Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences

Published by Royal Society, The
Print ISSN: 0080-4614
Life arose on Earth within a billion years (1 Ga) after planetary accretion and core formation. The geological record, which begins 3.8 Ga BP, indicates environmental conditions much like today's, except for the absence of oxygen. By 3.5 Ga BP microbial ecosystems were already colonizing shallow marine hydrothermal environments along shorelines of volcanic islands. Although similar environments could have existed more than 3.8 Ga BP, they may not have been the spawning grounds of life. Geophysical models of the first 600 Ma of Earth history following accretion and core formation point to a period of great environmental disequilibrium. In such an environment the passage of energy from Earth's interior and from the Sun through gas-liquid-solid domains and their boundaries with each other generated a dynamically interacting, complex hierarchy of self-organized structures, ranging from bubbles at the sea-air interface to tectonic plates. Nested within this hierarchy were the precursors of living systems. The ability of a planet to produce such a hierarchy is speculated to be a prerequisite for the origin and sustenance of life. Application of this criterion to Mars, which apparently experienced no plate tectonism, argues against the origin of martian life. Because only further geological and biogeochemical exploration of the planet can place these qualitative speculations on firm ground, the search for evidence of extinct life on Mars continues to be of highest scientific priority.
Two examples of uplifted basement have been studied in the Lhasa Terrane of the Tibetan Plateau. The Nyainqentanglha orthogneisses are bounded by staurolite--garnet schists to the north which record prograde metamorphism at 5.0 ± 1.3 kbar, 610 ± 70 degrees C Garnet--sillimanite xenoliths within the orthogneiss suggest that peak temperatures reached at least 700 ± 70 degrees C at 5.1 ± 2.5 kbar. These P/T fields reflect high T/low P metamorphism during Eocene subduction, and indicate that the syntectonic Nyainqentanglha orthogneiss was emplaced at depths greater than 10 km. Sillimanite-bearing assemblages from the Amdo gneisses in the northern Lhasa Terrane provide evidence of crustal anatexis at temperatures 680 degrees C. This event is poorly constrained in time but is probably Cambrian or earlier. Within the Kunlun Terrane, biotite and garnet isograds north of the Xidatan Fault indicate an increase in metamorphic grade from north to south, reaching peak metamorphism at 470 ± 30 degrees C, 4.3 ± 1.5 kbar synchronous with the emplacement of the Triassic batholith. Regional metamorphism was followed by uplift of at least 2 km before emplacement of post-tectonic, early Jurassic granites.
The concept of distributed moral responsibility (DMR) has a long history. When it is understood as being entirely reducible to the sum of (some) human, individual and already morally loaded actions, then the allocation of DMR, and hence of praise and reward or blame and punishment, may be pragmatically difficult, but not conceptually problematic. However, in distributed environments, it is increasingly possible that a network of agents, some human, some artificial (e.g. a program) and some hybrid (e.g. a group of people working as a team thanks to a software platform), may cause distributed moral actions (DMAs). These are morally good or evil (i.e. morally loaded) actions caused by local interactions that are in themselves neither good nor evil (morally neutral). In this article, I analyse DMRs that are due to DMAs, and argue in favour of the allocation, by default and overridably, of full moral responsibility (faultless responsibility) to all the nodes/agents in the network causally relevant for bringing about the DMA in question, independently of intentionality. The mechanism proposed is inspired by, and adapts, three concepts: back propagation from network theory, strict liability from jurisprudence and common knowledge from epistemic logic.
The recognition of Mesozoic and Cenozoic terranes can best be made from palaeomagnetic, structural and palaeontological studies, but older regions of continental crust require geochemical constraints to evaluate crustal growth through terrane accretion. For Precambrian shields, the pattern of Pb and Nd isotopic provinces may reveal the mechanism of crustal growth. The Afro-Arabian Shield was generated by calc-alkaline magmatism between 900 and 600 Ma ago. This example of Pan-African crustal growth underlies an area of at least 1.2 × 106 km2, which may extend to 3.5 × 106 km2 beneath Phanerozoic sediments and Tertiary volcanic cover. Field evidence and trace element geochemistry suggest that Pan-African tectonics began as a series of intra-oceanic island arcs that were accreted to form continental lithosphere over a period of 300 Ma. The great majority of Nd and Pb isotope ratios obtained for igneous rocks from the shield are indicative of a mantle magma source. Although many of the dismembered ophiolites cannot be identified with inter-terrane sutures in their present location, the eastern margin of the Nabitah orogenic belt is a major tectonic break that coincides with a critical boundary between Nd and Pb isotopic provinces and is marked by a linear array of ophiolite fragments across the length of the shield. Other terrane boundaries have not been identified conclusively, both because coeval island arcs can not be distinguished readily on isotopic grounds and because many ophiolites are allochthonous. However, the calculated rates of crustal growth (measured as volume of magma, extracted from the mantle per unit time) between 900 and 600 Ma are similar to those calculated for Phanerozoic terranes from the Canadian Cordillera. Such high rates in the Afro-Arabian Shield suggest that island arc terranes have accreted along a continental margin now exposed in NE Africa, together with minor continental fragments. If crustal growth rates during this time were no greater than contemporary rates, ca. 4000 km of arc length are required, which is considerably less than that responsible for crustal growth in the SW Pacific.
