No abstract

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

S U M M A R YTwo strategies are presented for obtaining the maximum spatial resolution in electrical resistivity tomography surveys using a limited number of four-electrode measurement configurations. Both methods use a linearized estimate of the model resolution matrix to assess the effects of including a given electrode configuration in the measurement set. The algorithms are described in detail, and their execution times are analysed in terms of the number of cells in the inverse model. One strategy directly compares the model resolution matrices to optimize the spatial resolution. The other uses approximations based on the distribution and linear independence of the Jacobian matrix elements. The first strategy produces results that are nearer to optimal, however the second is several orders of magnitude faster. Significantly however, both offer better optimization performance than a similar, previously published, method. Realistic examples are used to compare the results of each algorithm. Synthetic data are generated for each optimized set of electrodes using simple forward models containing resistive and/or conductive prisms. By inverting the data, it is demonstrated that the linearized model resolution matrix yields a good estimate of the actual resolution obtained in the inverted image. Furthermore, comparison of the inversion results confirms that the spatial distribution of the estimated model resolution is a reliable indicator of tomographic image quality.

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We investigate chaotic electron transport in the lowest miniband of a semiconductor superlattice with a tilted magnetic field. This experimentally accessible non-Kolmogorov-Arnol'd-Moser system involves only stationary electric and magnetic fields, but is dynamically equivalent to a time-dependent kicked harmonic oscillator. The onset of chaos strongly delocalizes the electron orbits, thus raising the electrical conductivity. When the cyclotron and Bloch frequencies are commensurate, the phase space is threaded by a stochastic web, which produces a further resonant increase in the conductivity.

Landslides pose significant risks to communities and infrastructure, and mitigating these risks relies on understanding landslide causes and triggering processes. It has been shown that geophysical surveys can significantly contribute to the characterization of unstable slopes. However, hydrological processes can be temporally and spatially heterogeneous, requiring their related properties to be monitored over time. Geoelectrical monitoring can provide temporal and volumetric distributions of electrical resistivity, which are directly related to moisture content. To date, studies demonstrating this capability have been restricted to 2‐D sections, which are insufficient to capture the full degree of spatial heterogeneity. This study is the first to employ 4‐D (i.e., 3‐D time lapse) resistivity imaging on an active landslide, providing long‐term data (3 years) highlighting the evolution of moisture content prior to landslide reactivation and showing its decline post reactivation. Crucially, the time‐lapse inversion methodology employed here incorporates movements of the electrodes on the unstable surface. Although seasonal characteristics dominate the shallow moisture dynamics during the first 2 years with surficial drying in summer and wetting in winter, in the months preceding reactivation, moisture content increased by more than 45% throughout the slope. This is in agreement with independent data showing a significant rise in piezometric heads and shallow soil moisture contents as a result of prolonged and intense rainfall. Based on these results, remediation measures could be designed and early‐warning systems implemented. Thus, resistivity monitoring that can allow for moving electrodes provides a new means for the effective mitigation of landslide risk.

A study of PCB concentrations and fluxes in lake sediments was conducted to test the “global fractionation” hypothesis that deposition of semivolatile organics will decline while more volatile congeners will be enriched in polar regions. Sediment cores were collected from 11 remote lakes in Canada ranging from 49° N to 82° N and were dated using excess 210Pb and 137Cs. Sediment extracts were analyzed for up to 90 PCB congeners by capillary GC-ECD with confirmation by GC/high-resolution MS. Total PCB (∑PCB) concentrations in surface slices ranged from 2.4 to 39 ng g-1 (dry wt) and showed no latitudinal trend. Fluxes (ng m-2 yr-1) and inventories of ∑PCB as well as total tetra- to octachlorobiphenyls declined with increasing north latitude while those for di/trichlorobiphenyls showed no latitudinal trend. The proportion of di/trichloro congeners of ∑PCB also increased significantly with latitude, while total octachlorobiphenyls declined. Maximum ∑PCB concentrations were observed in subsurface slices dating to the 1960−1970s in most lakes except those in the high Arctic, where maxima were generally in surface slices. The onset of elevated ∑PCB deposition was delayed in the high Arctic (1950−1960s) relative to the midlatitude and sub-Arctic lakes (1930−1940s). The high proportions of lower chlorinated congeners and the delayed appearance of PCBs are consistent with predictions of the global fractionation model.

For groundwater-surface water interactions to be understood in complex wetland settings, the architecture of the underlying deposits requires investigation at a spatial resolution sufficient to characterize significant hydraulic pathways. Discrete intrusive sampling using conventional approaches provides insufficient sample density and can be difficult to deploy on soft ground. Here a noninvasive geophysical imaging approach combining three-dimensional electrical resistivity tomography (ERT) and the novel application of gradient and isosurface-based edge detectors is considered as a means of illuminating wetland deposit architecture. The performance of three edge detectors were compared and evaluated against ground truth data, using a lowland riparian wetland demonstration site. Isosurface-based methods correlated well with intrusive data and were useful for defining the geometries of key geological interfaces (i.e., peat/gravels and gravels/ Chalk). The use of gradient detectors approach was unsuccessful, indicating that the assumption that the steepest resistivity gradient coincides with the associated geological interface can be incorrect. These findings are relevant to the application of this approach in settings with a broadly layered geology with strata of contrasting resistivities. In addition, ERT revealed substantial structures in the gravels related to the depositional environment (i.e., braided fluvial system) and a complex distribution of low-permeability putty Chalk at the bedrock surface-with implications for preferential flow and variable exchange between river and groundwater systems. These results demonstrate that a combined approach using ERT and edge detectors can provide valuable information to support targeted monitoring and inform hydrological modeling of wetlands.