, with important implications for the viscosity determination of particle samples from environmental chambers (used to simulate atmospheric conditions). The amount of sample needed is &lt; 1 μl, and the technique is capable of determining viscosities (η) ranging between 10&lt;sup&gt;−3&lt;/sup&gt; and 10&lt;sup&gt;3&lt;/sup&gt; Pascal seconds (Pa s) in samples that cover a range of chemical properties and with real-time relative humidity and temperature control; hence, the technique should be well-suited for determining the viscosities, under atmospherically relevant conditions, of particles collected from environmental chambers. In this technique, supermicron particles are first deposited on an inert hydrophobic substrate. Then, insoluble beads (~1 μm in diameter) are embedded in the particles. Next, a flow of gas is introduced over the particles, which generates a shear stress on the particle surfaces. The sample responds to this shear stress by generating internal circulations, which are quantified with an optical microscope by monitoring the movement of the beads. The rate of internal circulation is shown to be a function of particle viscosity but independent of the particle material for a wide range of organic and organic-water samples. A calibration curve is constructed from the experimental data that relates the rate of internal circulation to particle viscosity, and this calibration curve is successfully used to predict viscosities in multicomponent organic mixtures

Fermi liquid to Luttinger liquid transition at the edge of a two-dimensional electron gas

We present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with a GaAs/AlGaAs cleaved edge overgrown structure in a strong perpendicular magnetic field. While the 2DEG exhibits typical fractional quantum Hall features of a very high mobility sample, we observe the onset of a non-linear current-voltage characteristic in the vicinity of nu=1. For filling factor nu<1 the system is consistent with a non-Fermi liquid behavior, such as a Luttinger liquid, whereas for nu>1 we observe an Ohmic tunneling resistance between the edge and a three dimensional contact, typical for a Fermi liquid. Hence, at the edge, there is a transition from a Luttinger liquid to a Fermi liquid. Finally, we show that the Luttinger liquid exponent at a given filling factor is not universal but depends on sample parameters.Comment: 4 pages, 4 figure

Donor binding energy and thermally activated persistent photoconductivity in high mobility (001) AlAs quantum wells

A doping series of AlAs (001) quantum wells with Si delta-modulation doping on both sides reveals different dark and post-illumination saturation densities, as well as temperature dependent photoconductivity. The lower dark two-dimensional electron density saturation is explained assuming deep binding energy of Delta_DK = 65.2 meV for Si-donors in the dark. Persistent photoconductivity (PPC) is observed upon illumination, with higher saturation density indicating shallow post-illumination donor binding energy. The photoconductivity is thermally activated, with 4 K illumination requiring post-illumination annealing to T = 30 K to saturate the PPC. Dark and post-illumination doping efficiencies are reported.Comment: The values of binding energy changed from previous versions because of a better understanding for the dielectric permittivity. Also, the Gamma - X donor states are better explaine

Tunnelling Spectroscopy of Localized States near the Quantum Hall Edge

In the paper we dscuss experimental results of M. Grayson et al. on tunneling $I$-$V$ characteristics of the quantum Hall edge. We suggest a two step tunneling mechanism involving localized electron states near the edge, which might account for discrepancy between the experimental data and the predictions of the chiral Luttinger liquid theory of the quantum Hall edge.Comment: 4 pages, revte

Experiments on the Fermi to Tomonaga-Luttinger liquid transition in quasi-1D systems

We present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with GaAs/AlGaAs cleaved edge overgrown structures. The electronic properties of the edge of these systems can be described by a one-dimensional chiral Tomonaga-Luttinger liquid when the filling factor of the 2DEG is very small. Here we focus on the region where the Tomonaga-Luttinger liquid breaks down to form a standard Fermi liquid close to $\nu=1$ and show that we recover a universal curve, which describes all existing data.Comment: 5 pages, localisation 2002, conference proceeding

Nanometer-scale sharpness in corner-overgrown heterostructures

A corner-overgrown GaAs/AlGaAs heterostructure is investigated with transmission and scanning transmission electron microscopy, demonstrating self-limiting growth of an extremely sharp corner profile of 3.5 nm width. In the AlGaAs layers we observe self-ordered diagonal stripes, precipitating exactly at the corner, which are regions of increased Al content measured by an XEDS analysis. A quantitative model for self-limited growth is adapted to the present case of faceted MBE growth, and the corner sharpness is discussed in relation to quantum confined structures. We note that MBE corner overgrowth maintains nm-sharpness even after microns of growth, allowing the realization of corner-shaped nanostructures.Comment: 4 pages, 3 figure

Continuous quantum measurement of a Bose-Einstein condensate: a stochastic Gross-Pitaevskii equation

We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed within the Gross-Pitaevskii mean-field approach. Continuous weak measurements allow instead to replace, for timescales short enough, the exact problem with its mean-field approximation through a stochastic analogue of the Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark soliton undergoing a continuous imaging.Comment: 13 pages, 10 figure