Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

Impact of a drier Early-Mid-Holocene climate upon Amazonian forests

This paper uses a palaeoecological approach to examine the impact of drier climatic conditions of the Early-Mid-Holocene (ca 8000-4000 years ago) upon Amazonia's forests and their fire regimes. Palaeovegetation (pollen data) and palaeofire (charcoal) records are synthesized from 20 sites within the present tropical forest biome, and the underlying causes of any emergent patterns or changes are explored by reference to independent palaeoclimate data and present-day patterns of precipitation, forest cover and fire activity across Amazonia. During the Early-Mid-Holocene, Andean cloud forest taxa were replaced by lowland tree taxa as the cloud base rose while lowland ecotonal areas, which are presently covered by evergreen rainforest, were instead dominated by savannahs and/or semi-deciduous dry forests. Elsewhere in the Amazon Basin there is considerable spatial and temporal variation in patterns of vegetation disturbance and fire, which probably reflects the complex heterogeneous patterns in precipitation and seasonality across the basin, and the interactions between climate change, drought- and fire susceptibility of the forests, and Palaeo-Indian land use. Our analysis shows that the forest biome in most parts of Amazonia appears to have been remarkably resilient to climatic conditions significantly drier than those of today, despite widespread evidence of forest burning. Only in ecotonal areas is there evidence of biome replacement in the Holocene. From this palaeoecological perspective, we argue against the Amazon forest 'dieback' scenario simulated for the future.

Convergent evolution of floral signals underlies the success of Neotropical orchids

The great majority of plant species in the tropics require animals to achieve pollination, but the exact role of floral signals in attraction of animal pollinators is often debated. Many plants provide a floral reward to attract a guild of pollinators, and it has been proposed that floral signals of non-rewarding species may converge on those of rewarding species to exploit the relationship of the latter with their pollinators. In the orchid family (Orchidaceae), pollination is almost universally animal-mediated, but a third of species provide no floral reward, which suggests that deceptive pollination mechanisms are prevalent. Here, we examine floral colour and shape convergence in Neotropical plant communities, focusing on certain food-deceptive Oncidiinae orchids (e.g. Trichocentrum ascendens and Oncidium nebulosum) and rewarding species of Malpighiaceae. We show that the species from these two distantly related families are often more similar in floral colour and shape than expected by chance and propose that a system of multifarious floral mimicry—a form of Batesian mimicry that involves multiple models and is more complex than a simple one model–one mimic system—operates in these orchids. The same mimetic pollination system has evolved at least 14 times within the species-rich Oncidiinae throughout the Neotropics. These results help explain the extraordinary diversification of Neotropical orchids and highlight the complexity of plant–animal interactions.

Cultural phylogeography of the Bantu Languages of sub-Saharan Africa

There is disagreement about the routes taken by populations speaking Bantu languages as they expanded to cover much of sub-Saharan Africa. Here, we build phylogenetic trees of Bantu languages and map them onto geographical space in order to assess the likely pathway of expansion and test between dispersal scenarios. The results clearly support a scenario in which groups first moved south through the rainforest from a homeland somewhere near the Nigeria–Cameroon border. Emerging on the south side of the rainforest, one branch moved south and west. Another branch moved towards the Great Lakes, eventually giving rise to the monophyletic clade of East Bantu languages that inhabit East and Southeastern Africa. These phylogenies also reveal information about more general processes involved in the diversification of human populations into distinct ethnolinguistic groups. Our study reveals that Bantu languages show a latitudinal gradient in covering greater areas with increasing distance from the equator. Analyses suggest that this pattern reflects a true ecological relationship rather than merely being an artefact of shared history. The study shows how a phylogeographic approach can address questions relating to the specific histories of certain groups, as well as general cultural evolutionary processes.

Retrieval of phytoplankton size from bio-optical measurements: theory and applications

The absorption coefficient of a substance distributed as discrete particles in suspension is less than that of the same material dissolved uniformly in a medium—a phenomenon commonly referred to as the flattening effect. The decrease in the absorption coefficient owing to flattening effect depends on the concentration of the absorbing pigment inside the particle, the specific absorption coefficient of the pigment within the particle, and on the diameter of the particle, if the particles are assumed to be spherical. For phytoplankton cells in the ocean, with diameters ranging from less than 1 µm to more than 100 µm, the flattening effect is variable, and sometimes pronounced, as has been well documented in the literature. Here, we demonstrate how the in vivo absorption coefficient of phytoplankton cells per unit concentration of its major pigment, chlorophyll a, can be used to determine the average cell size of the phytoplankton population. Sensitivity analyses are carried out to evaluate the errors in the estimated diameter owing to potential errors in the model assumptions. Cell sizes computed for field samples using the model are compared qualitatively with indirect estimates of size classes derived from high performance liquid chromatography data. Also, the results are compared quantitatively against measurements of cell size in laboratory cultures. The method developed is easy-to-apply as an operational tool for in situ observations, and has the potential for application to remote sensing of ocean colour data.

Arenavirus budding resulting from viral-protein-associated cell membrane curvature

Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations.