The main characteristics that differentiate a developed fast reactor fuel cycle from the thermal reactor fuel cycles operating now are the higher fissile content of the fuel, the greater incentive to reprocess fuel at shorter delay times and the elimination of uranium mining. The local and global environmental impacts of a typical fuel cycle normalized to 1 GWe a of output are estimated, including those from the fabrication, transport and reprocessing of fuel and from reactor operations. Radioactive emissions and radiation doses arising from these operations are compared with those from thermal reactor cycles. The risks of accidental discharges from reprocessing plants are discussed, but reactor accidents are not included. The requirements for safeguards are described. Typical inventories of radioactive wastes arising from reprocessing and from decommissioning have been calculated; the management and disposal of these wastes will pose no significant new problems. The overall result is that a transition from thermal to fast reactor fuel cycles should not result in any increase in environmental impact.
Schematic of how BXD works with a reaction coordinate, ρ, split into m boxes.
In this article we briefly review the Boxed Molecular Dynamics (BXD) method, which allows analysis of thermodynamics and kinetics in complicated molecular systems. BXD is a multiscale technique, in which thermodynamics and long-time dynamics are recovered from a set of short-time simulations. In this article, we review previous applications of BXD to peptide cyclization, diamond etching, solution-phase organic reaction dynamics, and desorption of ions from self-assembled monolayers (SAMs). We also report preliminary results of simulations of diamond etching mechanisms and protein unfolding in AFM experiments. The latter demonstrate a correlation between the protein’s structural motifs and its potential of mean force (PMF). Simulations of these processes by standard molecular dynamics (MD) is typically not possible, since the experimental timescales are very long. However, BXD yields well-converged and physically meaningful results. Compared to other methods of accelerated MD, our BXD approach is very simple; it is easy to implement, and it provides an integrated approach for simultaneously obtaining both thermodynamics and kinetics. It also provides a strategy for obtaining statistically meaningful dynamical results in regions of configuration space that standard MD approaches would visit only very rarely.
Palaeomagnetic data from Permian, Triassic and Jurassic bedded rocks, to which attitudinal corrections can be applied, yield palaeolatitudes concordant with those of ancestral North America, but very large predominantly anticlockwise rotations about vertical axes. Data from Cretaceous rocks yield apparent palaeolatitudinal displacements that increase westward. Small or negligible displacements are obtained from the Omineca Belt. Intermediate displacements (1000-2000 km) from the Intermontane Belt, are based on data from Cretaceous bedded sequences. Further to the west in the Coast Belt, larger apparent displacements (greater than 2000 km) have been obtained from plutons for which no attitudinal control is yet available. Data from Eocene rocks are concordant. Possibilities to consider are as follows: (a) little or no displacement and tilting to the southwest at about 30 degrees; (b) large (greater than 2000 km in the Coast Belt) northward displacement since mid-Cretaceous time preceded by southward displacement of comparable magnitude in Juro-Cretaceous time; (c) lesser (1000-2000 km) overall displacement coupled with variable and lesser tilts to the south and southeast of plutons of the Coast Belt. Under hypothesis (a) the western Cordillera was formed and has remained in approximately its present position relative to ancestral North America; data from bedded volcanics of the Intermontane Belt are not consistent with this hypothesis. From the evidence currently available we favour hypotheses (b) or (c), although more data from bedded sequences are required. It is noteworthy that hypotheses (a) and (c) predict tilt directions that differ by about 90 degrees and hence ought to be distinguishable by geological studies.
The overall status of the fast breeder reactor (FBR) system is periodically reviewed in France. In 1983, a report was prepared on the status and prospects of the FBR system at the request of the then Minister of Industry. Five years later, Electricite de France (EdF) and the French Atomic Energy Commission (CEA) jointly updated this report. The FBR reactor system economic considerations mentioned here are taken from the work performed in 1987-88 for this updating. The position in 1983 is reviewed to highlight concrete developments. Developments that have occurred since then are presented, along with the prospects that today enable us to define better the technical and economic potential of the FBR system. In conclusion, the effects of these findings on desirable directions are discussed, in particular with regard to European FBR cooperation.
CopperII complexes of the fatty acids exhibit a thermotropic liquid crystalline phase of the columnar type. X-ray diffraction studies of this mesophase indicate that the spine of a column is made of regularly stacked dicopper tetracarboxylate cores, which are surrounded by disordered, liquid-like alkyl chains. In turn, the column axes occupy the nodes of a two-dimensional hexagonal lattice. Examination of the local environment of the copper atoms by Cu Kα EXAFS spectroscopy reveals insignificant changes in bond lengths within the binuclear core upon the transition from the lamellar crystalline phase to the columnar mesophase. However, a slight, but sharp, decrease of the magnetic moment of the dicopper unit is observed at the solid-mesophase transition temperature (Δ μ eff≈ -0.04 μ B). The columnar mesophase, and the crystalline phase alike, obey a Bleaney-Bowers relation. The singlet-triplet gap is higher in the former (-2J = 310-330 cm-1 against 290-300 cm-1). DirhodiumII, II complexes of selected fatty acids were prepared, and their thermal behaviour was investigated. They exhibit the same thermotropic columnar mesophase as their CuII congeners, reflecting the presence of isostructural dimetallic cores in both series. The metal-metal single bond that is present in these dirhodiumII, II mesogens is Raman active (ν Rh-Rh≈ 350 cm-1); it is a potential probe of the change in molecular and supramolecular structures of this class of compounds at their phase transition. DirutheniumII, II complexes of fatty acids were obtained by CrII reduction of the mixed-valence chlorodirutheniumII, III tetrabutyrate, followed by ligand exchange with the appropriate carboxylic acid. Magnetic susceptibility studies indicate that these dirutheniumII, II carboxylates have an Ms = 0 ground state and a thermally accessible Ms = ± 1 excited state, suggesting a zero-field split (D ≈ 300 cm-1) σ 2π 4δ 2(δ *π *)4 configuration. The formation of a columnar liquid-crystalline phase is reflected by a sharp increase in the magnetic moment of these complexes at the phase transition (Δ μ eff≈ + 0.15 μ B).
The basic advantage, not to say the raison d'etre of fast neutron reactors, is clear cut. This type of nuclear reactor is the only one which makes possible to use in principle the whole and in practice a large part of the fission energy of natural uranium. By this it is meant the energy which would be released if all nuclei present in natural uranium could be fissioned. Slow neutron reactors in current use today release only a small fraction of the total energy.
Twenty-three trees from widely different geographic locations and different environments were analysed for the δ D and δ 13C records. The δ D values suggested that the temperature of the Earth's surface rose over the past 100 years and probably for the past 1000 years. The rate of warming appears to be latitude dependent, greatest in the cooler areas. The δ 13C record, obtained for seven of the 23 trees, contain the δ 13C decrease due to the anthropogenic effect, the addition of CO2 from coal and petroleum burning. This effect appears to be twice as high in the Northern Hemisphere as in the Southern Hemisphere.
The seismic velocity anomalies resolved by seismic tomography are associated with variations in density that lead to convective flow and to dynamically maintained topography at the Earth's surface, the core--mantle boundary (CMB), and any interior chemical boundaries that might exist. The dynamic topography resulting from a given density field is very sensitive to viscosity structure and to chemical stratification. The mass anomalies resulting from dynamic topography have a major effect on the geoid, which places strong constraints on mantle structure. Almost 90% of the observed geoid can be explained by density anomalies inferred from tomography and a model of subducted slabs, along with the resulting dynamic topography predicted for an Earth model with a low-viscosity asthenosphere (ca. 10^(20) Pa s) overlying a moderate viscosity (ca. 10^(22.5) Pa s) lower mantle. This viscosity stratification would lead to rapid mixing in the asthenosphere, with little mixing in the lower mantle. Chemically stratified models can also explain the geoid, but they predict hundreds of kilometres of dynamic topography at the 670 km discontinuity, a prediction currently unsupported by observation. A low-viscosity or chemically distinct D" layer tends to decouple CMB topography from convective circulation in the overlying mantle. Dynamic topography at the surface should result in long-term changes in eustatic sea level.
The present state of research and development into optical fibre systems for applications in telecommunications is reviewed and some of the principal problems remaining are discussed. Attenuations close to the intrinsic limits of the materials available have been reached in laboratory fibres and losses in optical cables installed under normal working conditions are below 5 dB/km. Bandwidths available range from 20 MHz km, in step-index multimode fibres with light emitting diode sources, to 10 GHz km with single-mode fibres and semiconductor lasers. If a truly monochromatic laser source operating in the region of minimum material dispersion becomes available then individual fibre capacities up to, or beyond, 100 GHz km are feasible. The major problems in cabling have already been largely overcome but further improvements in fibre strength, homogeneity and reproducibility are awaited. The difficulties are technological rather than fundamental and will succumb to good innovative engineering within the next few years. The same may be said of the requirements for such mundane, but vitally important, components as splices, connectors, couplers and even the lowly jack plug. Excellent and encouraging progress is being made with all of these items. Of the major hurdles remaining, that of a suitable optical source is by far the most difficult. The lifetime and reliability of existing semiconductor lasers are improving only slowly and need to be increased by at least an order of magnitude. It would also be an advantage if their line width, coherence and beam quality could be made to approximate more closely those of an ideal laser. Fortunately light emitting diodes can also be used if adequate lasers do not become available, but at the expense of system bandwidth and repeater spacing. Technological forecasting is fraught with hazards for the unwary but it is reasonable to expect systems to be operating in the telephone network in the 1980s at capacities from 140 Mbit/s to 500 Mbit/s at repeater spacings of at least 5 km and perhaps as high as 20 km. Serious study of the application of optical fibres to underwater cables will also have begun. If simple fibre cables can be made cheaply enough for use in installations to individual subscribers a wide range of new developments become possible, but these problems are more relevant to the 1990s.
