Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.Comment: 10 pages, 4 figures, includes supplementary material. This version adds 2D experiment

Measuring raw-material criticality of product systems through an economic product importance indicator: a case study of battery-electric vehicles

Purpose: The concept of criticality concerns the probability and the possible impacts of shortages in raw-material supply and is usually applied to regional economies or specific industries. With more and more products being highly dependent on potentially critical raw materials, efforts are being made to also incorporate criticality into the framework of life cycle sustainability assessment (LCSA). However, there is still some need for methodological development of indicators to measure raw-material criticality in LCSA. Methods: We therefore introduce "economic product importance" (EPI) as a novel parameter for the product-specific evaluation of the relevance and significance of a certain raw material for a particular product system. We thereby consider both the actual raw-material flows (life cycle inventories) and the life cycle cost. The EPI thus represents a measure for the material-specific product-system vulnerability (another component being the substitutability). Combining the product-system vulnerability of a specific product system towards a certain raw material with the supply disruption probability of that same raw material then yields the product-system specific overall criticality with regard to that raw material. In order to demonstrate our novel approach, we apply it to a case study on a battery-electric vehicle. Results: Since our approach accounts for the actual amounts of raw materials used in a product and relates their total share of costs to the overall costs of the product, no under- or over-estimation of the mere presence of the raw materials with respect to their relevance for the product system occurs. Consequently, raw materials, e.g. rare earth elements, which are regularly rated highly critical, do not necessarily reach higher criticality ranks within our approach, if they are either needed in very small amounts only or if their share in total costs of the respective product system is very low. Accordingly, in our case study on a battery-electric vehicle product system, most rare earth elements are ranked less critical than bulk materials such as copper or aluminium. Conclusion: Our EPI approach constitutes a step forward towards a methodology for the raw-material criticality assessment within the LCSA framework, mainly because it allows a product-specific evaluation of product-system vulnerability. Furthermore, it is compatible with common methods for the supply disruption probability calculation -- such as GeoPolRisk, ESP or ESSENZ -- as well as with available substitutability evaluations. The practicability and usefulness of our approach has been shown by applying it to a battery-electric vehicle

Realizing efficient topological temporal pumping in electrical circuits

Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and non-adiabatic effects. In this work, we realize a topological adiabatic pump in an electrical circuit network that supports remarkably stable and long-lasting pumping of a voltage signal. We further characterize the topology of our system by deducing the Chern number from the measured edge band structure. To achieve this, the experimental setup makes use of active circuit elements that act as time-variable voltage-controlled inductors.Comment: main (5 pages, 3 figures) plus supplement (8 pages, 4 figures

Simulating hyperbolic space on a circuit board

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter

Resilience trinity: safeguarding ecosystem functioning and services across three different time horizons and decision contexts

Ensuring ecosystem resilience is an intuitive approach to safeguard the functioning of ecosystems and hence the future provisioning of ecosystem services (ES). However, resilience is a multi-faceted concept that is difficult to operationalize. Focusing on resilience mechanisms, such as diversity, network architectures or adaptive capacity, has recently been suggested as means to operationalize resilience. Still, the focus on mechanisms is not specific enough. We suggest a conceptual framework, resilience trinity, to facilitate management based on resilience mechanisms in three distinctive decision contexts and time-horizons: i) reactive, when there is an imminent threat to ES resilience and a high pressure to act, ii) adjustive, when the threat is known in general but there is still time to adapt management, and iii) provident, when time horizons are very long and the nature of the threats is uncertain, leading to a low willingness to act. Resilience has different interpretations and implications at these different time horizons, which also prevail in different disciplines. Social ecology, ecology, and engineering are often implicitly focussing on provident, adjustive, or reactive resilience, respectively, but these different notions and of resilience and their corresponding social, ecological, and economic trade-offs need to be reconciled. Otherwise, we keep risking unintended consequences of reactive actions, or shying away from provident action because of uncertainties that cannot be reduced. The suggested trinity of time horizons and their decision contexts could help ensuring that longer-term management actions are not missed while urgent threats to ES are given priority