Dopant-vacancy binding effects in Li-doped magnesium hydride

We use a combination of ab initio calculations and statistical mechanics to investigate the substitution of Li+ for Mg2+ in magnesium hydride (MgH2) accompanied by the formation of hydrogen vacancies with positive charge (with respect to the original ion at the site). We show that the binding energy between dopants and vacancy defects leads to a significant fraction of trapped vacancies and therefore a dramatic reduction in the number of free vacancies available for diffusion. The concentration of free vacancies initially increases with dopant concentration but reaches a maximum at around 1 mol % Li doping and slowly decreases with further doping. At the optimal level of doping, the corresponding concentration of free vacancies is much higher than the equilibrium concentrations of charged and neutral vacancies in pure MgH2 at typical hydrogen storage conditions. We also show that Li-doped MgH2 is thermodynamically metastable with respect to phase separation into pure magnesium and lithium hydrides at any significant Li concentration, even after considering the stabilization provided by dopant-vacancy interactions and configurational entropic effects. Our results suggest that lithium doping may enhance hydrogen diffusion hydride but only to a limited extent determined by an optimal dopant concentration and conditioned to the stability of the doped phase.

Regional climate change mitigation with crops: context and assessment

The intention of this review is to place crop albedo biogeoengineering in the wider picture of climate manipulation. Crop biogeoengineering is considered within the context of the long-term modification of the land surface for agriculture over several thousand years. Biogeoengineering is also critiqued in relation to other geoengineering schemes in terms of mitigation power and adherence to social principles for geoengineering. Although its impact is small and regional, crop biogeoengineering could be a useful and inexpensive component of an ensemble of geoengineering schemes to provide temperature mitigation. The method should not detrimentally affect food security and there may even be positive impacts on crop productivity, although more laboratory and field research is required in this area to understand the underlying mechanisms.

Highly contrasting effects of different climate forcing agents on terrestrial ecosystem services

Many atmospheric constituents besides carbon dioxide (CO2) contribute to global warming, and it is common to compare their influence on climate in terms of radiative forcing, which measures their impact on the planetary energy budget. A number of recent studies have shown that many radiatively active constituents also have important impacts on the physiological functioning of ecosystems, and thus the ‘ecosystem services’ that humankind relies upon. CO2 increases have most probably increased river runoff and had generally positive impacts on plant growth where nutrients are non-limiting, whereas increases in near-surface ozone (O3) are very detrimental to plant productivity. Atmospheric aerosols increase the fraction of surface diffuse light, which is beneficial for plant growth. To illustrate these differences, we present the impact on net primary productivity and runoff of higher CO2, higher near-surface O3, and lower sulphate aerosols, and for equivalent changes in radiative forcing.We compare this with the impact of climate change alone, arising, for example, from a physiologically inactive gas such as methane (CH4). For equivalent levels of change in radiative forcing, we show that the combined climate and physiological impacts of these individual agents vary markedly and in some cases actually differ in sign. This study highlights the need to develop more informative metrics of the impact of changing atmospheric constituents that go beyond simple radiative forcing.

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Cost effectiveness of mitigation measures for water security and water quality in the River Thames catchment: impacts of changing climate, land use and water scarcity

The catchment of the River Thames, the principal river system in southern England, provides the main water supply for London but is highly vulnerable to changes in climate, land use and population. The river is eutrophic with significant algal blooms with phosphorus assumed to be the primary chemical indicator of ecosystem health. In the Thames Basin, phosphorus is available from point sources such as wastewater treatment plants and from diffuse sources such as agriculture. In order to predict vulnerability to future change, the integrated catchments model for phosphorus (INCA-P) has been applied to the river basin and used to assess the cost-effectiveness of a range of mitigation and adaptation strategies. It is shown that scenarios of future climate and land-use change will exacerbate the water quality problems, but a range of mitigation measures can improve the situation. A cost-effectiveness study has been undertaken to compare the economic benefits of each mitigation measure and to assess the phosphorus reductions achieved. The most effective strategy is to reduce fertilizer use by 20% together with the treatment of effluent to a high standard. Such measures will reduce the instream phosphorus concentrations to close to the EU Water Framework Directive target for the Thames.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

Endocannabinoids in neuroendopsychology: multiphasic control of mitochondrial function

The endocannabinoid system (ECS) is a construct based on the discovery of receptors that are modulated by the plant compound tetrahydrocannabinol and the subsequent identification of a family of nascent ligands, the 'endocannabinoids'. The function of the ECS is thus defined by modulation of these receptors-in particular, by two of the best-described ligands (2-arachidonyl glycerol and anandamide), and by their metabolic pathways. Endocannabinoids are released by cell stress, and promote both cell survival and death according to concentration. The ECS appears to shift the immune system towards a type 2 response, while maintaining a positive energy balance and reducing anxiety. It may therefore be important in resolution of injury and inflammation. Data suggest that the ECS could potentially modulate mitochondrial function by several different pathways; this may help explain its actions in the central nervous system. Dose-related control of mitochondrial function could therefore provide an insight into its role in health and disease, and why it might have its own pathology, and possibly, new therapeutic directions.