This paper extends the work described in a previous paper by one of the authors (Altmann 1957). The spherical harmonics that belong to the irreducible representations of the cubic groups are now given up to and including l = 12. Also, for all point groups the expansions in spherical harmonics that are given belong to the separate columns of the irreducible representations (whereas before they were linear combinations of such functions). Accordingly, full tables for the irreducible representations for all crystallographic point groups are required and are given in the paper. Finally, a technique is described, and used throughout in the tables, to orthogonalize several expansions that belong to the same column of the same irreducible representation. Therefore, the different expansions listed in the tables are always fully orthogonal.
A number of approaches to multispectral image segmentation and classification are considered. The methods range from the simple Bayesian decision rule for classification of image data on pixel-by-pixel basis, to sophisticated algorithms using contextual information. Both the spatial pixel category dependencies and the two-dimensional correlation-type contextual information have been incorporated in decision-making schemes. The aim of these algorithms is to achieve a greater reliability in the process of interpretation of remote-sensing data. -Author
Interpretation of lunar seismic data results in a lunar model consisting of at least four and possibly five distinguishable zones: (I) the 50-60 km thick crust characterized by seismic velocities appropriate for plagioclaise rich materials, (II) the 250 km thick upper mantle characterized by seismic velocities consistent with an olivine-pyroxene composition, (III) the 500 km thick middle mantle characterized by a high Poisson's ratio, (IV) the lower mantle characterized by high shear-wave attenuation, and possibly (V) a core of radius between 170 and 360 km characterized by a greatly reduced compressional wave velocity. The Apollo seismic network detects several thousand deep moonquake signals annually. Repetitive signals from 60 deep moonquake hypocentres can be identified. The occurrence characteristics of the moonquakes from the individual moonquake hypocentres are well correlated with lunar tidal phases and display tidal periodicities of 1 month, 7$\frac{1}{2}$ months, and 6 years. With several possible exceptions, the deep moonquake foci located to date occur in three narrow belts on the near side of the Moon, and are concentrated at depths of 800-1000 km. The locations of 17 shallow moonquake foci, although not as accurate as those of the deep foci, show fair agreement with the deep moonquake belts. Focal depths calculated for the shallow moonquakes range from 0-300 km. The moonquakes of a particular moonquake belt, or a region within a belt, tend to occur near the same tidal phase suggesting similar focal mechanisms. Deep moonquake magnitudes range from about 0.5 to 1.3 on the Richter scale with a total energy release estimated to be about 10$^{11}$ ergs (10$^{4}$ J) annually. The largest shallow moonquakes have magnitudes of 4-5 and release about 10$^{15}$-10$^{18}$ ergs (10$^{8}$-10$^{11}$ J) each. Tidal deformation of a rigid lunar lithosphere overlying a reduced-rigidity asthenosphere leads to concentrations of strain energy near the base of the lithosphere. Although tidal strain energy can account for the deep moonquakes in this model, it cannot account for the shallow moonquakes. Tidal stresses within the lunar lithosphere range from about 0.1 to 1 bar (10$^{4}$-10$^{15}$ Pa). This low level of tidal stresses suggests that tides act as a triggering mechanism. The secular accumulation of strain implied by the uniform polarities of the deep moonquake signals probably results from weak convection. A convective mechanism could explain the distribution of moonquakes, the Earth-side topographic bulge, the distribution of filled mare basins, and the ancient lunar magnetic field.
Geochronological data from the Golmud--Lhasa section across the Tibetan Plateau indicate progressively younger periods of magmatism from north to south associated with successively younger ocean closures. Pre-collision Eocene magmatism (50-40 Ma) exposed along the southern margin of the Lhasa Terrane in the Gangdise Belt resulted from anatexis of mid-Proterozoic crust (~ 1000 Ma) at depths greater than 10 km, but at higher crustal levels subduction-related intrusions were predominantly mantle-derived with ~ 30% crustal assimilation. Intrusions from the northern Lhasa Terrane are early Cretaceous in age (130-110 Ma). These form a bimodal suite comprised of two-mica granites derived from anatexis of Mid-Proterozoic crust and of biotite-hornblende granodiorites from about 60% crustal assimilation by mantle magmas above a post-collision subduction zone. They place a minimum constraint on collision between the Lhasa and Qiangtang Terranes of 130 Ma. Granite magmatism from the Kunlun Mountains is late Permian--early Jurassic in age (260-190 Ma). The Kunlun batholith represents reworked mid-Proterozoic crust (1400-1000 Ma) at an active continental margin from 260-240 Ma. Post-tectonic granites were emplaced in a post-collision setting (200-190 Ma). Collision between the Qiangtang and Kunlun Terranes is dated as end-Triassic. Nd model ages of sediments from across the plateau record uplift and erosion of young source regions throughout the Phanerozoic confirming that the Tibetan Plateau is the site of multiple continental collision through time. Phanerozoic magmagenesis throughout the plateau requires considerable crustal reworking and limited crustal growth which suggests thickened continental crust in the region may predate the most recent Eocene collision.
