SARS-CoV-2 is currently causing hundreds of deaths everyday in European countries, mostly in not yet vaccinated elderly.

Vaccine shortage poses relevant challenges to health authorities, called to act in a timely manner with scarcity of data.

We modelled the mortality reduction of the elderly according to a schedule of mRNA SARS-CoV-2 vaccine that prioritized first dose administration. For the case study of Italy, we show an increase in protected individuals up to 53.4% and a decrease of deaths up to 19.8% in the cohort of over 80s compared to the standard vaccine recalls after 3 or 4 weeks.

Our model supports the adoption of vaccination campaigns that prioritize administration of the first doses in the elderly.

# Category Archives: Highlights on physics papers

# Gravitational collapse from cold uniform asymmetric initial conditions

Francesco Sylos Labini, Michael Joyce

Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite *N* fluctuations and perturbations induced by the anisotropic gravitational field compete to determine the physical properties of the asymptotic quasi-stationary state. When finite *N* fluctuations dominate the dynamics, the particle energy distribution changes greatly and the final density profile {decays outside its core} as *r*^(-4) with an *N*-dependent amplitude. On the other hand, in the limit where the anisotropic perturbations dominate, the collapse is softer and the density profile shows a decay as *r*^(−3), as is typical of halos in cosmological simulations. However, even in this limit, convergence with *N* of the macroscopic properties of the virialized system, such as the particle energy distributions, the bound mass, and the density profile, is very slow and not clearly established, including for our largest simulations (with *N*∼10^6). Our results illustrate the challenges of accurately simulating the first collapsing structures in standard-type cosmological models

Comments: | 8 pages, 6 figures. Accepted for publication in Astronomy and Astrophysics |

Subjects: | Cosmology and Nongalactic Astrophysics (astro-ph.CO) |

Cite as: | arXiv:2106.02388 [astro-ph.CO] |

(or arXiv:2106.02388v1 [astro-ph.CO] for this version) |

# Zipf’s law for cosmic structures: how large are the greatest structures in the universe?

The statistical characterization of the distribution of visible matter in the universe is a central problem inmodern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greateststructures in the universe. This point is closely related to whether or not such a distribution can be approximated as beinghomogeneous on large enough scales. Here we assess this problem by considering the size distribution of superclustersof galaxies and by leveraging on the properties of Zipf-Mandelbrot law, providing a novel approach which complementsstandard analysis based on the correlation functions. We find that galaxy superclusters are well described by a pureZipf’s law with no deviations and this implies that all the catalogs currently available are not sufficiently large to spot atruncation in the power-law behavior. This finding provides evidence that structures larger than the greatest superclustersalready observed are expected to be found when deeper redshift surveys will be completed. As a consequence the scalebeyond which galaxy distribution crossovers toward homogeneity, if any, should increase accordingly

# Prioritizing the first doses of SARS-CoV-2 vaccine to save the elderly: the case study of Italy

Many countries are currently facing high mortality caused by the circulation of SARS-CoV-2 among the elderly not yet vaccinated. Vaccine shortage poses relevant challenges to health authorities, called to act in a timely manner, and with scarcity of vaccine, and data. We have developed a model for estimating of the impact of vaccination on the mortality of the elderly following a schedule of mRNA SARS-CoV-2 vaccine that prioritize first dose administration, as alternative to the standard schedule of two doses administered 3 to 4 weeks apart. We studied the Italian scenario, considering it representative of other Countries facing similar conditions in terms of virus circulation, mortality, and vaccine shortage, in the period from February 10 to April 14 2021. Under different conditions of quantity of vaccine administration, the schedule prioritizing first doses showed always significant increase of protected individuals, and a decrease of deaths, up to 19.8% less than the standard schedule. These findings support the vaccination option of prioritizing the first dose in the elderly until vaccine supplies are adequate.

# PRE Editor’s suggetion: “Formation of disks with long-lived spiral arms from violent gravitational dynamics”

Formation of disks with long-lived spiral arms from violent

gravitational dynamics

by Francesco Sylos Labini, Luis Diego Pinto, and Roberto

Capuzzo-Dolcetta

Dear Dr. Sylos-Labini,

We are pleased to inform you that your paper has been selected by the

editors of Physical Review E to be an Editors’ Suggestion.

# Properties of self gravitating quasi-stationary states

On a possibile solution of the core-cusp problem and the fundamental properties of self gravitating quasi-stationary states.

One of the crucial problems for the galaxy formation theory is to explain the cusp-core paradox: while the simulations of the theoretical models give rise to a diverging density profile at a small distance (1 / r) from the center, observations of galaxy profiles show that these are constant.

