Explore the vast range of titles available.

We revisit Duff, Okun, and Veneziano’s divergent views on the number of fundamental constants and argue that the issue can be set to rest by having spacetime as the starting point. This procedure disentangles the resolution in what depends on the assumed spacetime (whether relativistic or not) from the theories built over it. By defining that the number of fundamental constants equals the minimal number of independent standards necessary to express all observables, as assumed by Duff, Okun, and Veneziano, it is shown that the same units fixed by the apparatuses used to construct the spacetimes are enough to express all observables of the physical laws defined over them. As a result, the number of fundamental constants equals one in relativistic spacetimes.

The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates (u,v) describing a non-stationary charged black hole with varying mass m(v) and charge q(v). The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity.

By using rather conservative estimates based on the simplest polar cap model, we search the ATNF Pulsar Catalogue for strongly magnetized stars that could accelerate relativistic protons up to the curvature pion production threshold. The best candidate turns out to be the 16 ms pulsar J0537-6910, but the corresponding characteristic parameter χ = a / m p is yet too small to give origin to observable signals. We show that, for pulsars with period P ≈1 ms, a surface polar magnetic field B ≈10 12  G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered.

We revisit here the mathematical model for ATP production in mitochondria introduced recently by Bertram, Pedersen, Luciani, and Sherman (BPLS) as a simplification of the more complete but intricate Magnus and Keizer’s model. We identify some inaccuracies in the BPLS original approximations for two flux rates, namely the adenine nucleotide translocator rate J ANT and the calcium uniporter rate J uni . We introduce new approximations for such flux rates and then analyze some of the dynamical properties of the model. We infer, from exhaustive numerical explorations, that the enhanced BPLS equations have a unique attractor fixed point for physiologically acceptable ranges of mitochondrial variables and respiration inputs, as one would indeed expect from homeostasis. We determine, in the stationary regime, the dependence of the mitochondrial variables on the respiration inputs, namely the cytosolic concentration of calcium Ca c and the substrate fructose 1,6-bisphosphate FBP. The same dynamical effects of calcium and FBP saturations reported for the original BPLS model are observed here. We find out, however, a novel nonstationary effect, which could be, in principle, physiologically interesting: some response times of the model tend to increase considerably for high concentrations of calcium and/or FBP. In particular, the larger the concentrations of Ca c and/or FBP, the larger the necessary time to attain homeostasis.

We revisit in this note the Hénon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the Hénon's parabolae and get all isochrone central potentials under mild smoothness assumptions on the potential function. Our approach also allows us to conclude that isochronous radial periods with explicit energy dependence are necessarily Keplerian, i.e., \\(T^{2}\\propto|E|^{-3}\\), and that their corresponding orbits can be easily integrated by mapping them into the usual Kepler problem. It can also be employed to study some other inverse central-force problems and, in particular, it provides a proof of Bertrand's theorem.

We introduce the relativistic version of the well-known Henon's isochrone spherical models: static spherically symmetrical spacetimes in which all bounded trajectories are isochrone in Henon's sense, i.e., their radial periods do not depend on their angular momenta. Analogously to the Newtonian case, these \"isochrone spacetimes\" have as particular cases the so-called Bertrand spacetimes, in which all bounded trajectories are periodic. We propose a procedure to generate isochrone spacetimes by means of an algebraic equation, present explicitly several families of these spacetimes, and discuss briefly their main properties. We identify, in particular, the family whose Newtonian limit corresponds to the Henon's isochrone potentials and that could be considered as the relativistic extension of the original Henon's proposal for the study of globular clusters. Nevertheless, isochrone spacetimes generically violate the weak energy condition and may exhibit naked singularities, challenging their physical interpretation in the context of General Relativity.

In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. We show, namely, that the presence of certain symmetries in the interlayer connection pattern tends to diminish the synchronization capability of the whole network or, in other words, asymmetries in the interlayer connections would enhance synchronization in such structured networks. Our results might help the understanding not only of the AISync mechanism itself, but also its possible role in the determination of the interlayer connection pattern of multilayer and other structured networks with optimal synchronization properties.

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies \\(\\omega_i\\), such that a fraction of them is subject to an external periodic force with frequency \\(\\Omega\\), the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that \\(|\\omega_i-\\Omega|\\) is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization are desired properties. Some properties of the optimal forced networks and its relation to recent results in the literature are also discussed.