Two large east-trending granitic batholiths are exposed on the plateau of Central Tibet. In the southern Lhasa Terrane, north of the Zangbo Suture, the Gangdise Belt is a calc-alkaline composite batholith dominated by monzodiorites, tonalites, granodiorites and monzogranites. Trace elements indicate that strongly fractionated melts were emplaced at an active continental margin; deeper crustal levels of the batholith are exposed in the crustally-derived Nyainqentanglha orthogneiss. Along the northern edge of the plateau, a syn-tectonic calcic to calc-alkaline suite of tonalites, granodiorites and monzogranites forms the Kunlun batholith with posttectonic post-tectonic granites emplaced to the south. The Kunlun intrusions are derived from anatexis of a garnet-bearing source at intermediate crustal depths above an active or recently active continental margin. Between these two batholiths, a bimodal suite of metaluminous tonalite-granodiorite and peraluminous two-mica granite is exposed in the northern Lhasa Terrane, indicative of melting both in the upper crust and at deeper levels in the crust or upper mantle. This association suggests a post-collision setting.
Technical prototypes of air retaining surfaces. (a) First measurement with a 7 m boat with a hydrophobic air retaining hull at the German Development Centre for Ship Technology and Transport Systems (DST) resulted in a drag reduction about 10%. (b) SEM image of the micropillars on a prototypical bionic surface. (c) Submerged sample of surface covered with hydrophobic carbon nanotubes (CNT), retaining an air layer under water. (d) Schematic of the Air Retaining Grids (AirGrids).
Possible savings within the three scenarios selected.
Biological prototypes with persistent air layers. (a) Leaf of the floating fern Salvinia molesta. (b) Backswimmer Notonecta. (c) SEM of the hierarchically structured, eggbeater like shaped trichomes on the surface of Salvinia responsible for the air retention. (d) Hierarchical structure on the surface of Notonecta. Long hairs (setae) and a dense floor of 'microtrichia' stabilize the air layer. Sources: (a) [29]; (b) [30].
Images of the ships included in this study. (a) The bulk Carrier Ikuna, (b) Crude Oil Tanker comparable to Prem Divya, (c) a container ship representing the Five Container Ships of this class, (d) the Ultra Large Container Vessel Emma Maersk and (e) the Cruise Ship Queen Mary II. Sources: (a) with kind permission from Cody Williams [43]; (b) adapted [44]; (c) [45]; (d) adapted from [46]; (e) adapted from [47].
Cite this article: Busch J, Barthlott W, Brede M, Terlau W, Mail M. 2019 Bionics and green technology in maritime shipping: an assessment of the effect of Salvinia air-layer hull coatings for drag and fuel reduction. One contribution of 14 to a theme issue 'Bioinspired materials and surfaces for green science and technology'.
Monitoring sea ice and iceberg activity in West Antarctica. (a) Monitoring sites, using automated cameras (black circles) and manual observations (white circle), of sea-ice extent in time and space. Monitoring sites of both sea-ice extent and annual iceberg scouring (red circles) at Rothera (bottom red circle) and Carlini (top red circle) [9,21]. (b) Relationship between duration of fast-ice cover each year and ice scouring on the seabed at Rothera and Carlini (inner bay in orange, outer bay in red) stations. The y-axis shows the proportion of the monitored seabed from a 5-25 m depth hit by icebergs. Pearson's correlation line (−0.86, p < 0.001) drawn through Rothera data only. 
Sea ice, including icebergs, has a complex relationship with the carbon held within animals (blue carbon) in the polar regions. Sea-ice losses around West Antarctica’s continental shelf generate longer phytoplankton blooms but also make it a hotspot for coastal iceberg disturbance. This matters because in polar regions ice scour limits blue carbon storage ecosystem services, which work as a powerful negative feedback on climate change (less sea ice increases phytoplankton blooms, benthic growth, seabed carbon and sequestration). This resets benthic biota succession (maintaining regional biodiversity) and also fertilizes the ocean with nutrients, generating phytoplankton blooms, which cascade carbon capture into seabed storage and burial by benthos. Small icebergs scour coastal shallows, whereas giant icebergs ground deeper, offshore. Significant benthic communities establish where ice shelves have disintegrated (giant icebergs calving), and rapidly grow to accumulate blue carbon storage. When 5000km2 giant icebergs calve, we estimate that they generate approximately 106 tonnes of immobilized zoobenthic carbon per year (tCyr−1). However, their collisions with the seabed crush and recycle vast benthic communities, costing an estimated 4×104 tCyr−1. We calculate that giant iceberg formation (ice shelf disintegration) has a net potential of approximately 106 tCyr−1 sequestration benefits as well as more widely known negative impacts. This article is part of the theme issue ‘The marine system of the West Antarctic Peninsula: status and strategy for progress in a region of rapid change’.
