On the parametrization of solutions of the Yang--Baxter equations

We study all five-, six-, and one eight-vertex type two-state solutions of the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13} A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of these solution. Starting with algebraic solutions, whose parameters have no specific interpretation, and then using these symmetries we can construct a parametrization where we can identify global, color and spectral parameters. We show in particular how the distribution of these parameters may be changed by a change of gauge.Comment: 19 pages in LaTe

An exercise in experimental mathematics: calculation of the algebraic entropy of a map

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where different approaches are in such perfect agreement that we can trust we get to an exact result. This is an instructive example of experimental mathematics

Solvable Chaos

We present classes of discrete reversible systems which are at the same time chaotic and solvable

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations

Integrable lattice equations with vertex and bond variables

We present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables. In some of the models the vertex dynamics is independent of the evolution of the bond variables, and one can write the equations as non-autonomous "Yang-Baxter maps". We also present a model in which the vertex and bond variables are fully coupled. Integrability is tested with algebraic entropy as well as multidimensional consistencyComment: 15 pages, remarks added, other minor change

Scattering of cosmic strings by black holes: loop formation

We study the deformation of a long cosmic string by a nearby rotating black hole. We examine whether the deformation of a cosmic string, induced by the gravitational field of a Kerr black hole, may lead to the formation of a loop of cosmic string. The segment of the string which enters the ergosphere of a rotating black hole gets deformed and, if it is sufficiently twisted, it can self-intersect chopping off a loop of cosmic string. We find that the formation of a loop, via this mechanism, is a rare event. It will only arise in a small region of the collision phase space, which depends on the string velocity, the impact parameter and the black hole angular momentum. We conclude that generically, the cosmic string is simply scattered or captured by the rotating black hole.Comment: 11 pages, 2 figures, RevTe

3D hydrodynamic simulations of carbon burning in massive stars

We present the first detailed 3D hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon-burning shell within a 15 M⊙ 1D stellar evolution model. We consider models with 1283, 2563, 5123, and 10243 zones. The turbulent flow properties of these carbon-burning simulations are very similar to the oxygen-burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier–Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30 per cent and 10 per cent of the local pressure scaleheights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell-burning simulations, we observe entrainment at both boundaries in our carbon-shell-burning simulations. In the large Péclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, RiB (∝RiB−α, 0.5 ≲ α ≲ 1.0). We thus suggest the use of RiB as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing

Deciphering species-specific pollen tube guidance in Solanum

Small, secreted cysteine-rich proteins (CRPs)combine a highly stable cysteine spacing,ensuring conservation of their 3D structure andfunction, and hypervariable inter-cysteine blocks, allowing quick evolution of specific recognition domains. Interestingly, several CRPs were shown to control key pollen-pistil interactions in aspecies-specific way. The most emblematicexample is perhaps the LURE defensin-likefamily, controlling directional guidance of pollentubes (PTs) in Torenia and Arabidopsis.We chose wild potatoes (Solanum sect. Petota) asa case study to investigate the impact of rapidCRP divergence in plant speciation. Gathering ~200 close species with overlapping distribution areas, this taxon indeed exhibits strong reproductive isolation. Lab-on-a-chipmicrofluidic experiments carried out on 4 species show that species-preferential PT attraction is a key factor in this isolation. We suspect polymorphic CRPs to control this attraction. High-throughput sequencing technologies were applied to profile the ovule secretome as well as the reproductive transcriptomes of our 4 speciesof interest. To screen out candidate genes, we developped KAPPA, a sequence search algorithm specifically dedicated to CRPs, and obtained a set of 32 defensin-like groups expressed in ovules. Five promising chemoattractant candidates exhibiting (i) ovule-specific expression, (ii) down-regulation in guidance-defective ovules, and (iii) interspecific divergence were selectedfor further characterization. They are currently being investigated with on-gel assays and specific microfluidic devices tailored for Solanum PTs. This study will lead to a better understanding of CRP-mediated PT chemoattraction as one of the major species-specificity checkpoints that mustbe unlocked by pollen tubes in the pistil.Fil: Joly, V.. Institut de Recherche En Biologie Végétale; CanadáFil: Viallet, C.. Institut de Recherche En Biologie Végétale; CanadáFil: Liu, Y.. Institut de Recherche En Biologie Végétale; CanadáFil: Zaro, A.. Universidad de Barcelona; EspañaFil: Ceriotti, Luis Federico. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Biología Agrícola de Mendoza. Universidad Nacional de Cuyo. Facultad de Ciencias Agrarias. Instituto de Biología Agrícola de Mendoza; ArgentinaFil: Matton, D. P.. Institut de Recherche En Biologie Végétale; CanadáEastern Regional MeetingMontrealCanadáCanadian Society of Plant BiologistsMcGill Universit