A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of this forced symmetry breaking by studying the perturbed dynamics induced on $M(\epsilon)$ by the above reaction-diffusion system. We prove that depending on the frequency vectors of the rotating waves that form the relative equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating waves or SO(2)-orbits of modulated rotating waves (if some transversality conditions hold). The orbital stability of these solutions is established as well. Our main tools are the orbit space reduction, Poincare map and implicit function theorem

Density functional theory study of rutile VO2 surfaces

We present the results of a density functional theory (DFT) investigation of the surfaces of rutile-like vanadium dioxide, VO2(R). We calculate the surface energies of low Miller index planes, and find that the most stable surface orientation is the (110). The equilibrium morphology of a VO2(R) particle has an acicular shape, laterally confined by (110) planes and topped by (011) planes. The redox properties of the (110) surface are investigated by calculating the relative surface free energies of the non-stoichiometric compositions as a function of oxygen chemical potential. It is found that the VO2(110) surface is oxidized with respect to the stoichiometric composition, not only at ambient conditions but also at the more reducing conditions under which bulk VO2 is stable in comparison with bulk V2O5. The adsorbed oxygen forms surface vanadyl species much more favorably than surface peroxo species

Genomic innovation for crop improvement

Crop production needs to increase to secure future food supplies, while reducing its impact on ecosystems. Detailed characterization of plant genomes and genetic diversity is crucial for meeting these challenges. Advances in genome sequencing and assembly are being used to access the large and complex genomes of crops and their wild relatives. These have helped to identify a wide spectrum of genetic variation and permitted the association of genetic diversity with diverse agronomic phenotypes. In combination with improved and automated phenotyping assays and functional genomic studies, genomics is providing new foundations for crop-breeding systems

A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation

We focus on the Gibbs free energy \u394G for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of \u394G on the droplet volume V, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic logarithmic term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy \u394G(V) once more develops a term logarithmic on V, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the logarithmic term in the droplet free energy, as determined from the optimization of its near-coexistence profile

Is 8:30 a.m. Still Too Early to Start School? A 10:00 a.m. School Start Time Improves Health and Performance of Students Aged 13-16.

While many studies have shown the benefits of later school starts, including better student attendance, higher test scores, and improved sleep duration, few have used starting times later than 9:00 a.m. Here we report on the implementation and impact of a 10 a.m. school start time for 13 to 16-year-old students. A 4-year observational study using a before-after-before (A-B-A) design was carried out in an English state-funded high school. School start times were changed from 8:50 a.m. in study year 0, to 10 a.m. in years 1-2, and then back to 8:50 a.m. in year 3. Measures of student health (absence due to illness) and academic performance (national examination results) were used for all students. Implementing a 10 a.m. start saw a decrease in student illness after 2 years of over 50% (p < 0.0005 and effect size: Cohen's d = 1.07), and reverting to an 8:50 a.m. start reversed this improvement, leading to an increase of 30% in student illness (p < 0.0005 and Cohen's d = 0.47). The 10:00 a.m. start was associated with a 12% increase in the value-added number of students making good academic progress (in standard national examinations) that was significant (<0.0005) and equivalent to 20% of the national benchmark. These results show that changing to a 10:00 a.m. high school start time can greatly reduce illness and improve academic performance. Implementing school start times later than 8:30 a.m., which may address the circadian delay in adolescents' sleep rhythms more effectively for evening chronotypes, appears to have few costs and substantial benefits

Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei

The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte Carlo simulations at densities inside the two-phase coexistence region of fluid and solid. Choosing a geometry where the system is confined between two flat walls, and a wall-colloid potential that leads to incomplete wetting of the crystal at the wall, conditions can be created where a single nanoscopic wall-attached crystalline cluster coexists with fluid in the remainder of the simulation box. Following related ideas that have been useful to study heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we estimate the contact angles from observations of the crystalline clusters in thermal equilibrium. We find fair agreement with a prediction based on Young's equation, using estimates of interface and wall tension from the study of flat surfaces. It is shown that the pressure versus density curve of the finite system exhibits a loop, but the pressure maximum signifies the "droplet evaporation-condensation" transition and thus has nothing in common with a van der Waals-like loop. Preparing systems where the packing fraction is deep inside the two-phase coexistence region, the system spontaneously forms a "slab state", with two wall-attached crystalline domains separated by (flat) interfaces from liquid in full equilibrium with the crystal in between; analysis of such states allows a precise estimation of the bulk equilibrium properties at phase coexistence

Phase Separation of Crystal Surfaces: A Lattice Gas Approach

We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic crystal with nearest--neighbor attractive interactions and weak next--nearest--neighbor repulsive interactions. It is likely applicable to alkali halides with the sodium chloride structure. Emphasis is placed on the fact that the equilibrium crystal shape can be interpreted as a phase diagram and that the details of its structure tell us into which surface orientations an unstable surface will decompose. We find that, depending on the temperature and growth conditions, a number of interesting behaviors are expected. For a crystal in equilibrium with its vapor, these include a low temperature regime with logarithmically--slow separation into three symmetrically--equivalent facets, and a higher temperature regime where separation proceeds as a power law in time into an entire one--parameter family of surface orientations. For a crystal slightly out of equilibrium with its vapor (slow crystal growth or etching), power--law growth should be the rule at late enough times. However, in the low temperature regime, the rate of separation rapidly decreases as the chemical potential difference between crystal and vapor phases goes to zero.Comment: 16 pages (RevTex 3.0); 12 postscript figures available on request ([email protected]). Submitted to Physical Review E. SFU-JDSDJB-94-0

Polyploid plants have faster rates of multivariate niche differentiation than their diploid relatives

Polyploid speciation entails substantial and rapid postzygotic reproductive isolation of nascent species that are initially sympatric with one or both parents. Despite strong postzygotic isolation, ecological niche differentiation has long been thought to be important for polyploid success. Using biogeographic data from across vascular plants, we tested whether the climatic niches of polyploid species are more differentiated than their diploid relatives and if the climatic niches of polyploid species differentiated faster than those of related diploids. We found that polyploids are often more climatically differentiated from their diploid parents than the diploids are from each other. Consistent with this pattern, we estimated that polyploid species generally have higher rates of multivariate niche differentiation than their diploid relatives. In contrast to recent analyses, our results confirm that ecological niche differentiation is an important component of polyploid speciation and that niche differentiation is often significantly faster in polyploids.Polyploid speciation entails substantial and rapid postzygotic reproductive isolation of nascent species that are initially sympatric with one or both parents. Despite strong postzygotic isolation, ecological niche differentiation has long been thought to be important for polyploid success. Using biogeographic data from across vascular plants, we tested whether the climatic niches of polyploid species are more differentiated than their diploid relatives and if the climatic niches of polyploid species differentiated faster than those of related diploids.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/1/ele13402-sup-0001-TableS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/2/ele13402_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/3/ele13402-sup-0007-TableS7.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/4/ele13402-sup-0003-TableS3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/5/ele13402-sup-0005-TableS5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/6/ele13402.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/7/ele13402-sup-0006-TableS6.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/8/ele13402-sup-0002-TableS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153074/9/ele13402-sup-0004-TableS4.pd