Simultaneous optimization of gait and design parameters for bipedal robots

A walking bipedal robot’s energy efficiency depends on its gait as well as its design, whereas design changes affect the optimal gaits. We propose a method to take these interdependencies into account via simultaneous optimization of gait as well as design parameters. The method is applied to a planar robot with hybrid zero dynamics control and a torsion spring between its thighs. Periodic gaits are simulated by means of the hybrid zero dynamics. The implementation of the simultaneous optimization of gait parameters and spring stiffness via sequential quadratic programming is presented. Subsequently, an error analysis is performed to gain good convergence and short computation times of the optimization. The evaluation of gradients is identified as crucial for the algorithm’s convergence and therefore performed via complex step derivative approximations. The resulting implementation exhibits good convergence behavior and is provided as supplement to this paper. At 2.3 m/s, the simultaneous optimization results in savings in energy expenditure of up to 55%. A consecutive optimization of first gait and then stiffness yields only 11%, demonstrating the advantage of the presented method

Evolution of Atmospheric O2 Through the Phanerozoic, Revisited

An oxygen-rich atmosphere is essential for complex animals. The early Earth had an anoxic atmosphere, and understanding the rise and maintenance of high O2 levels is critical for investigating what drove our own evolution and for assessing the likely habitability of exoplanets. A growing number of techniques aim to reproduce changes in O2 levels over the Phanerozoic Eon (the past 539 million years). We assess these methods and attempt to draw the reliable techniques together to form a consensus Phanerozoic O2 curve. We conclude that O2 probably made up around 5–10% of the atmosphere during the Cambrian and rose in pulses to ∼15–20% in the Devonian, reaching a further peak of greater than 25% in the Permo-Carboniferous before declining toward the present day. Evolutionary radiations in the Cambrian and Ordovician appear consistent with an oxygen driver, and the Devonian “Age of the Fishes” coincides with oxygen rising above 15% atm. ▪ An oxygen-rich atmosphere is essential for complex animals such as humans. ▪ We review the methods for reconstructing past variation in oxygen levels over the past 539 million years (the Phanerozoic Eon). ▪ We produce a consensus plot of the most likely evolution of atmospheric oxygen levels. ▪ Evolutionary radiations in the Cambrian, Ordovician, and Devonian periods may be linked to rises in oxygen concentration

VisualPDE: rapid interactive simulations of partial differential equations

Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we provide a means to go one step further in using computers to understand complex models through instantaneous and interactive exploration. This ubiquitous infrastructure has enormous potential in education, outreach and research. Here, we present VisualPDE, an online, interactive solver for a broad class of 1D and 2D partial differential equation (PDE) systems. Abstract dynamical systems concepts such as symmetry-breaking instabilities, subcritical bifurcations and the role of initial data in multistable nonlinear models become much more intuitive when you can play with these models yourself, and immediately answer questions about how the system responds to changes in parameters, initial conditions, boundary conditions or even spatiotemporal forcing. Importantly, VisualPDE is freely available, open source and highly customisable. We give several examples in teaching, research and knowledge exchange, providing high-level discussions of how it may be employed in different settings. This includes designing web-based course materials structured around interactive simulations, or easily crafting specific simulations that can be shared with students or collaborators via a simple URL. We envisage VisualPDE becoming an invaluable resource for teaching and research in mathematical biology and beyond. We also hope that it inspires other efforts to make mathematics more interactive and accessible.Comment: 19 pages, 7 figures. This is a companion paper to the website https://visualpde.com

How frequent are close supermassive binary black holes in powerful jet sources?

24 pages, 36 figures. © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)Supermassive black hole binariesmay be detectable by an upcoming suite of gravitationalwave experiments. Their binary nature can also be revealed by radio jets via a short-period precession driven by the orbital motion as well as the geodetic precession at typically longer periods. We have investigated Karl G. Jansky Very Large Array and Multi-Element Radio Linked Interferometer Network (MERLIN) radio maps of powerful jet sources for morphological evidence of geodetic precession. For perhaps the best-studied source, Cygnus A, we find strong evidence for geodetic precession. Projection effects can enhance precession features, for which we find indications in strongly projected sources. For a complete sample of 33 3CR radio sources, we find strong evidence for jet precession in 24 cases (73 per cent). The morphology of the radio maps suggests that the precession periods are of the order of 10 6- 10 7 yr. We consider different explanations for the morphological features and conclude that geodetic precession is the best explanation. The frequently observed gradual jet angle changes in samples of powerful blazars can be explained by orbital motion. Both observations can be explained simultaneously by postulating that a high fraction of powerful radio sources have subparsec supermassive black hole binaries.We consider complementary evidence and discuss if any jetted supermassive black hole with some indication of precession could be detected as individual gravitational wave source in the near future. This appears unlikely, with the possible exception of M87.Peer reviewedFinal Published versio

