Dynamical system analysis of interacting models

We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically stable critical point, future limit of any expanding solution. Our analysis also shows that the Minkowski spacetime is an unstable critical point, which eventually collapses to a singularity. In this way, such a prescription for the vacuum decay not only predicts the correct future de Sitter limit, but also forbids the existence of a stable Minkowski universe. We also study the effect of matter creation on the growth of structures and their peculiar velocities, showing that it is inside the current errors of redshift space distortions observations.Comment: 6 pages, 3 figures. A section was added with an analysis of structures growth rate and peculiar velocities. To appear in General Relativity and Gravitatio

On dark degeneracy and interacting models

Cosmological background observations cannot fix the dark energy equation of state, which is related to a degeneracy in the definition of the dark sector components. Here we show that this degeneracy can be broken at perturbation level by imposing two observational properties on dark matter. First, dark matter is defined as the clustering component we observe in large scale structures. This definition is meaningful only if dark energy is unperturbed, which is achieved if we additionally assume, as a second condition, that dark matter is cold, i.e. non-relativistic. As a consequence, dark energy models with equation-of-state parameter $-1 \le\omega< 0$ are reduced to two observationally distinguishable classes with $\omega = -1$, equally competitive when tested against observations. The first comprises the $\Lambda$CDM model with constant dark energy density. The second consists of interacting models with an energy flux from dark energy to dark matter.Comment: Version accepted for publication in JCA

A unified time scale for quantum chaotic regimes

We present a generalised time scale for quantum chaos dynamics, motivated by nonextensive statistical mechanics. It recovers, as particular cases, the relaxation (Heisenberg) and the random (Ehrenfest) time scales. Moreover, we show that the generalised time scale can also be obtained from a nonextensive version of the Kolmogorov-Sinai entropy by considering the graininess of quantum phase space and a generalised uncorrelation between subsets of the phase space. Lyapunov and regular regimes for the fidelity decay are obtained as a consequence of a nonextensive generalisation of the $m$th point correlation function for a uniformly distributed perturbation in the classical limit

Schwarzites for Natural Gas Storage: A Grand-Canonical Monte Carlo Study

The 3D porous carbon-based structures called Schwarzites have been recently a subject of renewed interest due to the possibility of being synthesized in the near future. These structures exhibit negatively curvature topologies with tuneable porous sizes and shapes, which make them natural candidates for applications such as CO2 capture, gas storage and separation. Nevertheless, the adsorption properties of these materials have not been fully investigated. Following this motivation, we have carried out Grand-Canonical Monte Carlo simulations to study the adsorption of small molecules such as CO2, CO, CH4, N2 and H2, in a series of Schwarzites structures. Here, we present our preliminary results on natural gas adsorptive capacity in association with analyses of the guest-host interaction strengths. Our results show that Schwarzites P7par, P8bal and IWPg are the most promising structures with very high CO2 and CH4 adsorption capacity and low saturation pressure (<1bar) at ambient temperature. The P688 is interesting for H2 storage due to its exceptional high H2 adsorption enthalpy value of -19kJ/mol

Two loops calculation in chiral perturbation theory and the unitarization program of current algebra

In this paper we compare two loop Chiral Perturbation Theory (ChPT) calculation of pion-pion scattering with the unitarity second order correction to the current algebra soft-pion theorem. It is shown that both methods lead to the same analytic structure for the scattering amplitude.Comment: 13 pages, Revtex 3.0, no figures, submitted to Phys. Lett.

Network induces burst synchronisation in cat brain

The brain of mammals are divided into different cortical areas that are anatomically connected forming larger networks which perform cognitive tasks. The cat cerebral cortex is composed of 65 areas organised into the visual, auditory, somatosensory-motor and frontolimbic cognitive regions. We have built a network of networks, in which networks are connected among themselves according to the connections observed in the cat cortical areas aiming to study how inputs drive the synchronous behaviour in this cat brain-like network. We show that without external perturbations it is possible to observe high level of bursting synchronisation between neurons within almost all areas, except for the auditory area. Bursting synchronisation appears between neurons in the auditory region when an external perturbation is applied in another cognitive area. This is a clear evidence that pattern formation and collective behaviour in the brain might be a process mediated by other brain areas under stimulation

Subcovers and codes on the Xn,rX_{n,r} curves

In this work, subcovers $\mathcal{X}_{n,r}^s$ of the curve $\mathcal{X}_{n,r}$ are constructed, the Weierstrass semigroup $H(P_\infty)$ at the point $P_\infty \in \mathcal{X}_{n,r}^s$ is determined and the corresponding one-point AG codes are investigated. Codes establishing new records on the parameters with respect to the previously known ones are discovered, and $108$ improvements on MinT tables are obtained

Fisher metric from relative entropy group

In this work we consider the Fisher metric which results from the Hessian of the relative entropy group, that we called Fisher metric group, and we obtain the corresponding ones to the Boltzmann-Gibbs, Tsallis, Kaniadakis and Abe-Borges-Roditi classes. We prove that the scalar curvature of the Fisher metric group results a multiple of the standard Fisher one, with the factor of proportionality given by the local properties of the entropy group. For the Tsallis class, the softening and strengthening of the scalar curvature is illustrated with the $2D$ correlated model, from which their associated indexes for the canonical ensemble of a pair of interacting harmonic oscillators, are obtained

Self-Dual Codes over Z_2xZ_4

Self-dual codes over $\Z_2\times\Z_4$ are subgroups of $\Z_2^\alpha \times\Z_4^\beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exist a code \C\subseteq \Z_2^\alpha \times\Z_4^\beta are established. Moreover, the construction of a \add-linear code for each type and possible pair $(\alpha,\beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.Comment: Submitted to Designs, Codes and Cryptograph

Number Counts and Dynamical Vacuum Cosmologies

We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, $\rho_{\Lambda} \propto H$, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses ($M \gtrsim 10^{14} M_{\odot}h^{-1}$) when compared to the standard $\Lambda$CDM model. Since these models are not reducible to each other, this number counts signature can in principle be tested in future surveys.Comment: 6 pages, 3 figures. Accepted for publication in MNRA