Search

We address the level of complexity that can be observed in the dynamics near a robust heteroclinic network. We show that infinite switching, which is a path towards chaos, does not exist near a heteroclinic network such that the eigenvalues of the Jacobian matrix at each node are all real. Furthermore, for a path starting at a node that belongs to more than one heteroclinic cycle, we find a bound for the number of such nodes that can exist in any such path. This constricted dynamics is in stark contrast with examples in the literature of heteroclinic networks such that the eigenvalues of the Jacobian matrix at one node are complex.

In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive $$- \Delta_{\Phi} u +V(x)\phi(|u|)u= K(x)f(u)\mbox{ in } \mathbb{R}^{N}$$ where $N\geq2$, $V,K$ are nonnegative continuous functions and $f$ is a continuous function with a quasicritical growth. Here we extend the Hardy-type inequalities presented in \cite{AlvesandMarco} to nonreflexive Orlicz spaces. Through inequalities together with a variational method for non-differentiable functionals we will obtain a ground state solution. We analyze also the problem with $V=0$.

Luminosity, which is the total amount of radiant energy emitted by an object, is one of the most critical quantities in astrophysics for characterizing stars. Equally important is the temporal evolution of a star's luminosity because of its intimate connection with the stellar energy budget, large-scale convective motion, and heat storage in the stellar interior. Here, we model the solar luminosity by extending a semi-empirical total solar irradiance (TSI) model that uses solar-surface magnetism to reconstruct solar irradiance over the entire 4{\pi} solid angle around the Sun. This model was constrained by comparing its output to the irradiance in the Earth's direction with the measured TSI. Comparing the solar luminosity to the TSI on timescales from days to for cycles 23 and 24, we find poor agreement on short timescales (< solar rotation). On longer timescales, however, we find good agreement between the luminosity model and the TSI, which suggests that the extrapolation of luminosities to multi-cycle timescales based on TSI reconstructions may be possible. We show that the solar luminosity is not constant but varies in phase with the solar cycle. This variation has an amplitude of 0.14% from minimum to maximum for solar cycle 23. Considering the energetics in the solar convection zone, it is therefore obvious that a steady-state input from the radiative zone at the solar minimum level would lead to a gradual reduction in the energy content in the convection zone over multi-century timescales. We show that the luminosity at the base of the convection zone should be approximately 0.032% higher than that at the solar surface during solar minimum to maintain net energy equilibrium through the solar cycle. These different energy-input scenarios place constraints on the long-term evolution of the total solar irradiance and its impact on the solar forcing of climate variability., Comment: Accepted for publication in ApJS. (26.March.2022)

Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a $d$-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann-Gibbs exponential factor is generically substituted by its $q$-generalisation, and is recovered in the $q=1$ limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas., Comment: 8 pages and 4 figures

The static and time-dependent behaviours of adhesively bonded polyethylene Double-Strap (DS) joints were investigated to assess the viability of this joint configuration relative to the Single-Lap (SL) joints. Both experiments and finite element simulations are conducted. First, we individually characterise the tensile and creep behaviour of the adhesive and adherent materials; an epoxy-based adhesive and polyethylene, respectively. This information is used to develop suitable constitutive models that are then implemented in the commercial finite element package ABAQUS by means of user material subroutines, UMATs. The numerical models are used to design the creep tests on the adhesive joints. Afterwards, an extensive experimental campaign is conducted where we characterise the static and creep behaviour of two joint configurations, SL and DS joints, and three selected values of the overlap length. In regard to the static case, results reveal an increase in the failure load with increasing overlap length, of up to 10% for an overlap length of 39 mm. Also, slightly better performance is observed for the SL joint configuration. For the creep experiments, we show that the DS adhesive joint configuration leads to much shorter elongations, relative to the SL joints. These differences diminish with increasing overlap length but remain substantial in all cases. In both joint configurations, the elongation increases with decreasing overlap length. For instance, increasing the overlap length to 39 mm led to a 50% and a 30% reduction in elongation for SL and DS joints, respectively. Moreover, the numerical predictions show a good agreement with the experiments. The stress redistribution is investigated and it is found that the shear stress is highly sensitive to the testing time, with differences being more noticeable for the DS joint system.

The amplification of the relative Fresnel (Goos-Haenchen) phase by an appropriate number of total internal reflections and the choice of favorable incidence angles allow to observe full oscillations in the power of a DPSS laser transmitted through sequential BK7 blocks. The experimental results confirm the theoretical predictions. The optical apparatus used in this letter can be seen as a new type of two-phase ellipsometric system where the phase of the complex refractive index is replaced by the relative Fresnel (Goos-Haenchen) phase., Comment: 7 pages, 3 figures, 1 table

We present a study of social networks based on the analysis of Brazilian and Portuguese family names (surnames). We construct networks whose nodes are names of families and whose edges represent parental relations between two families. From these networks we extract the connectivity distribution, clustering coefficient, shortest path and centrality. We find that the connectivity distribution follows an approximate power law. We associate the number of hubs, centrality and entropy to the degree of miscegenation in the societies in both countries. Our results show that Portuguese society has a higher miscegenation degree than Brazilian society. All networks analyzed lead to approximate inverse square power laws in the degree distribution. We conclude that the thermodynamic limit is reached for small networks (3 or 4 thousand nodes). The assortative mixing of all networks is negative, showing that the more connected vertices are connected to vertices with lower connectivity. Finally, the network of surnames presents some small world characteristics., Comment: 13 pages, 5 figures