A numerical investigation of the solution of a class of fourth-order eigenvalue problems

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre-Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite-element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite-element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non-convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator

Evolutionary synchrony of Earth's biosphere and sedimentary-stratigraphic record

The landscapes and seascapes of Earth’s surface provide the theatre for life, but to what extent did the actors build the stage? The role of life in the long-term shaping of the planetary surface needs to be understood to ascertain whether Earth is singular among known rocky planets, and to frame predictions of future changes to the biosphere. Modern geomorphic observations and modelling have made strides in this respect, but an under-utilized lens through which to interrogate these questions resides in the most complete tangible record of our planetary history: the sedimentary-stratigraphic record (SSR). The characteristics of the SSR have been frequently explained with reference to changes in boundary conditions such as relative sea level, climate, and tectonics. Yet despite the fact that the long-term accrual of the SSR was contemporaneous with the evolution of almost all domains of life on Earth, causal explanations related to biological activity have often been overlooked, particularly within siliciclastic strata. This paper explores evidence for the ways in which organisms have influenced the SSR throughout Earth history and emphasizes that further investigation can help lead us towards a mechanistic understanding of how the planetary surface has co-evolved with life. The practicality of discerning life signatures in the SSR is discussed by: 1) distinguishing biologically-dependent versus biologically-influenced sedimentary signatures; 2) emphasizing the importance of determining relative time-length scales of processes and demonstrating how different focal lengths of observation (individual geological outcrops and the complete SSR) can reveal different insights; and 3) promoting an awareness of issues of equifinality and underdetermination that may hinder the recognition of life signatures. Multiple instances of life signatures and their historic range within the SSR are reviewed, with examples covering siliciclastic, biogenic and chemogenic strata, and trigger organisms from across the spectrum of Earth’s extant and ancient life. With this novel perspective, the SSR is recognised as a dynamic archive that expands and complements the fossil and geochemical records that it hosts, rather than simply being a passive repository for them. The SSR is shown to be both the record and the result of long-term evolutionary synchrony between life and planetary surface processes

Low electronic conductivity of Li7La3Zr2 O12 solid electrolytes from first principles

Lithium-rich garnets such as Li7La3Zr2O12 (LLZO) are promising solid electrolytes with potential application in all-solid-state batteries that use lithium-metal anodes. The practical use of garnet electrolytes is limited by pervasive lithium-dendrite growth, which leads to short-circuiting and cell failure. One proposed mechanism of lithium-dendrite growth is the direct reduction of lithium ions to lithium metal within the electrolyte, and lithium garnets have been suggested to be particularly susceptible to this dendrite-growth mechanism due to high electronic conductivities relative to other solid electrolytes. The electronic conductivities of LLZO and other lithium-garnet solid electrolytes, however, are not yet well characterized. Here, we present a general scheme for calculating the intrinsic electronic conductivity of a nominally insulating material under variable synthesis conditions from first principles, and apply this to the prototypical lithium-garnet LLZO. Our model predicts that under typical battery operating conditions, electron and hole mobilities are low (<1cm2V-1s-1), and bulk electron and hole carrier concentrations are negligible, irrespective of initial synthesis conditions or dopant levels. These results suggest that the bulk electronic conductivity of LLZO is not sufficiently high to cause bulk lithium-dendrite growth during cell operation, and that any non-negligible electronic conductivity in lithium garnet samples is likely due to extended defects or surface contributions

A litho-tectonic event stratigraphy from dynamic Late Devensian ice flow of the North Sea Lobe, Tunstall, east Yorkshire, UK

The central sector of the British-Irish Ice Sheet during the last glaciation was characterised by complex ice-flow reflecting interacting ice streams and changing dominance of different ice dispersal centres. At Tunstall, east Yorkshire, two subglacial till units have been traditionally identified as the Late Devensian Skipsea and Withernsea tills, and thought to record two separate ice advances onto the Holderness coast, from divergent ice flow directions. Our study presents the first quantitative lithological, sedimentological and structural evaluation of glacial sediments at the site. The lithological composition of both till units suggests that ice extended southwards from southern Scotland, incorporating material from north-east England and the western margin of the North Sea Basin. Notably, the bulk lithological properties of both the Skipsea and Withernsea tills are very similar. Subtle variations in colour, texture and lithology that do occur simply appear to reflect spatial and temporal variability in subglacial entrainment along the flow path of the North Sea Lobe. The relative arrangements of the units plus the fracture sets also indicates phases of intra-till thrust-stacking and unloading (F2), consolidation and shrinkage (F1, F3) suggestive of cycles of ice re-advance (thrusting) and ice-marginal retreat (unloading and shrinkage) possibly relating to active recession. The findings from this study reveal a sedimentary and structural complexity that is not recognised by the current Late Devensian till stratigraphy of east Yorkshire

