Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Journal of Statistical Physics - The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a...     

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive \(N\) -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.     

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.     

X‐ray‐excited optical luminescence and X‐ray absorption fine‐structures studies of CdWO4 scintillator

X‐ray‐excited optical luminescence (XEOL) emission and excitation spectra as well as the EXAFS signal of CdWO₄ were measured in the energy region of the Cd and W absorption edges. From EXAFS refinement, structural parameters such as number of atoms, distance from the absorbing atom and width of coordination shells in the W neighborhood were determined. The role of W–O interactions on the intrinsic luminescence of CdWO₄ is discussed. The efficiencies of conversion, transfer and emission processes involved in the scintillation mechanism showed to be high when self‐trapped excitons are formed locally by direct excitation of W ions. Annihilation of these excitons provides the characteristic scintillation of CdWO₄, a broad band emission with maximum at 500 nm. The presence of two energetically different O positions in the lattice gives rise to the composite structure of the luminescence band, and no influence of extrinsic defects was noticed. A mismatch between the X‐ray absorption coefficient and the zero‐order luminescence curves corroborates that the direct excitation of Cd ions induces secondary electronic excitations not very effective in transferring energy to the luminescent group, WO₆.     

Extreme value theory for singular measures

In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and He?non maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.     

Black holes in scalar-tensor gravity

Hawking has proven that black holes which are stationary as the end point of gravitational collapse in Brans-Dicke theory (without a potential) are no different than in general relativity. We extend this proof to the much more general class of scalar-tensor and f(R) gravity theories, without assuming any symmetries apart from stationarity.     

Beam profile monitor for annihilation cross section measurements of antiprotons at 100 keV

The ASACUSA (the Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration is planning to measure the cross sections of antiproton annihilations at kinetic energy 100 keV on targets of various mass numbers (C,?Ni, Sn, and Pt) using the Antiproton Decelerator (AD) of CERN. No previous measurement exists in this region where the A-dependence of the cross section is expected to deviate from the A $^{\frac{2}{3}}$ (Batty et al, Nucl Phys A 689:721, 2001) as reported by the Obelix collaboration. A beam profile monitor based on secondary electron emission with a grid of electrode pads fabricated on an FR4-type glass-epoxy circuit board was developed for this measurement. The advantage of this kind of detector is that it is simple, lightweight, and low cost. It was used to measure the spatial profile of 100-ns-long beam pulses containing > 6 × 10⁴ antiprotons with an active area of 40?mm?× 40 mm and a spatial resolution of 4 mm.     

X-ray excited optical luminescence of Ce-doped BaAl2O4

The luminescence properties of Ce³⁺ in BaAl₂O₄ are reported. The results of simultaneous measurements of XEOL and XAS in the X-ray energy range that includes the Ba L_II,III-edges and Ce L_III edge are shown. The XEOL yield increases as the energy of the photons increases. The radioluminescence spectra, taken from 200 to 1100 nm, showed broad emission bands corresponding to 5d¹→²F_5/2, ²F_7/2 transitions of Ce³⁺ when incorporated into two nonequivalent Ba sites. The lifetime of the light emission was also measured using the single bunch operation mode at the Brazilian National Synchrotron Laboratory (LNLS), and BaAl₂O₄:Ce³⁺ showed single exponential decay time component of about 44.3 ns.     

Universal Behaviour of Extreme Value Statistics for Selected Observables of Dynamical Systems

The main results of the extreme value theory developed for the investigation of the observables of dynamical systems rely, up to now, on the block maxima approach. In this framework, extremes are identified with the block maxima of the time series of the chosen observable, in the limit of infinitely long blocks. It has been proved that, assuming suitable mixing conditions for the underlying dynamical systems, the extremes of a specific class of observables are distributed according to the so called Generalised Extreme Value (GEV) distribution. Direct calculations show that in the case of quasi-periodic dynamics the block maxima are not distributed according to the GEV distribution. In this paper we show that considering the exceedances over a given threshold instead of the block-maxima approach it is possible to obtain a Generalised Pareto Distribution also for extremes computed in systems which do not satisfy mixing conditions. Requiring that the invariant measure locally scales with a well defined exponent—the local dimension—, we show that the limiting distribution for the exceedances of the observables previously studied with the block maxima approach is a Generalised Pareto distribution where the parameters depend only on the local dimensions and the values of the threshold but not on the number of observations considered. We also provide connections with the results obtained with the block maxima approach. In order to provide further support to our findings, we present the results of numerical experiments carried out considering the well-known Chirikov standard map.