Array optimisation for multichannel electrical resistivity tomography instruments

In recent years there has been considerable research into the selection of near-optimal arrays of electrode configurations that enhance the resolution of electrical resistivity tomography (ERT) images. Several algorithms have been developed that select resistivity measurements based on their contribution to the cumulative sensitivity of the array (Furman et al., 2004; Hennig and Weller, 2005) or its model resolution matrix (Stummer et al. , 2004; Wilkinson et al., 2006a; 2006b). Homogeneous subsurface resistivity distributions were assumed for these studies, although better results can be obtained using the same algorithms if the resistivity distribution is known a priori (Anthansiou, 2006). When compared to standard arrays, such as dipole-dipole or Wenner- Schlumberger, optimised arrays can substantially improve the resolution of the ERT image for the same number of measurements (Wilkinson et al., 2006b). The driver for researching array optimisation techniques has been the development of computer controlled ERT systems that can address arbitrary combinations of current and potential electrodes. Unfortunately all the published optimisation algorithms share a problem that is likely to impede their wider use: the arrays that they produce are inherently ‘single channel’ (SC). Since they do not take advantage of the multichannel (MC) capability of modern ERT instruments, the optimised arrays that they produce are rather inefficient to use compared to many standard arrays that are well suited to MC operation. However, we have developed a simple extension that constrains our previous algorithm to choose near-optimal configurations that also fit well into a MC measurement scheme. This extension could easily be adapted to work with the other optimisation schemes cited above

Energy absorption by "sparse" systems: beyond linear response theory

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".Comment: 8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref correcte

Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems

We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly govern the equilibration process. Multiplicity of quantum systems having the same semiclassical limit is not sufficient to obtain equilibration of any spectral modes in two-dimensional systems, while in three-dimensional systems equilibration for some spectral modes is possible if the classical relaxation rate is slow. Connections are made with upper bounds on semiclassical accuracy and with fidelity decay in the presence of a weak perturbation.Comment: 13 pages, 6 figures, submitted to Phys Rev

The detection and tracking of mine-water pollution from abandoned mines using electrical tomography

Increasing emphasis is being placed on the environmental and societal impact of mining, particularly in the EU, where the environmental impacts of abandoned mine sites (spoil heaps and tailings) are now subject to the legally binding Water Framework and Mine Waste Directives. Traditional sampling to monitor the impact of mining on surface waters and groundwater is laborious, expensive and often unrepresentative. In particular, sparse and infrequent borehole sampling may fail to capture the dynamic behaviour associated with important events such as flash flooding, mine-water break-out, and subsurface acid mine drainage. Current monitoring practice is therefore failing to provide the information needed to assess the socio-economic and environmental impact of mining on vulnerable eco-systems, or to give adequate early warning to allow preventative maintenance or containment. BGS has developed a tomographic imaging system known as ALERT ( Automated time-Lapse Electrical Resistivity Tomography) which allows the near real-time measurement of geoelectric properties "on demand", thereby giving early warning of potential threats to vulnerable water systems. Permanent in-situ geoelectric measurements are used to provide surrogate indicators of hydrochemical and hydrogeological properties. The ALERT survey concept uses electrode arrays, permanently buried in shallow trenches at the surface but these arrays could equally be deployed in mine entries or shafts or underground workings. This sensor network is then interrogated from the office by wireless telemetry (e.g: GSM, low-power radio, internet, and satellite) to provide volumetric images of the subsurface at regular intervals. Once installed, no manual intervention is required; data is transmitted automatically according to a pre-programmed schedule and for specific survey parameters, both of which may be varied remotely as conditions change (i.e: an adaptive sampling approach). The entire process from data capture to visualisation on the web-portal is seamless, with no manual intervention. Examples are given where ALERT has been installed and used to remotely monitor (i) seawater intrusion in a coastal aquifer (ii) domestic landfills and contaminated land and (iii) vulnerable earth embankments. The full potential of the ALERT concept for monitoring mine-waste has yet to be demonstrated. However we have used manual electrical tomography surveys to characterise mine-waste pollution at an abandoned metalliferous mine in the Central Wales orefield in the UK. Hydrogeochemical sampling confirms that electrical tomography can provide a reliable surrogate for the mapping and long-term monitoring of mine-water pollution

New methods ring changes for the tree of life

Relationships among prokaryotes and the origin of eukaryotes have both proven controversial, with results depending upon the gene sequences and methods used. Extensive horizontal gene transfer is one possible reason why inferring such deep phylogenetic relationships is difficult. In two recent papers, Lake and Rivera introduce new methods that can be used to reconstruct the genomic tree in the presence of horizontal gene transfers, but which suggest that a ring rather than a tree is a better representation of some parts of the history of life on Earth

FLOWERS FOR ALGERNON: THE ETHICS OF HUMAN EXPERIMENTATION ON THE INTELLECTUALLY DISABLED

Flowers for Algernon is a novel written in 1966 by Daniel Keyes. Since its publication, it has received significant critical acclaim, earning a Nebula science-fiction award, and was also adapted into a feature film. Set in the 1960s, the novel follows the story of Charlie Gordon, an intellectually disabled man who lives a simple but happy life working a cleaning job at a local bakery. Charlie’s life, however, faces an abrupt change when he is offered the opportunity to participate in a novel surgical procedure to improve his intellect. Although he doesn’t fully understand the risks of the operation, consent is provided on his behalf by his estranged sister and Charlie undergoes the experiment. The experiment is a success and Charlie develops intellectually at an alarming pace, soon surpassing the experimenters themselves. The rest of the book follows the, not all positive, changes that this intellect brings to Charlie’s life. The novel is set in a time when American scientific experimentation could often occur without fully informed consent. This article explores the ethical side of such experiments like the one performed on Charlie, namely if it is morally right to perform a potentially dangerous experimental procedure on someone who doesn’t fully understand the risks, even if it will potentially help them

New methods ring changes for the tree of life

Relationships among prokaryotes and the origin of eukaryotes have both proven controversial, with results depending upon the gene sequences and methods used. Extensive horizontal gene transfer is one possible reason why inferring such deep phylogenetic relationships is difficult. In two recent papers, Lake and Rivera introduce new methods that can be used to reconstruct the genomic tree in the presence of horizontal gene transfers, but which suggest that a ring rather than a tree is a better representation of some parts of the history of life on Earth

The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest neighbor level spacings. It was calculated for a variety of nearest neighbor level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulas obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.Comment: 26 pages, including 6 figure

Spectral correlations : understanding oscillatory contributions

We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models