To understand the origin of these profiles it is necessary to understand the fundamental properties of the quasi-equilibrium states of gravitational systems and in particular what kind of dynamical path they followed during their formation.

We have found that, depending on the initial conditions, these stationary states can exhibit a small-scale divergent profile or a flat profile. This difference corresponds to a different dynamical nature underlying their origin.

Coming back to galaxies, the profiles indicate that the dynamic that gave them origin is a violent type of relaxation. That is, a dynamical process different from the “standard” one of cold dark matter models.

15 pages, 24 figures, Accepted for publication in Astronomy and Astrophysics

by Francesco Sylos Labini, Roberto Capuzzo-Dolcetta

Continue reading Properties of self gravitating quasi-stationary states

# Formation of disk galaxies with long-lived and non-stationary spiral arms

*
*

*This work represents a development of the study of the collapses of purely self-gravitating systems (see https://physics.aps.org/articles/v12/s19) to the case in which a dissipational gas component is also present. These latter systems show much richer morphological and kinematical structures that may have important observational implications to understand the kinematic and dynamics of the Milky Way as revealed by ongoing surveys such as the Gaia Mission. *

** by **Francesco Sylos Labini, Luis Diego Pinto, Roberto Capuzzo-Dolcetta** **

Continue reading Formation of disk galaxies with long-lived and non-stationary spiral arms

# Gaia-DR2 extended kinematical maps. Part III: Rotation curves analysis, dark matter, and Modified Newtonian dynamics tests

Ž. Chrobáková, M. López-Corredoira, F. Sylos Labini, H.-F. Wang, R. Nagy

Recent statistical deconvolution methods have produced extended kinematical maps in a range of heliocentric distances that are a factor of two to three larger than those analysed in the Gaia Collaboration based on the same data. In this paper, we use such maps to derive the rotation curve both in the Galactic plane and in off-plane regions and to analyse the density distribution. By assuming stationary equilibrium and axisymmetry, we used the Jeans equation to derive the rotation curve. Then we fit it with density models that include both dark matter and predictions of the MOND (Modified Newtonian dynamics) theory. Since the Milky Way exhibits deviations from axisymmetry and equilibrium, we also considered corrections to the Jeans equation. To compute such corrections, we ran N-body experiments of mock disk galaxies where the departure from equilibrium becomes larger as a function of the distance from the centre. The rotation curve in the outer disk of the Milky Way that is constructed with the Jeans equation exhibits very low dependence on R and z and it is well-fitted both by dark matter halo and MOND models. The application of the Jeans equation for deriving the rotation curve, in the case of the systems that deviate from equilibrium and axisymmetry, introduces systematic errors that grow as a function of the amplitude of the average radial velocity. In the case of the Milky Way, we can observe that the amplitude of the radial velocity reaches ∼10% that of the azimuthal one at R≈20 kpc. Based on this condition, using the rotation curve obtained from the Jeans equation to calculate the mass may overestimate its measurement.

Comments: | 11 pages, 8 figures, accepted to be published in A&A |

Subjects: | Astrophysics of Galaxies (astro-ph.GA) |

Cite as: | arXiv:2007.14825 [astro-ph.GA] |

(or arXiv:2007.14825v1 [astro-ph.GA] for this version) |

# Dynamics in the Galactic disk explaining radial and vertical velocities

Aims: Here, we investigate the dynamical effects produced by different mechanisms that can explain the radial and vertical components of these extended kinematic maps, including a decomposition of bending and breathing of the vertical components. This paper as a whole tries to be a compendium of different dynamical mechanisms whose predictions can be compared to the kinematic maps.

Methods: Using analytical methods or simulations, we are able to predict the main dynamical factors and compare them to the predictions of the extended kinematic maps of Gaia-DR2.

Results: The gravitational influence of Galactic components that are different from the disk, such as the long bar or bulge, the spiral arms, or a tidal interaction with Sagittarius dwarf galaxy, may explain some features of the velocity maps, especially in the inner parts of the disk. However, they are not sufficient in explaining the most conspicuous gradients in the outer disk. Vertical motions might be dominated by external perturbations or mergers, although a minor component may be due to a warp whose amplitude evolves with time. Here, we show with two different methods, which analyze the dispersion of velocities, that the mass distribution of the disk is flared. Despite these partial explanations, the main observed features can only be explained in terms of out-of-equilibrium models, which are either due to external perturbers or to the fact that the disk has not had time to reach equilibrium since its formation.

# PRE Editor’s suggestion

Spiral galaxies are well-known astrophysical structures, but how they form is not fully understood. This paper describes simulations showing that they could be transient, nonequilibrium structures originating from the collapse of clouds of matter interacting solely through self-gravity.