The West Antarctic Peninsula (WAP) is a climatically sensitive region where periods of strong warming have caused significant changes in the marine ecosystem and food-web processes. Tight coupling between phytoplankton and higher trophic levels implies that the coastal WAP is a bottom-up controlled system, where changes in phytoplankton dynamics may largely impact other food-web components. Here, we analysed the inter-decadal time series of year-round chlorophyll- a (Chl) collected from three stations along the coastal WAP: Carlini Station at Potter Cove (PC) on King George Island, Palmer Station on Anvers Island and Rothera Station on Adelaide Island. There were trends towards increased phytoplankton biomass at Carlini Station (PC) and Palmer Station, while phytoplankton biomass declined significantly at Rothera Station over the studied period. The impacts of two relevant climate modes to the WAP, the El Niño-Southern Oscillation and the Southern Annular Mode, on winter and spring phytoplankton biomass appear to be different among the three sampling stations, suggesting an important role of local-scale forcing than large-scale forcing on phytoplankton dynamics at each station. The inter-annual variability of seasonal bloom progression derived from considering all three stations together captured ecologically meaningful, seasonally co-occurring bloom patterns which were primarily constrained by water-column stability strength. Our findings highlight a coupled link between phytoplankton and physical and climate dynamics along the coastal WAP, which may improve our understanding of overall WAP food-web responses to climate change and variability. This article is part of the theme issue ‘The marine system of the West Antarctic Peninsula: status and strategy for progress in a region of rapid change’.
In former Papers on the Fossil Mammals of Australia ( Thylacoleo , Parts I. & II.) I inferred, from the size and position of the socket of the anterior tooth, from the structure of the root of the tooth therein implanted, and, above all, from the characters of the associated and completely preserved teeth, that such front tooth must have been laniariform, i. e. subcompressed and pointed, adapted for piercing, holding, and lacerating, like the canine of a Carnivore. To this the late laborious and experienced palæontologist, Dr. Falconer, has objected that, in referring to my paper, he finds “that the body of the tooth, of which the shape and direction are adduced as terms of comparison, together with the fore part of the symphysis, is wanting”.
Schematic for gravitationally-driven viscous flow down an inclined plane at an angle β to the horizontal. The channel expands with opening angle α to the downslope direction, which we take to be the X axis, while the Y axis is in the cross-slope direction.
Contours of the steady flow depth for the case α = π. Contours of the numerical result (continuous coloured lines) are plotted at h = 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The thick black line represents the wall. Contours of the exact solution (5.4), plotted as dashed lines for h = 0.01, h = 0.4 and h = 0.7 show excellent agreement.
The position of the contact line as a function of downstream distance, x, obtained from our numerical method for three values of α. The translated similarity solution (which is also the exact solution for α = π) provides a much better prediction for the contact line than the untranslated similarity solution. The agreement is good for all α but better for wider opening angles.
The distance along the wall, d, at which detachment occurs as a function of the channel opening angle, α. The prediction from our numerical simulations is plotted as a continuous black line and the red pluses indicate the experimental results (table 1). The prediction from the similarity solution (equation 6.2) is plotted as a blue dashed line and we also include its behaviour as α → 0, which is d = (η 0 /α) 2 (a yellow dot-dashed line).
The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.
(a) Mare basalt stratigraphy in Mare Serenitatis exposed in the wall of the 16 km diameter impact crater Bessel (21.8°N, 17.9°E; LROC image M135073175R/NASA/GSFC/ASU). (b) Similar layering exposed in walls of a collapse pit in Mare Ingenii on the farside (36.0°S, 166.1°E LROC image M184810930L/NASA/GSFC/ASU). (c) Metre-scale basalt layers exposed in the wall of Hadley Rille (26.1°N, 3.6°E) photographed by Apollo 15 astronaut David Scott using a 500mm focal length lens; the outcrop is about 1300m from the camera (NASA image AS15-89-12104).
(a) A prominent lava flow (arrows) on the surface of Mare Imbrium (31.5°N, 338.0°E; Kaguya Terrain Camera/JAXA). Based on CSFD measurements (see ESM), we obtain an absolute model age of 3.03 !".$% &".$' Gyr for this lava flow, and an age of 3.30 !"."( &".")