Enhanced clay formation key in sustaining the Middle Eocene Climatic Optimum

The Middle Eocene Climatic Optimum (around 40 million years ago) was a roughly 400,000-year-long global warming phase associated with an increase in atmospheric CO2 concentrations and deep-ocean acidifcation that interrupted the Eocene’s long-term cooling trend. The unusually long duration, compared with early Eocene global warming phases, is puzzling as temperature-dependent silicate weathering should have provided a negative feedback, drawing down CO2 over this timescale. Here we investigate silicate weathering during this climate warming event by measuring lithium isotope ratios (reported as δ7 Li), which are a tracer for silicate weathering processes, from a suite of open-ocean carbonate-rich sediments. We fnd a positive δ7 Li excursion—the only one identifed for a warming event so far —of ~3‰. Box model simulations support this signal to refect a global shift from congruent weathering, with secondary mineral dissolution, to incongruent weathering, with secondary mineral formation. We surmise that, before the climatic optimum, there was considerable soil shielding of the continents. An increase in continental volcanism initiated the warming event, but it was sustained by an increase in clay formation, which sequestered carbonate-forming cations, short-circuiting the carbonate–silicate cycle. Clay mineral dynamics may play an important role in the carbon cycle for climatic events occurring over intermediate (i.e., 100,000 year) timeframes

Not So Fast: Swimming Behavior of Sailfish during Predator–Prey Interactions using High-Speed Video and Accelerometry

Billfishes are considered among the fastest swimmers in the oceans. Despite early estimates of extremely high speeds, more recent work showed that these predators (e.g., blue marlin) spend most of their time swimming slowly, rarely exceeding 2 m s(-1). Predator-prey interactions provide a context within which one may expect maximal speeds both by predators and prey. Beyond speed, however, an important component determining the outcome of predator-prey encounters is unsteady swimming (i.e., turning and accelerating). Although large predators are faster than their small prey, the latter show higher performance in unsteady swimming. To contrast the evading behaviors of their highly maneuverable prey, sailfish and other large aquatic predators possess morphological adaptations, such as elongated bills, which can be moved more rapidly than the whole body itself, facilitating capture of the prey. Therefore, it is an open question whether such supposedly very fast swimmers do use high-speed bursts when feeding on evasive prey, in addition to using their bill for slashing prey. Here, we measured the swimming behavior of sailfish by using high-frequency accelerometry and high-speed video observations during predator-prey interactions. These measurements allowed analyses of tail beat frequencies to estimate swimming speeds. Our results suggest that sailfish burst at speeds of about 7 m s(-1) and do not exceed swimming speeds of 10 m s(-1) during predator-prey interactions. These speeds are much lower than previous estimates. In addition, the oscillations of the bill during swimming with, and without, extension of the dorsal fin (i.e., the sail) were measured. We suggest that extension of the dorsal fin may allow sailfish to improve the control of the bill and minimize its yaw, hence preventing disturbance of the prey. Therefore, sailfish, like other large predators, may rely mainly on accuracy of movement and the use of the extensions of their bodies, rather than resorting to top speeds when hunting evasive prey

Integrating network analysis, sensor tags, and observation to understand shark ecology and behavior

Group living in animals is a well-studied phenomenon, having been documented extensively in a wide range of terrestrial, freshwater, and marine species. Although social dynamics are complex across space and time, recent technological and analytical advances enable deeper understanding of their nature and ecological implications. While for some taxa, a great deal of information is known regarding the mechanistic underpinnings of these social processes, knowledge of these mechanisms in elasmobranchs is lacking. Here, we used an integrative and novel combination of direct observation, accelerometer biologgers, and recent advances in network analysis to better understand the mechanistic bases of individual-level differences in sociality (leadership, network attributes) and diel patterns of locomotor activity in a widespread marine predator, the lemon shark (Negaprion brevirostris). We found that dynamic models of interaction based on Markov chains can accurately predict juvenile lemon shark social behavior and that lemon sharks did not occupy consistent positions within their network. Lemon sharks did however preferentially associate with specific group members, by sex as well as by similarity or nonsimilarity for a number of behavioral (nonsimilarity: leadership) and locomotor traits (similarity: proportion of time swimming "fast," mean swim duration; nonsimilarity: proportion of swimming bursts/transitions between activity states). Our study provides some of the first information on the mechanistic bases of group living and personality in sharks and further, a potential experimental approach for studying fine-scale differences in behavior and locomotor patterns in difficult-to-study organisms

Potential Direct and Indirect Effects of Climate Change on a Shallow Natural Lake Fish Assemblage

