On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Representing some non-representable matroids

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave under duality and minors, we extend Tutte's representability criterion to this new class, and we study the generator matrices of the chain groups. An example shows that the class of matroids representable over a skew partial field properly contains the class of matroids representable over a skew field. Next, we show that every multilinear representation of a matroid can be seen as a representation over a skew partial field. Finally we study a class of matroids called quaternionic unimodular. We prove a generalization of the Matrix Tree theorem for this class.Comment: 29 pages, 2 figure

Geomagnetic storm dependence on the solar flare class

Content. Solar flares are often used as precursors of geomagnetic storms. In particular, Howard and Tappin (2005) recently published in A&A a dependence between X-ray class of solar flares and Ap and Dst indexes of geomagnetic storms which contradicts to early published results. Aims. We compare published results on flare-storm dependences and discuss possible sources of the discrepancy. Methods. We analyze following sources of difference: (1) different intervals of observations, (2) different statistics and (3) different methods of event identification and comparison. Results. Our analysis shows that magnitude of geomagnetic storms is likely to be independent on X-ray class of solar flares.Comment: 3 pages, 1 tabl

Natural variation in ovule morphology is influenced by multiple tissues and impacts downstream grain development in barley (Hordeum vulgare L.).

The ovule plays a critical role in cereal yield as it is the site of fertilization and the progenitor of the grain. The ovule primordium is generally comprised of three domains, the funiculus, chalaza, and nucellus, which give rise to distinct tissues including the integuments, nucellar projection, and embryo sac. The size and arrangement of these domains varies significantly between model eudicots, such as Arabidopsis thaliana, and agriculturally important monocotyledonous cereal species, such as Hordeum vulgare (barley). However, the amount of variation in ovule development among genotypes of a single species, and its functional significance, remains unclear. To address this, wholemount clearing was used to examine the details of ovule development in barley. Nine sporophytic and gametophytic features were examined at ovule maturity in a panel of 150 European two-row spring barley genotypes, and compared with grain traits from the preceding and same generation. Correlations were identified between ovule traits and features of grain they produced, which in general highlighted a negative correlation between nucellus area, ovule area, and grain weight. We speculate that the amount of ovule tissue, particularly the size of the nucellus, may affect the timing of maternal resource allocation to the fertilized embryo sac, thereby influencing subsequent grain development.Laura G. Wilkinson, Xiujuan Yang, Rachel A. Burton, Tobias Würschum and Matthew R. Tucke

A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function

We present a mathematical model for the formation of an avascular tumor based on the loss by gene mutation of the tumor suppressor function of p53. The wild type p53 protein regulates apoptosis, cell expression of growth factor and matrix metalloproteinase, which are regulatory functions that many mutant p53 proteins do not possess. The focus is on a description of cell movement as the transport of cell population density rather than as the movement of individual cells. In contrast to earlier works on solid tumor growth, a model is proposed for the initiation of tumor growth. The central idea, taken from the mathematical theory of dynamical systems, is to view the loss of p53 function in a few cells as a small instability in a rest state for an appropriate system of differential equations describing cell movement. This instability is shown (numerically) to lead to a second, spatially inhomogeneous, solution that can be thought of as a solid tumor whose growth is nutrient diffusion limited. In this formulation, one is led to a system of nine partial differential equations. We show computationally that there can be tumor states that coexist with benign states and that are highly unstable in the sense that a slight increase in tumor size results in the tumor occupying the sample region while a slight decrease in tumor size results in its ultimate disappearance

Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic

We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of 1+1-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip ``soft'' stochastic dynamic. The soft dynamic is characterized by the property that the effects of changes in field energy and interaction energy factorize in the transition rate, in contrast to the nonfactorizing nature of the traditional Glauber and Metropolis rates (``hard'' dynamics). This work extends our previous studies of the Ising model with a hard dynamic and the unrestricted SOS model with soft and hard dynamics. [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002).] The Ising model with soft dynamics is found to have closely similar properties to the SOS model with the same dynamic. In particular, the local interface width does not diverge with increasing field, as it does for hard dynamics. The skewness of the interface at nonzero field is very weak and has the opposite sign of that obtained with hard dynamics.Comment: 19 pages LaTex with 7 imbedded figure

Wear and Friction Behavior of Metal Impregnated Microporous Carbon Composites

Metal-matrix composites have been prepared by pressure-infiltration casting of copper-base alloy melts into microporous carbon preforms. The carbon preforms contained varying proportions of amorphous carbon and graphite. Load dependence of the wear and friction behavior of the composite pins has been examined under ambient conditions against cast-iron plates, using a pin-on-plate reciprocating wear tester. The wear resistance of the composite is significantly improved, as compared with the base alloy. Contrary to the normally expected behavior, the addition of graphite to the amorphous carbon does not reduce the friction coefficient, especially at high loads. The wear and friction behavior of the composites is very sensitive to the size and distribution of the microstructural constituents

The first long-read nuclear genome assembly of Oryza australiensis, a wild rice from northern Australia

Oryza australiensis is a wild rice native to monsoonal northern Australia. The International Oryza Map Alignment Project emphasises its significance as the sole representative of the EE genome clade. Assembly of the O. australiensis genome has previously been challenging due to its high Long Terminal Repeat (LTR) retrotransposon (RT) content. Oxford Nanopore long reads were combined with Illumina short reads to generate a high-quality ~ 858 Mbp genome assembly within 850 contigs with 46× long read coverage. Reference-guided scaffolding increased genome contiguity, placing 88.2% of contigs into 12 pseudomolecules. After alignment to the Oryza sativa cv. Nipponbare genome, we observed several structural variations. PacBio Iso-Seq data were generated for five distinct tissues to improve the functional annotation of 34,587 protein-coding genes and 42,329 transcripts. We also report SNV numbers for three additional O. australiensis genotypes based on Illumina re-sequencing. Although genetic similarity reflected geographical separation, the density of SNVs also correlated with our previous report on variations in salinity tolerance. This genome re-confirms the genetic remoteness of the O. australiensis lineage within the O. officinalis genome complex. Assembly of a high-quality genome for O. australiensis provides an important resource for the discovery of critical genes involved in development and stress tolerance.Aaron L. Phillips, Scott Ferguson, Nathan S. Watson, Haigh, Ashley W. Jones, Justin O. Borevitz, Rachel A. Burton, Brian J. Atwel

Microstructure and Velocity of Field-Driven SOS Interfaces: Analytic Approximations and Numerical Results

The local structure of a solid-on-solid (SOS) interface in a two-dimensional kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field, is studied by an analytic mean-field, nonlinear-response theory [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field-dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.Comment: 18 pages RevTex4 with imbedded figure