Static and dynamic simulation in the classical two-dimensional anisotropic Heisenberg model

By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex developed in such a model exhibit two different behaviors depending if the value of the anisotropy $\lambda$ lies below or above a critical value $\lambda_c$ . The in-plane and out-of-plane correlation functions ($S^{xx}$ and $S^{zz}$) were obtained numerically for $\lambda \lambda_c$ . We found that the out-of-plane dynamical correlation function exhibits a central peak for $\lambda > \lambda_c$ but not for $\lambda < \lambda_c$ at temperatures above $T_{BKT}$ .Comment: 7 page

4-dimensional compact manifolds with nonnegative biorthogonal curvature

The goal of this article is to study the pinching problem proposed by S.-T. Yau in 1990 replacing sectional curvature by one weaker condition on biorthogonal curvature. Moreover, we classify 4-dimensional compact oriented Riemannian manifolds with nonnegative biorthogonal curvature. In particular, we obtain a partial answer to Yau Conjecture on pinching theorem for 4-dimensional compact manifolds.Comment: To appear in the Michigan Mathematical Journa

Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4-manifolds

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.Comment: To appear in Mathematische Nachrichte

The harmonic oscillator, dimensional analysis and inflationary solutions

In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.Comment: 6 pages, revtex4, no figure

A description of several coordinate systems for hyperbolic spaces

This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.Comment: 26 pages, standard LaTeX article (uses packages graphics and fancyheadings), 3 figure

Stability of branched pull-back projective foliations

We prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in ${\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general position and $f:{\mathbb P^n}--->{\mathbb P^2}$, $deg(f)=\nu\geq2,$ is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets $\{\mathcal {F}= f^{*}(\mathcal{G})\}$ are new irreducible components of the space of holomorphic foliations of certain degrees.Comment: arXiv admin note: substantial text overlap with arXiv:1503.07827, arXiv:1503.0071

Coupled quintessence with a possible transient accelerating phase

We discuss some cosmological consequences of a general model of coupled quintessence in which the phenomenological coupling between the cold dark matter and dark energy is a function of the cosmic scale factor $\epsilon(a)$. This class of models presents cosmological solutions in which the Universe is currently dominated by an exotic component, but will eventually be dominated by cold dark matter in the future. This dynamical behavior is considerably different from the standard $\Lambda$CDM evolution, and may alleviate some conflicts in reconciling the idea of the dark energy-dominated universe with observables in String/M-theory. Finally, we investigate some observational features of this model and discuss some constraints on its parameters from current SNe Ia, BAO and CMB data.Comment: 7 pages, 5 figures, LaTe

Branched pull-back components of the space of codimension 1 foliations on Pn\mathbb P^n

Let $\mathcal{F}$ be written as $f^{*}\mathcal{G}$, where $\mathcal{G}$ is a foliation in ${\mathbb P^2}$ with three invariant lines in general position, say $(XYZ)=0$, and $f:{\mathbb P^n}--->{\mathbb P^2}$, $f=(F^\alpha_{0}:F^\beta_{1}:F^\gamma_{2})$ is a nonlinear rational map. Using local stability results of singular holomorphic foliations, we prove that: if $n\geq 3$, the foliation $\mathcal{F}$ is globally stable under holomorphic deformations. As a consequence we obtain new irreducible componentes for the space of codimension one foliations on $\mathbb P^n$. We present also a result which characterizes holomorphic foliations on ${\mathbb P^n}, n\geq 3$ which can be obtained as a pull back of foliations on ${\mathbb P^2}$ of degree $d\geq2$ with three invariant lines in general position.Comment: arXiv admin note: text overlap with arXiv:1503.0071

A possible analogy between the dynamics of a skydiver and a scalar field: cosmological consequences

The cosmological consequences of a slow rolling scalar field with constant kinetic term in analogy to the vertical movement of a skydiver after reaching terminal velocity are investigated. It is shown that the terminal scalar field hypothesis is quite realistic. In this approach, the scalar field potential is given by a quadratic function of the field. This model provides solutions in which the Universe was dominated in the past by a mixture of baryons and dark matter, is currently accelerating (as indicated by type Ia supernovae data), but will be followed by a contraction phase. The theoretical predictions of this model are consistent with current observations, therefore, a terminal scalar field is a viable candidate to dark energy.Comment: Accepted for publicatio

Irreducible components of the space of foliations by surfaces

Let $\mathcal{F}$ be written as $f^{*}(\mathcal{G})$, where $\mathcal{G}$ is a $1$-dimensional foliation on ${\mathbb P^{n-1}}$ and $f:{\mathbb P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local stability results of singular holomorphic foliations, to prove that: if $n\geq 4$, a foliation $\mathcal{F}$ by complex surfaces on $\mathbb P^n$ is globally stable under holomorphic deformations. As a consequence, we obtain irreducible components for the space of two-dimensional foliations in $\mathbb P^n$. We present also a result which characterizes holomorphic foliations on ${\mathbb P^n}, n\geq 4$ which can be obtained as a pull back of 1- foliations in ${\mathbb P^{n-1}}$ of degree $d\geq2$