Mobilising knowledge in complex health systems: A call to action

Worldwide, policymakers, health system managers, practitioners and researchers struggle to use evidence to improve policy and practice. There is growing recognition that this challenge relates to the complex systems in which we work. The corresponding increase in complexity-related discourse remains primarily at a theoretical level. This paper moves the discussion to a practical level, proposing actions that can be taken to implement evidence successfully in complex systems. Key to success is working with, rather than trying to simplify or control, complexity. The integrated actions relate to co-producing knowledge, establishing shared goals and measures, enabling leadership, ensuring adequate resourcing, contributing to the science of knowledge-to-action, and communicating strategically. This is the final version of the article. It first appeared from Policy Press via http://dx.doi.org/10.1332/174426416X1471255375031

Engineering the Fab fragment of the anti-IgE omalizumab to prevent Fab crystallization and permit IgE-Fc complex crystallization

Immunoglobulin E (IgE) plays a central role in the allergic response, in which cross-linking of allergen by Fc[epsilon]RI-bound IgE triggers mast cell and basophil degranulation and the release of inflammatory mediators. The high-affinity interaction between IgE and Fc[epsilon]RI is a long-standing target for therapeutic intervention in allergic disease. Omalizumab is a clinically approved anti-IgE monoclonal antibody that binds to free IgE, also with high affinity, preventing its interaction with Fc[epsilon]RI. All attempts to crystallize the pre-formed complex between the omalizumab Fab and the Fc region of IgE (IgE-Fc), to understand the structural basis for its mechanism of action, surprisingly failed. Instead, the Fab alone selectively crystallized in different crystal forms, but their structures revealed intermolecular Fab/Fab interactions that were clearly strong enough to disrupt the Fab/IgE-Fc complexes. Some of these interactions were common to other Fab crystal structures. Mutations were therefore designed to disrupt two recurring packing interactions observed in the omalizumab Fab crystal structures without interfering with the ability of the omalizumab Fab to recognize IgE-Fc; this led to the successful crystallization and subsequent structure determination of the Fab/IgE-Fc complex. The mutagenesis strategy adopted to achieve this result is applicable to other intractable Fab/antigen complexes or systems in which Fabs are used as crystallization chaperones

Expanding the Anti-Phl p 7 Antibody Toolkit: An Anti-Idiotype Nanobody Inhibitor.

We have previously produced a toolkit of antibodies, comprising recombinant human antibodies of all but one of the human isotypes, directed against the polcalcin family antigen Phl p 7. In this work, we complete the toolkit of human antibody isotypes with the IgD version of the anti-Phl p 7 monoclonal antibody. We also raised a set of nanobodies against the IgD anti-Phl p 7 antibody and identify and characterize one paratope-specific nanobody. This nanobody also binds to the IgE isotype of this antibody, which shares the same idiotype, and orthosterically inhibits the interaction with Phl p 7. The 2.1 Å resolution X-ray crystal structure of the nanobody in complex with the IgD Fab is described

Crystal structures of the human IgD Fab reveal insights into CH1 domain diversity

Antibodies of the IgD isotype remain the least well characterized of the mammalian immunoglobulin isotypes. Here we report three-dimensional structures for the Fab region of IgD, based on four different crystal structures, at resolutions of 1.45–2.75 Å. These IgD Fab crystals provide the first high-resolution views of the unique Cδ1 domain. Structural comparisons identify regions of conformational diversity within the Cδ1 domain, as well as among the homologous domains of Cα1, Cγ1 and Cμ1. The IgD Fab structure also possesses a unique conformation of the upper hinge region, which may contribute to the overall disposition of the very long linker sequence between the Fab and Fc regions found in human IgD. Structural similarities observed between IgD and IgG, and differences with IgA and IgM, are consistent with predicted evolutionary relationships for the mammalian antibody isotypes