(a) Dark pyroclastic materials surrounding a presumed volcanic vent in the Schrӧdinger Basin on the lunar farside (75.3°S, 139.2°E; LROC image/NASA/GSFC/ASU). (b) Schematic illustration of a pyroclastic eruption covering a pre-existing regolith to preserve a palaeoregolith underneath (adapted with thanks from LPI CLSE Higher Education Resources).
The lunar surface has been exposed to the space environment for billions of years and during this time has accumulated records of a wide range of astrophysical phenomena. These include solar wind particles and the cosmogenic products of solar particle events which preserve a record of the past evolution of the Sun, and cosmogenic nuclides produced by high-energy galactic cosmic rays which potentially record the galactic environment of the Solar System through time. The lunar surface may also have accreted material from the local interstellar medium, including supernova ejecta and material from interstellar clouds encountered by the Solar System in the past. Owing to the Moon's relatively low level of geological activity, absence of an atmosphere, and, for much of its history, lack of a magnetic field, the lunar surface is ideally suited to collect these astronomical records. Moreover, the Moon exhibits geological processes able to bury and thus both preserve and ‘time-stamp' these records, although gaining access to them is likely to require a significant scientific infrastructure on the lunar surface. This article is part of a discussion meeting issue ‘Astronomy from the Moon: the next decades'.
Cost functional decrease as a function of PDE simulations for a nonlinear CG and L-BFGS-B algorithm applied to a typical wind-farm optimization window. Filled circles, LES; open circles, adjoint. (Online version in colour.)
LES streamwise velocity field for a 12 × 6 aligned wind farm. The black lines represent the turbine rotors. The black dashed line indicates a buffer region for the imposition of inflow conditions [4,9]. (Online version in colour.)  
Plan views of time-averaged axial velocity ¯ u throughout the wind farm, averaged over all six turbine columns. (a) Reference case ¯ u R . (b)–(d) Differences = ¯ u − ¯ u R between optimized cases and reference case for C3t0, C3t30 and C2t0, respectively. (Online version in colour.)  
Dynamic behaviour of optimized power extraction normalized by a greedy control reference case (smoother line, shown in black): (a) T A = T/2 = 120 s; (b) T A = T/4 = 60 s. The dashed vertical lines indicate the flow advancement windows. (Online version in colour.)  
Complex turbine wake interactions play an important role in overall energy extraction in large wind farms. Current control strategies optimize individual turbine power, and lead to significant energy losses in wind farms compared with lone-standing wind turbines. In recent work, an optimal coordinated control framework was introduced (Goit & Meyers 2015 J. Fluid Mech.768, 5?50 (doi:10.1017/jfm.2015.70)). Here, we further elaborate on this framework, quantify the influence of optimization parameters and introduce new simulation results for which gains in power production of up to 21% are observed. This article is part of the themed issue ?Wind energy in complex terrains?.
We present the first spatially resolved distribution of the δD-CH4 signature of wetland methane emissions and assess its impact on atmospheric δD-CH4. The δD-CH4 signature map is derived by relating δD-H2O of precipitation to measured δD-CH4 of methane wetland emissions at a variety of wetland types and locations. This results in strong latitudinal variation in the wetland δD-CH4 source signature. When δD-CH4 is simulated in a global atmospheric model, little difference is found in global mean, inter-hemispheric difference and seasonal cycle if the spatially varying δD-CH4 source signature distribution is used instead of a globally uniform value. This is because atmospheric δD-CH4 is largely controlled by OH fractionation. However, we show that despite these small differences, using atmospheric records of δD-CH4 to infer changes in the wetland emissions distribution requires the use of the more accurate spatially varying δD-CH4 source signature. We find that models will only be sensitive to changes in emissions distribution if spatial information can be exploited through the spatially resolved source signatures. In addition, we also find that on a regional scale, at sites measuring excursions of δD-CH4 from background levels, substantial differences are simulated in atmospheric δD-CH4 if using spatially varying or uniform source signatures.
When a long line of stationary touching balls is hit on its end by another ball, the line fragments: some balls fly off at the far end, some in the middle hardly move, and the impacting ball rebounds backwards taking with it some nearby balls. Two laws for the contact force are studied, both elastic and cohesionless. First a simple law linear in the compression and then the nonlinear 3 over 2-power law of Hertz for touching spheres. For the linear force and for a line of N balls being impacted by a ball at velocity V, 1.5N1/3 balls fly off from the far end, the furthest at a velocity 1.4VN-1/6, the others at similar but slower speeds, while the majority rebound, the impacting ball at -0.13V and the nth from the end at a velocity -0.16Vn-5/6 at large n. For the nonlinear Hertz law, only two balls fly off from the far end with significant velocities, at 0.986V and 0.149V, the majority hardly move, and a few rebound, the impacting ball at -0.07V and the nth from the end at a velocity -0.084Ve-0.55n.
