Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.Comment: 23 pages, typos added, minor change

Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Small-amplitude solitons in a nonlocal sine-Gordon model

It is shown that small amplitude solitons of a nonlocal sine-Gordon model corresponding to different frequencies of the carrier wave can create coupled states. The effect is due to a change of the dispersion originated by a nonlocal nonlinearity. Within the framework of the multiscale expansion such pulses are described by a system of nonlinear Schtidinger equations which possesses coupled mode solutions in the form of running localized waves (breathers). Such breathers consist of modes with different frequencies and are characterized by two internal frequencies.info:eu-repo/semantics/publishedVersio

Using synchronization to improve earthquake forecasting in a cellular automaton model

A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.Comment: 4 pages, 3 figure

Non conservative Abelian sandpile model with BTW toppling rule

A non conservative Abelian sandpile model with BTW toppling rule introduced in [Tsuchiya and Katori, Phys. Rev. E {\bf 61}, 1183 (2000)] is studied. Using a scaling analysis of the different energy scales involved in the model and numerical simulations it is shown that this model belong to a universality class different from that of previous models considered in the literature.Comment: RevTex, 5 pages, 6 ps figs, Minor change

Density and reproductive characteristics of female brown bears in the Cantabrian Mountains, NW Spain

Here we present annual nearest-neighbour distances (as a proxy of density) between females with cubs-of-the-year (hereafter FCOY) and reproductive characteristics of brown bears Ursus arctos in the Cantabrian Mountains (NW Spain), from 1989 to 2017. FCOY nearest-neighbour distances and reproduction parameters of 19 focal females followed over several consecutive years (from 2004 to 2017) were obtained from bears inhabiting the western sector of the Cantabrian Mountains, where most of the bear population resides. In contrast, general reproductive characteristics were studied in the whole Cantabrian Mountains (western and eastern sectors together) on a sample of 362 litter sizes and 695 cubs. Mean nearest-neighbour distance between FCOY was 2559 ± 1222 m (range = 1305–4757 m). Mean litter size was significantly larger in the west (1.8 ± 0.2 cubs) than in the east (1.3 ± 0.6 cubs). Mean litter size for the whole of the Cantabrian Mountains was 1.6 ± 0.3 cubs. Litter sizes of one, two and three cubs represented 33.4, 56.1 and 10.5% of observed family groups, respectively. Interannual variations in litter size were not significant for both the western and the eastern areas. Mean cub mortality was 0.2 ± 0.5 cubs and did not vary among years. Cub mortality per litter size was 3.9% for one cub, 69.2% for two cubs and 26.9% for three cubs. Mean reproductive rate of the 19 focal females was 1.5 ± 0.6 cubs (n = 58 litters). Litter size of focal FCOY did not differ from the litter size obtained from systematic observations in the whole Cantabrian Mountains. During this period, cub mortality occurred in 24.1% of the 58 litters. Females usually bred every second year (average litter interval = 2.2 years). The estimated reproductive rate for the bear population was 0.7 young born/year/reproductive adult female

Density probability distribution in one-dimensional polytropic gas dynamics

We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a hierarchical manner, we assume that density fluctuations follow a random multiplicative process. When the polytropic exponent $\gamma$ is equal to unity, the local Mach number is independent of the density, and our assumption leads us to expect that the probability density function (PDF) of the density field is a lognormal. This isothermal case is found to be singular, with a dispersion $\sigma_s^2$ which scales like the square turbulent Mach number $\tilde M^2$, where $s\equiv \ln \rho$ and $\rho$ is the fluid density. This leads to much higher fluctuations than those due to shock jump relations. Extrapolating the model to the case $\gamma \not =1$, we find that, as the Mach number becomes large, the density PDF is expected to asymptotically approach a power-law regime, at high densities when $\gamma<1$, and at low densities when $\gamma>1$. This effect can be traced back to the fact that the pressure term in the momentum equation varies exponentially with $s$, thus opposing the growth of fluctuations on one side of the PDF, while being negligible on the other side. This also causes the dispersion $\sigma_s^2$ to grow more slowly than $\tilde M^2$ when $\gamma\not=1$. In view of these results, we suggest that Burgers flow is a singular case not approached by the high-$\tilde M$ limit, with a PDF that develops power laws on both sides.Comment: 9 pages + 12 postscript figures. Submitted to Phys. Rev.