Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (110), and (100) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. Many of these metallic surfaces have technological or catalytic applications. We compare experimental reference values to those of the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), the PBEsol (PBE for solids) GGA, the SCAN meta-GGA, and SCAN+rVV10 (SCAN with a long-range van der Waals or vdW correction). The closest agreement with uncertain experimental values is achieved by the simplest density functional (LDA) and by the most sophisticated general-purpose one (SCAN+rVV10). The long-range vdW interaction increases the surface energies by about 10%, and the work functions by about 1%. LDA works for metal surfaces through a stronger-than-usual error cancellation. PBE yields the most-underestimated and presumably least accurate surface energies and work functions. Surface energies within the random phase approximation (RPA) are also reported. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment

The effect of topology on the structure and free energy landscape of DNA kissing complexes

We use a recently developed coarse-grained model for DNA to study kissing complexes formed by hybridization of complementary hairpin loops. The binding of the loops is topologically constrained because their linking number must remain constant. By studying systems with linking numbers -1, 0 or 1 we show that the average number of interstrand base pairs is larger when the topology is more favourable for the right-handed wrapping of strands around each other. The thermodynamic stability of the kissing complex also decreases when the linking number changes from -1 to 0 to 1. The structures of the kissing complexes typically involve two intermolecular helices that coaxially stack with the hairpin stems at a parallel four-way junction

Density-functional study of defects in two-dimensional circular nematic nanocavities

We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are obtained in a thermodynamically consistent way for defects with topological charge $k=+1$ (with radial and tangential symmetries) and $k=+1/2$. An independent calculation of the fluid elastic constants, within the same theory, allows us to connect with the local free--energy density predicted by elastic theory, which in turn provides a criterion to define a defect core boundary and a defect core free energy for the two types of defects. The radial and tangential defects turn out to have very different properties, a feature that a previous Maier--Saupe theory could not account for due to the simplified nature of the interactions --which caused all elastic constants to be equal. In the case with two $k=+1/2$ defects in the cavity, the elastic r\'egime cannot be reached due to the small radii of the cavities considered, but some trends can already be obtained.Comment: 9 figures. Accepted for publication in liquid crystal

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Dimensional analysis using toric ideals: Primitive invariants

© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1

Continental-scale patterns of pathogen prevalence: a case study on the corncrake

Pathogen infections can represent a substantial threat to wild populations, especially those already limited in size. To determine how much variation in the pathogens observed among fragmented populations is caused by ecological factors, one needs to examine systems where host genetic diversity is consistent among the populations, thus controlling for any potentially confounding genetic effects. Here, we report geographic variation in haemosporidian infection among European populations of corncrake. This species now occurs in fragmented populations, but there is little genetic structure and equally high levels of genetic diversity among these populations. We observed a longitudinal gradient of prevalence from western to Eastern Europe negatively correlated with national agricultural yield, but positively correlated with corncrake census population sizes when only the most widespread lineage is considered. This likely reveals a possible impact of local agriculture intensity, which reduced host population densities in Western Europe and, potentially, insect vector abundance, thus reducing the transmission of pathogens. We conclude that in the corncrake system, where metapopulation dynamics resulted in variations in local census population sizes, but not in the genetic impoverishment of these populations, anthropogenic activity has led to a reduction in host populations and pathogen prevalence

Genotype imputation accuracy in a F2 pig population using high density and low density SNP panels

Background: F2 resource populations have been used extensively to map QTL segregating between pig breeds. A limitation associated with the use of these resource populations for fine mapping of QTL is the reduced number of founding individuals and recombinations of founding haplotypes occurring in the population. These limitations, however, become advantageous when attempting to impute unobserved genotypes using within family segregation information. A trade-off would be to re-type F2 populations using high density SNP panels for founding individuals and low density panels (tagSNP) in F2 individuals followed by imputation. Subsequently a combined meta-analysis of several populations would provide adequate power and resolution for QTL mapping, and could be achieved at relatively low cost. Such a strategy allows the wealth of phenotypic information that has previously been obtained on experimental resource populations to be further mined for QTL identification. In this study we used experimental and simulated high density genotypes (HD-60K) from an F2 cross to estimate imputation accuracy under several genotyping scenarios. Results: Selection of tagSNP using physical distance or linkage disequilibrium information produced similar imputation accuracies. In particular, tagSNP sets averaging 1 SNP every 2.1 Mb (1,200 SNP genome-wide) yielded imputation accuracies (IA) close to 0.97. If instead of using custom panels, the commercially available 9K chip is used in the F2, IA reaches 0.99. In order to attain such high imputation accuracy the F0 and F1 generations should be genotyped at high density. Alternatively, when only the F0 is genotyped at HD, while F1 and F2 are genotyped with a 9K panel, IA drops to 0.90. Conclusions: Combining 60K and 9K panels with imputation in F2 populations is an appealing strategy to re-genotype existing populations at a fraction of the cost.Fil: Gualdron Duarte, Jose Luis. Michigan State University; Estados Unidos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bates, Ronald O.. Michigan State University; Estados UnidosFil: Ernst, Catherine W.. Michigan State University; Estados UnidosFil: Raney, Nancy E.. Michigan State University; Estados UnidosFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Steibel, Juan P.. Michigan State University; Estados Unido

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic