Exponential asymptotics and Stokes lines in a partial differential equation

A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution identifies asymptotic contributions from saddle points, end points and poles, and the Stokes lines across which these may be switched on and off. These results are then derived directly from the equation by optimally truncating the naïve perturbation expansion and smoothing the Stokes discontinuities. The analysis reveals two new types of Stokes switching: a higher-order Stokes line which is a Stokes line in the approximation of the late terms of the asymptotic series, and which switches on or off Stokes lines themselves; and a second-generation Stokes line, in which a subdominant exponential switched on at a primary Stokes line is itself responsible for switching on another smaller exponential. The ‘new’ Stokes lines discussed by Berk et al. (Berk et al. 1982 J. Math. Phys.23, 988–1002) are second-generation Stokes lines, while the ‘vanishing’ Stokes lines discussed by Aoki et al. (Aoki et al. 1998 In Microlocal analysis and complex Fourier analysis (ed. K. F. T. Kawai), pp. 165–176) are switched off by a higher-order Stokes line

Stress-dependent local oxidation of silicon

The two-dimensional isolation oxidation of silicon is considered for stress-dependent reaction and diffusion coefficients. The influence of such parameters is investigated numerically and asymptotically in the bird's beak problem and for curved geometries arising in the oxidation of cylindrical and spherical structures. In the bird's beak problem, the limit of large activation volume is described for a stress-dependent reaction coefficient, illustrating the significant growth retardation of the silicon/silicon oxide interface and reduced stresses in the silicon oxide. Novel high-order nonlinear evolution-type PDEs are derived and investigated using asymptotic and numerical techniques

Two different network topologies yield bistability in models of mesoderm and anterior mesendoderm specification in amphibians

AbstractUnderstanding the Gene Regulatory Networks (GRNs) that underlie development is a major question for systems biology. The establishment of the germ layers is amongst the earliest events of development and has been characterised in numerous model systems. The establishment of the mesoderm is best characterised in the frog Xenopus laevis and has been well studied both experimentally and mathematically. However, the Xenopus network has significant differences from that in mouse and humans, including the presence of multiple copies of two key genes in the network, Mix and Nodal. The axolotl, a urodele amphibian, provides a model with all the benefits of amphibian embryology but crucially only a single Mix and Nodal gene required for the specification of the mesoderm. Remarkably, the number of genes within the network is not the only difference. The interaction between Mix and Brachyury, two transcription factors involved in the establishment of the endoderm and mesoderm respectively, is not conserved. While Mix represses Brachyury in Xenopus, it activates Brachyury in axolotl. Thus, whilst the topology of the networks in the two species differs, both are able to form mesoderm and endoderm in vivo. Based on current knowledge of the structure of the mesendoderm GRN we develop deterministic models that describe the time evolution of transcription factors in a single axolotl cell and compare numerical simulations with previous results from Xenopus. The models are shown to have stable steady states corresponding to mesoderm and anterior mesendoderm, with the in vitro model showing how the concentration of Activin can determine cell fate, while the in vivo model shows that β-catenin concentration can determine cell fate. Moreover, our analysis suggests that additional components must be important in the axolotl network in the specification of the full range of tissues

A Standard Input Format for Computer Codes Which Solve Stochastic Programs with Recourse and a Library of Utilities to Simplify its Use

We explain our suggestions for standardizing input formats for computer codes which solve stochastic programs with recourse. The main reason to set some conventions is to allow programs implementing different methods of solution to be used interchangeably. The general philosophy behind our design is a) to remain fairly faithful to the de facto standard for the statement of LP problems established by IBM for use with MPSX and subsequently adopted by the authors of MINOS, b) to provide sufficient flexibility so that a variety of problems may be expressed in the standard format, c) to allow problems originally formulated as deterministic LP to be converted to stochastic problems with a minimum of effort, d) to permit new options to be added as the need arises, and e) to provide some routines to facilitate the task of reading files specified in the standard format

Mobile radio propagation prediction using ray tracing methods

The basic problem is to solve the two-dimensional scalar Helmholtz equation for a point source (the antenna) situated in the vicinity of an array of scatterers (such as the houses and any other relevant objects in 1 square km of urban environment). The wavelength is a few centimeters and the houses a few metres across, so there are three disparate length scales in the problem. The question posed by BT concerned ray counting on the assumptions that: (i) rays were subject to a reflection coefficient of about 0.5 when bouncing off a house wall and (ii) that diffraction at corners reduced their energy by 90%. The quantity of particular interest was the number of rays that need to be accounted for at any particular point in order for those neglected to only contribute 10% of the field at that point; a secondary question concerned the use of rays to predict regions where the field was less than 1% of that in the region directly illuminated by the antenna. The progress made in answering these two questions is described in the next two sections and possibly useful representations of the solution of the Helmholtz equations in terms other than rays are given in the final section

Experimentally testing and assessing the predictive power of species assembly rules for tropical canopy ants.

Understanding how species assemble into communities is a key goal in ecology. However, assembly rules are rarely tested experimentally, and their ability to shape real communities is poorly known. We surveyed a diverse community of epiphyte-dwelling ants and found that similar-sized species co-occurred less often than expected. Laboratory experiments demonstrated that invasion was discouraged by the presence of similarly sized resident species. The size difference for which invasion was less likely was the same as that for which wild species exhibited reduced co-occurrence. Finally we explored whether our experimentally derived assembly rules could simulate realistic communities. Communities simulated using size-based species assembly exhibited diversities closer to wild communities than those simulated using size-independent assembly, with results being sensitive to the combination of rules employed. Hence, species segregation in the wild can be driven by competitive species assembly, and this process is sufficient to generate observed species abundance distributions for tropical epiphyte-dwelling ants.TMF was funded by the UK Natural Environment Research Council, the project “Biodiversity of Forest Ecosystems” CZ.1.07/2.3.00/20.0064 co-financed by the European Social Fund and the state budget of the Czech Republic, an Australian Research Council Discovery Grant (DP140101541), Yayasan Sime Darby, and the Czech Science Foundation (Reg, nos. 14-32302S,14-04258S).This is the final published version. It first appeared at http://onlinelibrary.wiley.com/doi/10.1111/ele.12403/abstract

A Standard Input Format for Multiperiod Stochastic Linear Programs

Data conventions for the automatic input of multiperiod stochastic linear programs are described. The input format is based on the MPSX standard and is designed to promote the efficient conversion of originally deterministic problems by introducing stochastic variants in separate files. A flexible "header" syntax generates a useful variety of stochastic dependencies. An extension using the NETGEN format is proposed for stochastic network programs

Faster juvenile growth promotes earlier sex change in a protandrous hermaphrodite (barramundi Lates calcarifer)

The relationship between growth and sexual maturation is central to understanding the dynamics of animal populations which exhibit indeterminate growth. In sequential hermaphrodites, which undergo post-maturation sex change, the size and age at which sex change occurs directly affects reproductive output and hence population productivity. However, these traits are often labile, and may be strongly influenced by heterogenous growth and mortality rates. We analysed otolith microstructure of a protandrous (i.e., male-to-female) fish (barramundi Lates calcarifer) to examine growth in relation to individual variation in the timing of sex change. Growth trajectories of individuals with contrasting life histories were examined to elucidate the direction and extent to which growth rate influences the size and age individuals change sex. Then, the relationships between growth rate, maturation schedules and asymptotic maximum size were explored to identify potential trade-offs between age at female maturity and growth potential. Rapid growth was strongly associated with decreased age at sex change, but this was not accompanied by a decrease in size at sex change. Individuals that were caught as large females grew faster than those caught as males, suggesting that fast-growing individuals ultimately obtain higher fitness and therefore make a disproportionate contribution to population fecundity. These results indicate that individual-level variation in maturation schedules is not reflective of trade-offs between growth and reproduction. Rather, we suggest that conditions experienced during the juvenile phase are likely to be a key determinant of post-maturation fitness. These findings highlight the vulnerability of sex-changing species to future environmental change and harvest

Blow up in a periodic semilinear heat equation

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel results include asymptotic approximations of the solution on different timescales that are, in combination, valid over the entire space and time interval right up to and including the blow-up time. Both the asymptotic analysis and the numerical methods benefit from a well-known reciprocal substitution that transforms the problem into one that does not blow up but remains bounded. This allows for highly accurate computations of blow-up times and the solution profile at the critical time, which are then used to confirm the asymptotics. The approach also makes it possible to continue a solution numerically beyond the singularity. The specific post-blow-up dynamics are believed to be presented here for the first time

Invasion genetics of the Pacific oyster Crassostrea gigas in the British Isles inferred from microsatellite and mitochondrial markers

The Pacific oyster, Crassostrea gigas, native to northeast Asia, is one of the most important cultured shellfish species. In Europe, Pacific oysters first settled along the Atlantic coasts of France at the end of the 1960s but rapidly spread and are now widely established. Twenty-two sites in the United Kingdom (UK), Ireland, Denmark, France and Spain were sampled to assess genetic diversity and differentiation. Hatchery-propagated stocks from two hatcheries located in the UK also were included. Two main genetic clusters were identified from pairwise genetic differentiation indexes, Bayesian clustering methods or neighbour-joining analysis, based on 7 microsatellite loci: (1) a Northeast cluster (including feral samples from East England, Ireland and Denmark as well as UK hatchery stocks) and (2) a Southwest cluster (including samples from South Wales, South West England, France and Spain). The Southwest cluster had significantly higher allelic richness (A) and expected heterozygosity (He) (A: 45.68, He: 0.928) than in the Northeast (A: 26.58, He: 0.883); the two diverging by a small but significant FST value (FST=0.017, 95% CI: 0.014-0.021). A 739-bp fragment of the major noncoding region of the mitochondrial genome was sequenced in 248 oysters from 12 of the studied samples in Europe and in 25 oysters from Miyagi prefecture (Japan). A total of 81 haplotypes were found. Haplotype frequency analyses identified the same two clusters observed using microsatellites. This study highlights how the number and size of introduction events, aquaculture practices, genetic bottlenecks followed by genetic drift and natural dispersal can act concurrently to shape the genetic diversity and structure of introduced populations