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

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 < 1 μl, and the technique is capable of determining viscosities (η) ranging between 10<sup>−3</sup> and 10<sup>3</sup> 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

Improving the Sensitivity of LISA

It has been shown in the past, that the six Doppler data streams obtained LISA configuration can be combined by appropriately delaying the data streams for cancelling the laser frequency noise. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of shot, acceleration noises. A rigorous and systematic formalism using the techniques of computational commutative algebra was developed which generates all the data combinations cancelling the laser frequency noise. The relevant data combinations form a first module of syzygies. In this paper we use this formalism for optimisation of the LISA sensitivity by analysing the noise and signal covariance matrices. The signal covariance matrix, averaged over polarisations and directions, is calculated for binaries whose frequency changes at most adiabatically. We then present the extremal SNR curves for all the data combinations in the module. They correspond to the eigenvectors of the noise and signal covariance matrices. We construct LISA `network' SNR by combining the outputs of the eigenvectors which improves the LISA sensitivity substantially. The maximum SNR curve can yield an improvement upto 70 % over the Michelson, mainly at high frequencies, while the improvement using the network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy model, in which LISA rotates in a plane. In this analysis, we estimate the improvement in the LISA sensitivity, if one switches from one data combination to another as it rotates. Here the improvement in sensitivity, if one switches optimally over three cyclic data combinations of the eigenvector is about 55 % on an average over the LISA band-width. The corresponding SNR improvement is 60 %, if one maximises over the module.Comment: 16 pages, 10 figures, Submitted to Class. Quant. Gravit

Notes from lockdown: A series of reflections on some of the political and cultural impacts of the pandemic

A series of reflections on Covid-19 that looks at: how the pandemic affects processes of bordering and increases the indeterminate grey zones within which so many people are forced to live; the way nurses are presented in the media and the hypocrisy of praising them in a moment of crisis while simultaneously devaluing their work and underpaying them; health inequalities in Newham; the inequalities in the craft sector spotlighted by the pandemic; the relationships between radical neighbourliness and local politics; how perceptions of time have been affected during lockdown - and how 24-7 capitalism may seek to take advantage of this radical reorganisation of time

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

Ultrastructural and Textural Properties of Restructured Beef Treated with a Bacterial Culture and Splenic Pulp

Scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Instron measurements were used to evaluate the effects of an Achromobacter iophagus culture {BC) and splenic pulp (SP) treatments one structural and textural properties of flaked and restructured beef steaks. Both treatments improved the textural character is tics of the product when conditioned at 35°C . Electron microscopy studies revealed that the bacterial culture treatment caused a greater effect than SP on the connective tissue elements, with a degradation of the endomysial sheath and sarcolemma. Treatment with splenic pulp produced an overall excessive disruption a t the Z-lines with little definition of the A-bands

Fecal colonization with vancomycin-resistant enterococci in Australia.

To assess the rate of fecal vancomycin-resistant enterococci (VRE) colon ization in Austalia, we examined specimens from 1,085 healthy volunteers. VRE was cultured from 2(0.2%) of 1,085 specimens; both were vanB Enter ococcus faecium, identical by pulsed-field gel electrophoresis, but with a pattern rare in Melbourne hospitals

On the Evolution Equation for Magnetic Geodesics

In this paper we prove the existence of long time solutions for the parabolic equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the parabolic equation for closed magnetic geodesic

Valley degeneracy in biaxially strained aluminum arsenide quantum wells

This paper details a complete formalism for calculating electron subband energy and degeneracy in strained multi-valley quantum wells grown along any orientation with explicit results for the AlAs quantum well case. A standardized rotation matrix is defined to transform from the conventional- cubic-cell basis to the quantum-well-transport basis whereby effective mass tensors, valley vectors, strain matrices, anisotropic strain ratios, and scattering vectors are all defined in their respective bases. The specific cases of (001)-, (110)-, and (111)-oriented aluminum arsenide (AlAs) quantum wells are examined, as is the unconventional (411) facet, which is of particular importance in AlAs literature. Calculations of electron confinement and strain in the (001), (110), and (411) facets determine the critical well width for crossover from double- to single-valley degeneracy in each system. The notation is generalized to include miscut angles, and can be adapted to other multi-valley systems. To help classify anisotropic inter-valley scattering events, a new primitive unit cell is defined in momentum space which allows one to distinguish purely in-plane inter-valley scattering events from those that requires an out-of-plane momentum scattering component.Comment: 17 pages, 4 figures, 2 table