Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin

Unambiguous quantum state elimination for qubit sequences

Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is rather than what it is not. Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography. We consider unambiguous quantum state elimination for two or more qubits, where each qubit can be in one of two possible states. Optimal measurements for eliminating one and two states out of four two-qubit states are given. We also prove that if we want to maximize the average number of eliminated overall N -qubit states, then individual measurements on each qubit are optimal

Integrated Modelling for Understanding Watershed Development Impacts on Social and Biophysical Systems

The intention of watershed development (WD) programs in India is to improve the livelihoods of people and preserve the natural resource base, particularly in areas where water scarcity limits the development potential of rural communities. In practice, there are many complications to implementing WD programs in an effective and equitable way for all people within and between villages in a catchment. Our understanding of the potential implications of a program is often limited by the way in which we investigate the biophysical-social-economic system. Two common failings are (a) not properly considering the importance of the place, scope and scale of a problem and (b) using a disciplinary approach to make conclusions about the system as a whole. This paper discusses how we are addressing these issues as part of an integrated assessment project looking at WD in the state of Andhra Pradesh, India. The multi-disciplinary project team includes agronomists, economists, environmental modellers, groundwater and surface water hydrologists, and social scientists who together are aiming to develop a holistic understanding of the impacts of WD on biophysical, social and economic systems. Key to the project philosophy is the inclusion of government representatives, communities, and non-government organisations (NGOs) in developing the researchers\u27 understanding of the issues and complexities associated with WD and the critical questions that need addressing by the project. An integrated model is being developed that will incorporate crop production water use and hydrological (surface water and groundwater) models in addition to knowledge gained from extensive household surveys in villages in two case study catchments. The household surveys were developed based on discussions with NGOs working with the rural communities in Andhra Pradesh and are being used to examine economic and social outcomes (positive and negative) of WD for households. Measures of equity and resilience are being developed to measure differences in outcomes between villages (e.g. upstream, downstream) and within villages (e.g. income groups, gender, land ownership, etc)

Surprising Evolution of the Parsec-scale Faraday Rotation Gradients in the Jet of the BL Lac Object B1803+784

Several multi-frequency polarization studies have shown the presence of systematic Faraday Rotation gradients across the parsec-scale jets of Active Galactic Nuclei (AGN), taken to be due to the systematic variation of the line-of-sight component of a helical magnetic (B) field across the jet. Other studies have confirmed the presence and sense of these gradients in several sources, thus providing evidence that these gradients persist over time and over large distances from the core. However, we find surprising new evidence for a reversal in the direction of the Faraday Rotation gradient across the jet of B1803+784, for which multi-frequency polarization observations are available at four epochs. At our three epochs and the epoch of Zavala & Taylor (2003), we observe transverse Rotation Measure (RM) gradients across the jet, consistent with the presence of a helical magnetic field wrapped around the jet. However, we also observe a "flip" in the direction of the gradient between June 2000 and August 2002. Although the origins of this phenomena are not entirely clear, possibly explanations include (i) the sense of rotation of the central supermassive black hole and accretion disc has remained the same, but the dominant magnetic pole facing the Earth has changed from North to South; (ii) a change in the direction of the azimuthal B field component as a result of torsional oscillations of the jet; and (iii) a change in the relative contributions to the observed rotation measures of the "inner" and "outer" helical fields in a magnetic-tower model. Although we cannot entirely rule out the possibility that the observed changes in the RM distribution are associated instead with changes in the thermal-electron distribution in the vicinity of the jet, we argue that this explanation is unlikely.Comment: 21 pages, 10 figures. Accepted for publication in MNRA

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Analysing the Transverse Structure of the Relativistic Jets of AGN

This paper describes a method of fitting total intensity and polarization profiles in VLBI images of astrophysical jets to profiles predicted by a theoretical model. As an example, the method is used to fit profiles of the jet in the Active Galactic Nucleus Mrk501 with profiles predicted by a model in which a cylindrical jet of synchrotron plasma is threaded by a magnetic field with helical and disordered components. This fitting yields model Stokes Q profiles that agree with the observed profiles to within the 1-2 \sigma uncertainties; the I model and observed profiles are overall not in such good agreement, with the model I profiles being generally more symmetrical than the observed profiles. Consistent fitting results are obtained for profiles derived from 6cm VLBI images at two distances from the core, and also for profiles obtained for different wavelengths at a single location in the VLBI jet. The most striking success of the model is its ability to reproduce the spine-sheath polarization structure observed across the jet. Using the derived viewing angle in the jet rest frame, \delta' approximately 83 degrees, together with a superluminal speed reported in the literature, \beta apparent = 3.3, yields a solution for the viewing angle and velocity of the jet in the observer's frame \delta degrees and \beta approximately 0.96. Although these results for Mrk501 must be considered tentative, the combined analysis of polarization profiles and apparent component speeds holds promise as a means of further elucidating the magnetic field structures and other parameters of parsec-scale AGN jets

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential