Designing electronic properties of two-dimensional crystals through optimization of deformations

One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of two-dimensional electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with graphene's elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters that result in a graphene deformation whose associated pseudomagnetic field profile best matches a prescribed target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of two-dimensional systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other two-dimensional electronic membranes.Comment: 37 pages, 9 figures. This submission contains low-resolution bitmap images; high-resolution images can be found in version 1, which is ~13.5 M

Optimal control of plate shape with incompatible strain fields

A flat plate can bend into a curved surface if it experiences an inhomogeneous growth field. In this article a method is described that numerically determines the optimal growth field giving rise to an arbitrary target shape, optimizing for closeness to the target shape and for growth field smoothness. Numerical solutions are presented, for the full non-symmetric case as well as for simplified one-dimensional and axisymmetric geometries. This system can also be solved semi-analytically by positing an ansatz for the deformation and growth fields in a circular disk with given thickness profile. Paraboloidal, cylindrical and saddle-shaped target shapes are presented as examples, of which the last two exemplify a soft mode arising from a non-axisymmetric deformation of a structure with axisymmetric material properties.Comment: 21 pages, 6 figure

Modeling growth in biological materials

The biomechanical modeling of growing tissues has recently become an area of intense interest. In particular, the interplay between growth patterns and mechanical stress is of great importance, with possible applications to arterial mechanics, embryo morphogenesis, tumor development, and bone remodeling. This review aims to give an overview of the theories that have been used to model these phenomena, categorized according to whether the tissue is considered as a continuum object or a collection of cells. Among the continuum models discussed is the deformation gradient decomposition method, which allows a residual stress field to develop from an incompatible growth field. The cell-based models are further subdivided into cellular automata, center-dynamics, and vertex-dynamics models. Of these the second two are considered in more detail, especially with regard to their treatment of cell-cell interactions and cell division. The review concludes by assessing the prospects for reconciliation between these two fundamentally different approaches to tissue growth, and by identifying possible avenues for further research. © 2012 Society for Industrial and Applied Mathematics

Novel Bacillus sphaericus binary toxin active against bin-resistant culex mosquito larvae

Some Bacillus sphaericus strains (e.g. IAB59, LP1G and 47-6B) can overcome resistance in Culex mosquito larvae, raised against the well characterised binary toxin from this bacterium. A common spore protein (P49), of approximately 49 kDa, produced by these strains has previously been proposed to be responsible for this toxicity. Protein fingerprint analysis of sporulated cultures of these strains identified a number of candidate toxins. Their N-terminal sequences were determined and used to design degenerate oligonucleotide probes. Southern blotting, cloning and colony hybridisation allowed the identification of clones containing genes encoding the putative toxins Cry49Aal (P49) and Cry48Aal (P135) from IAB59. The 1,395 bp cry49Aal gene encodes a protein of 53.3 kDa, showing homology to BinA and BinB from B. sphaericus as well as Cry36Aal and the Cry35 binary toxins from Bacillus thuringiensis. The 3,534 bp cry48Aal gene encodes a 135.6 kDa protein showing homology to the three-domain Cry toxins from B. thuringiensis, including the mosquitocidal Cry4Aa and Cry4Ba from B. thuringiensis subsp. israelensis. Individual expression of these proteins in an acrystalliferous B. thuringiensis subsp. israelensis strain, followed by bioassays against mosquito larvae revealed no toxicity. However, a Cry48Aal/Cry49Aal combination was toxic to both Bin-susceptible and Bin-resistant Culex quinquefasciatus larvae. Aedes aegypti and Anopheles gambiae mosquito larvae were insensitive to the combination, as were a range of other dipteran, coleopteran and lepidopteran insects. The components of this novel binary toxin from B. sphaericus are highly conserved among strains able to overcome resistance. Differential processing of Cry48Aal by C. quinquefasciatus and A. aegypti larval gut proteinases is not responsible for the non-toxicity towards the latter mosquito. Cry49Aal and Cry48Aal form bipyramidal and amorphous crystals respectively at sporulation and their expression involves RNA polymerase factor cr6 in B. subtilis. Discovery of Cry49Aal and Cry48Aal may prove central in the development of strategies to avoid resistance development against B. sphaericus in Culex populations

Analysing vote choice in a multinational state:National identity and territorial differentiation in the 2016 Brexit vote

Striking territorial variations in the 2016 Brexit referendum are neglected in the explanatory literature, a gap our analysis of British Election Study helps to fill. Rather than modelling Britain as one political system, we present parallel models for England, Scotland and Wales. Typical in other multi-national states, this approach is innovative for ‘British politics’. To analyse complex multi-level national identities, we develop a Relative Territorial Identity (RTI) measure. Substantively, RTI predicts Brexit vote-choice. Since voters who prioritise English identity tended to vote Leave, while the obverse was true in Wales and Scotland, RTI helps to explain territorial differentiation