Much uncertainty exists around how fish communities in shallow lakes will respond to climate change. In this study, we modelled the effects of increased water temperatures on consumption and growth rates of two piscivores (northern pike [Esox lucius] and largemouth bass [Micropterus salmoides]) and examined relative effects of consumption by these predators on two prey species (bluegill [Lepomis macrochirus] and yellow perch [Perca flavescens]). Bioenergetics models were used to simulate the effects of climate change on growth and food consumption using predicted 2040 and 2060 temperatures in a shallow Nebraska Sandhill lake, USA. The patterns and magnitude of daily and cumulative consumption during the growing season (April–October) were generally similar between the two predators. However, growth of northern pike was always reduced (–3 to –45% change) compared to largemouth bass that experienced subtle changes (4 to –6% change) in weight by the end of the growing season. Assuming similar population size structure and numbers of predators in 2040–2060, future consumption of bluegill and yellow perch by northern pike and largemouth bass will likely increase (range: 3–24%), necessitating greater prey biomass to meet future energy demands. The timing of increased predator consumption will likely shift towards spring and fall (compared to summer), when prey species may not be available in the quantities required. Our findings suggest that increased water temperatures may affect species at the edge of their native range (i.e. northern pike) and a potential mismatch between predator and prey could exist

Assessing hydrological controls on the lithium isotope weathering tracer

To investigate the impact of riverine discharge and weathering intensity on lithium isotopes (δ7Li) in a mono-lithological terrain, this study examines the dissolved load and leached suspended load (exchangeable, oxide, and clay fractions) from Icelandic rivers spanning a wide range of discharge, weathering rates, and weathering intensity. The δ7Lidissolved co-varies inversely with the discharge, confirming that water-rock interaction time is a primary control on the secondary mineral formation that fractionates Li isotopes. The “boomerang” shape observed in global rivers between the weathering intensity (i.e. W/D = weathering rate/denudation rate) and δ7Lidissolved also exists for these basaltic rivers at low to medium W/D. However, these rivers do not extend to such low δ7Lidissolved values as seen in the global compilation at low W/D, indicating that there is a lithological control on this relationship arising from the type of the lithology-specific secondary minerals forming and their precipitation rates. In addition, the Δ7Lix-dissolved between each leached solid phase and the dissolved load also co-varies with discharge. At low discharge (long water-rock interaction times), Δ7Lix-dissolved values agree with experimentally-determined equilibrium values, whereas less fractionated values are observed at higher discharge (shorter water-rock interaction times). As a result, there is a different relationship between W/D and Δ7Liclay-source in this basaltic terrain than previously reported from global multi-lithological river sediment samples, with clay leachates from Iceland more closely mimicking the boomerang shape of the dissolved load. However, the relationship between δ7Li and weathering processes is complicated because the fractionation between the clay fraction and the dissolved load is not constant but varies with both W/D and discharge. Overall, this study confirms the utility of Li isotopes as a tracer of modern and palaeo-weathering processes, and also has important implications for the specific interpretations of detrital δ7Li values, which may be more sensitive to weathering parameters than previously thought

Assessing hydrological controls on the lithium isotope weathering tracer

To investigate the impact of riverine discharge and weathering intensity on lithium isotopes (δ7Li) in a mono-lithological terrain, this study examines the dissolved load and leached suspended load (exchangeable, oxide, and clay fractions) from Icelandic rivers spanning a wide range of discharge, weathering rates, and weathering intensity. The δ7Lidissolved co-varies inversely with the discharge, confirming that water-rock interaction time is a primary control on the secondary mineral formation that fractionates Li isotopes. The “boomerang” shape observed in global rivers between the weathering intensity (i.e. W/D = weathering rate/denudation rate) and δ7Lidissolved also exists for these basaltic rivers at low to medium W/D. However, these rivers do not extend to such low δ7Lidissolved values as seen in the global compilation at low W/D, indicating that there is a lithological control on this relationship arising from the type of the lithology-specific secondary minerals forming and their precipitation rates. In addition, the Δ7Lix-dissolved between each leached solid phase and the dissolved load also co-varies with discharge. At low discharge (long water-rock interaction times), Δ7Lix-dissolved values agree with experimentally-determined equilibrium values, whereas less fractionated values are observed at higher discharge (shorter water-rock interaction times). As a result, there is a different relationship between W/D and Δ7Liclay-source in this basaltic terrain than previously reported from global multi-lithological river sediment samples, with clay leachates from Iceland more closely mimicking the boomerang shape of the dissolved load. However, the relationship between δ7Li and weathering processes is complicated because the fractionation between the clay fraction and the dissolved load is not constant but varies with both W/D and discharge. Overall, this study confirms the utility of Li isotopes as a tracer of modern and palaeo-weathering processes, and also has important implications for the specific interpretations of detrital δ7Li values, which may be more sensitive to weathering parameters than previously thought