The Phanerozoic δ88/86Sr Record of Seawater: New Constraints on Past Changes in Oceanic Carbonate Fluxes

The isotopic composition of Phanerozoic marine sediments provides important information about changes in seawater chemistry. In particular, the radiogenic strontium isotope (87Sr/86Sr) system is a powerful tool for constraining plate tectonic processes and their influence on atmospheric CO2 concentrations. However, the 87Sr/86Sr isotope ratio of seawater is not sensitive to temporal changes in the marine strontium (Sr) output flux, which is primarily controlled by the burial of calcium carbonate (CaCO3) at the ocean floor. The Sr budget of the Phanerozoic ocean, including the associated changes in the amount of CaCO3 burial, is therefore only poorly constrained. Here, we present the first stable isotope record of Sr for Phanerozoic skeletal carbonates, and by inference for Phanerozoic seawater (δ88/86Srsw), which we find to be sensitive to imbalances in the Sr input and output fluxes. This δ88/86Srsw record varies from ∼0.25‰ to ∼0.60‰ (vs. SRM987) with a mean of ∼0.37‰. The fractionation factor between modern seawater and skeletal calcite Δ88/86Srcc-sw, based on the analysis of 13 modern brachiopods (mean δ88/86Sr of 0.176±0.016‰, 2 standard deviations (s.d.)), is -0.21‰ and was found to be independent of species, water temperature, and habitat location. Overall, the Phanerozoic δ88/86Srsw record is positively correlated with the Ca isotope record (δ44/40Casw), but not with the radiogenic Sr isotope record ((87Sr/86Sr)sw). A new numerical modeling approach, which considers both δ88/86Srsw and (87Sr/86Sr)sw, yields improved estimates for Phanerozoic fluxes and concentrations for seawater Sr. The oceanic net carbonate flux of Sr (F(Sr)carb) varied between an output of -4.7x1010mol/Myr and an input of +2.3x1010mol/Myr with a mean of -1.6x1010mol/Myr. On time scales in excess of 100Myrs the F(Sr)carb is proposed to have been controlled by the relative importance of calcium carbonate precipitates during the “aragonite” and “calcite” sea episodes. On time scales less than 20Myrs the F(Sr)carb seems to be controlled by variable combinations of carbonate burial rate, shelf carbonate weathering and recrystallization, ocean acidification, and ocean anoxia. In particular, the Permian/Triassic transition is marked by a prominent positive δ88/86Srsw-peak that reflects a significantly enhanced burial flux of Sr and carbonate, likely driven by bacterial sulfate reduction (BSR) and the related alkalinity production in deeper anoxic waters. We also argue that the residence time of Sr in the Phanerozoic ocean ranged from ∼1Myrs to ∼20Myrs

In Case of Doubt for the Suspicion?: When People Falsely Remember Facts in the News as Being Uncertain

Modern media report news remarkably fast, often before the information is confirmed. This general tendency is even more pronounced in times of an increasing demand for information, such as in the case of pressing natural phenomena or the pandemic spreading of diseases. Yet, even if early reports correctly identify their content as suspicions (rather than facts), recipients may not adequately consider the preliminary nature of such information. Theories on language processing suggest that understanding a suspicion requires its reconstruction as a factual assertion first—which can later be erroneously remembered. This would lead to a bias to remember and treat suspicions as if they were factual, rather than falling for the reverse mistake. In five experiments, however, we demonstrate the opposite pattern. Participants read news headlines with explanations for distinct events either in form of a fact or a suspicion (as still being under investigation). Both kinds of framings increased the participants’ belief in the correctness of the respective explanations to an equal extent (relative to receiving no explanation). Importantly, however, this effect was not mainly driven by a neglect of uncertainty cues. In contrast, three memory experiments (recognition and cued recall) revealed a reverse distortion: a bias to falsely remember and treat a presented “fact” as if it were merely a suspicion. These surprising results stress the importance of developing new theoretical accounts on the processing of (un-)certainty cues which take into account their broader context, such as source credibility and the presence of uncertainty in other unrelated headlines