Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.Comment: 17 pages, no figure

A simple model for heterogeneous flows of yield stress fluids

Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress $\Sigma$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $\dot{\Gamma}$, shear banding is predicted within a range of values of $\dot{\Gamma}$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.Comment: 13 pages, 13 figure

Inverse condensation of adsorbed molecules with two conformations

Conventional gas-liquid phase transitions feature a coexistence line that has a monotonic and positive slope in line with our intuition that cooling always leads to condensation. Here we study the inverse phenomenon, condensation of adsorbed organic molecules into dense domains upon heating. Our considerations are motivated by recent experiments [Aeschlimann et al., Angew. Chem. (2021)], which demonstrate the partial dissolution of an ordered molecular monolayer and the mobilization of molecules upon cooling. We introduce a simple lattice model in which each site can have three states corresponding to unoccupied and two discernible molecular conformations. We investigate this model through Monte Carlo simulations, mean-field theory, and exact results based on the analytical solution of the Ising model in two dimensions. Our results should be broadly applicable to molecules with distinct conformations that have sufficiently different entropies or heat capacities

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Semiclassical and quantum Liouville theory

We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere on the background of three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and of the further perturbative corrections. The zeta function regularization provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseudosphere by Zamolodchikov and Zamolodchikov we obtain the correct quantum conformal dimensions from the one loop calculation and we show explicitly that the two loop corrections do not change such dimensions. We then apply the method to the case of the pseudosphere with one finite singularity and compute the exact value for the quantum determinant. Such results are compared to those of the conformal bootstrap approach finding complete agreement.Comment: 12 pages, 1 figure, Contributed to 5th Meeting on Constrained Dynamics and Quantum Gravity (QG05), Cala Gonone, Sardinia, Italy, 12-16 Sep 200

In-situ Microwave Brightness Temperature Variability from Ground-based Radiometer Measurements at Dome C in Antarctica Induced by Wind-formed Features

Space-borne microwave radiometers are among the most useful tools to study snow and to collect information on the Antarctic climate. They have several advantages over other remote sensing techniques: high sensitivity to snow properties of interest (temperature, grain size, density), subdaily coverage in the polar regions, and their observations are independent of cloud conditions and solar illumination. Thus, microwave radiometers are widely used to retrieve information over snow-covered regions. For the Antarctic Plateau, many studies presenting retrieval algorithms or numerical simulations have assumed, explicitly or not, that the subpixel-scale heterogeneity is negligible and that the retrieved properties were representative of whole pixels. In this presentation, we investigate the spatial variations of brightness temperature over arange of a few kilometers in the Dome C area (Antarctic Plateau)

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H^3, for arbitrary values of the angular momentum. For this example, considering a quotient of H^3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.Comment: 16 pages, 13 figure

Diversity of modes of reproduction and sex determination systems in invertebrates, and the putative contribution of genetic conflict

About eight million animal species are estimated to live on Earth, and all except those belonging to one subphylum are invertebrates. Invertebrates are incredibly diverse in their morphologies, life histories, and in the range of the ecological niches that they occupy. A great variety of modes of reproduction and sex determination systems is also observed among them, and their mosaic-distribution across the phylogeny shows that transitions between them occur frequently and rapidly. Genetic conflict in its various forms is a long-standing theory to explain what drives those evolutionary transitions. Here, we review (1) the different modes of reproduction among invertebrate species, highlighting sexual reproduction as the probable ancestral state; (2) the paradoxical diversity of sex determination systems; (3) the different types of genetic conflicts that could drive the evolution of such different systems

Schistosome W-Linked genes inform temporal dynamics of sex chromosome evolution and suggest candidate for sex determination

Schistosomes, the human parasites responsible for snail fever, are female-heterogametic. Different parts of their ZW sex chromosomes have stopped recombining in distinct lineages, creating “evolutionary strata” of various ages. Although the Z-chromosome is well characterized at the genomic and molecular level, the W-chromosome has remained largely unstudied from an evolutionary perspective, as only a few W-linked genes have been detected outside of the model species Schistosoma mansoni. Here, we characterize the gene content and evolution of the W-chromosomes of S. mansoni and of the divergent species S. japonicum. We use a combined RNA/DNA k-mer based pipeline to assemble around 100 candidate W-specific transcripts in each of the species. About half of them map to known protein coding genes, the majority homologous to S. mansoni Z-linked genes. We perform an extended analysis of the evolutionary strata present in the two species (including characterizing a previously undetected young stratum in S. japonicum) to infer patterns of sequence and expression evolution of W-linked genes at different time points after recombination was lost. W-linked genes show evidence of degeneration, including high rates of protein evolution and reduced expression. Most are found in young lineage-specific strata, with only a few high expression ancestral W-genes remaining, consistent with the progressive erosion of nonrecombining regions. Among these, the splicing factor u2af2 stands out as a promising candidate for primary sex determination, opening new avenues for understanding the molecular basis of the reproductive biology of this group

Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids

With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite size effects. Although for the sake of simplicity most of our explicit formulae deal with a 2D situation, our statements hold for 3D situations as well.Comment: submitted to EPJ