The present paper investigates the impact behaviour of both pristine carbon-fibre-reinforced-plastic (CFRP) composite laminates and repaired CFRP laminates. For the patch-repaired CFRP specimen, the pristine CFRP panel specimen has been damaged by cutting out a central disc of the CFRP material and then repaired using an adhesively bonded patch of CFRP to cover the hole. Drop-weight, impact tests are performed on these two types of specimens and a numerical elastic-plastic, three-dimensional damage model is developed and employed to simulate the impact behaviour of both types of specimen. This numerical model is meso-scale in nature and assumes that cracks initiate in the CFRP at a nano-scale, in the matrix around fibres, and trigger sub-micrometre intralaminar matrix cracks during the impact event. These localized regions of intralaminar cracking then lead to interlaminar, i.e. delamination, cracking between the neighbouring plies which possess different fibre orientations. These meso-scale, intralaminar and interlaminar, damage processes are modelled using the numerical finite-element analysis model with each individual ply treated as a continuum. Good agreement is found between the results from the experimental studies and the predictions from the numerical simulations. This article is part of the theme issue ‘Nanocracks in nature and industry’.
Quantification of grid convergence rates in Fig. 3, obtained through a least-square linear fitting of the data points.
Quantification of grid convergence rates in Fig. 5, obtained through a least-square linear fitting of the data points.
Quantification of grid convergence rates in Fig. 6, obtained through a least-square linear fitting of the data points.
This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB within the two-relaxation-time (TRT) framework, which achieves a more standardized and easy to use algorithm due to the pivotal parametrization TRT properties. The LSOB explicitly reconstructs the unknown boundary populations in the form of a Chapman–Enskog expansion, where not only first- but also second-order momentum derivatives are locally extracted with the TRT symmetry argument, through a simple local linear algebra procedure, with no need to compute their non-local finite-difference approximations. Here, two LSOB strategies are considered to realize the wall boundary condition, the original one called Lwall and a novel one Lnode, which operate with the wall and node variables, roughly speaking. These two approaches are worked out for both plane and curved walls, including the corners. Their performance is assessed against well-established LBM boundary schemes such as the bounce-back, the local second-order accurate CLI scheme and two different parabolic multi-reflection (MR) schemes. They are all evaluated for 3D duct flows with rectangular, triangular, circular and annular cross-sections, mimicking the geometrical challenges of real porous structures. Numerical tests confirm that LSOB competes with the parabolic MR accuracy in this problem class, requiring only a single node to operate. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.
The Fischer--Tropsch synthesis of hydrocarbons probably involves an array of carbon--carbon bond-formation processes occurring to unite carbene, carbyne, alkyl, olefin, and related species on a metal surface. In seeking to understand the nature of such processes, model diruthenium complexes have been prepared and the products of their thermolysis and reactions with unsaturated hydrocarbons investigated. The combination at a diruthenium centre of two carbenes, of a carbene and an alkyne, and of a carbyne and an olefin is described, and the possible implications for metal surface processes are emphasized.
Schematic representations of the cell-level models. (a) Cell-centre model: the size and shape of the cells (bounded by solid lines and filled circles) are determined from a Voronoi tessellation of the cell centres (open circles). (b) Cell-vertex model: cell size and shape are defined by the positions of vertices at cell junctions (open circles). Evolution of the epithelium arises through motion of centres or vertices, as indicated by arrows.
Example simulations using (a) the cell-centre model and (b) the cell-vertex model. Proliferating cells, yellow; non-proliferating cells, pink.  
(a) Average area difference, A T − A, varies with distance from the crypt base, y, for cell-centre and cell-vertex models. (b) The pressure, p, varies with y in the continuum model. (c) The averaged vertical component of the cell velocity, v y , varies with y for all three models. (d) The average number of vertices for the cell-centre and cell-vertex models varies with y. Cellvertex model, solid line; cell-centre model, dashed line; continuum model, dashed-dotted line. The dotted vertical line separates the Wnt-stimulated, proliferating region (0 < y H W ) from the nonproliferating one (y > H W ).
Bifurcation diagram showing how, for the continuum model, the minimum value of the relative viscosity needed for downward movement of cells at the base of the mutant patch, f * M , increases as the initial height of the centre of the mutant patch, A 0 , increases. Parameter values: k = 1.  
In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cell-centre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts.
Causality has never gained the status of a ‘law’ or ‘principle’ in physics. Some recent literature has even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of the reversibility of the laws of physics, based either on the determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such a notion of causality appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establishing a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The notion of causality is logically completely independent of the misidentified concept of ‘determinism’, and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude by arguing that causality naturally establishes an arrow of time. This implies that the scenario of the ‘block Universe’ and the connected ‘past hypothesis’ are incompatible with causality, and thus with quantum theory: they are both doomed to remain mere interpretations and, as such, are not falsifiable, similar to the hypothesis of ‘super-determinism’. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.
Top-cited authors
Nigel Harris
  • The Open University (UK)
Bradford H. Hager
  • Massachusetts Institute of Technology
David Gubbins
  • University of Leeds
Jeremy Bloxham
  • Harvard University
C. J. Hawkesworth
  • University of St Andrews