Epidemic model on a network: analysis and applications to COVID-19

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic

Theoretical models for classical Cepheids. VIII. Effects of helium and heavy elements abundance on the Cepheid distance scale

Previous nonlinear fundamental pulsation models for classical Cepheids with metal content Z <= 0.02 are implemented with new computations at super-solar metallicity (Z=0.03, 0.04) and selected choices of the helium-to-metal enrichment ratio DeltaY/Delta Z. On this basis, we show that the location into the HR diagram of the Cepheid instability strip is dependent on both metal and helium abundance, moving towards higher effective temperatures with decreasing the metal content (at fixed Y) or with increasing the helium content (at fixed Z). The contributions of helium and metals to the predicted Period-Luminosity and Period-Luminosity-Color relations are discussed, as well as the implications on the Cepheid distance scale. Based on these new results, we finally show that the empirical metallicity correction suggested by Cepheid observations in two fields of the galaxy M101 may be accounted for, provided that the adopted helium-to-metal enrichment ratio is reasonably high (Delta Y/Delta Z ~ 3.5).Comment: 23 pages, including 6 postscript figures, accepted for publication on Ap

Theoretical insights into the RR Lyrae K-band Period-Luminosity relation

Based on updated nonlinear, convective pulsation models computed for several values of stellar mass, luminosity and metallicity, theoretical constraints on the K-band Period-Luminosity (PLK) relation of RR Lyrae stars are presented. We show that for each given metal content the predicted PLK is marginally dependent on uncertainties of the stellar mass and/or luminosity. Then, by considering the RR Lyrae masses suggested by evolutionary computations for the various metallicities, we obtain that the predicted infrared magnitude M_K over the range 0.0001< Z <0.02 is given by the relation MK=0.568-2.071logP+0.087logZ-0.778logL/Lo, with a rms scatter of 0.032 mag. Therefore, by allowing the luminosities of RR Lyrae stars to vary within the range covered by current evolutionary predictions for metal-deficient (0.0001< Z <0.006) horizontal branch models, we eventually find that the infrared Period-Luminosity- Metallicity (PLZK) relation is MK=0.139-2.071(logP+0.30)+0.167logZ, with a total intrinsic dispersion of 0.037 mag. As a consequence, the use of such a PLZK relation should constrain within +-0.04 mag the infrared distance modulus of field and cluster RR Lyrae variables, provided that accurate observations and reliable estimates of the metal content are available. Moreover, we show that the combination of K and V measurements can supply independent information on the average luminosity of RR Lyrae stars, thus yielding tight constraints on the input physics of stellar evolution computations. Finally, for globular clusters with a sizable sample of first overtone variables, the reddening can be estimated by using the PLZK relation together with the predicted MV-logP relation at the blue edge of the instability strip (Caputo et al. 2000).Comment: 8 pages, including 5 postscript figures, accepted for publication on MNRA

RR LYRAE VARIABLE STARS: PULSATIONAL CONSTRAINTS RELEVANT TO THE OOSTERHOFF CONTROVERSY

A solution to the old Oosterhoff controversy is proposed on the basis of a new theoretical pulsational scenario concerning RR Lyrae cluster variables (Bono and coworkers). We show that the observed constancy of the lowest pulsation period in both Oosterhoff type I (OoI) and Oosterhoff type II (OoII) prototypes (M3, M15) can be easily reproduced only by assuming the canonical evolutionary horizontal-branch luminosity levels of these Galactic globular clusters and therefore by rejecting the Sandage period shift effect (SPSE).Comment: postscript file of 7 pages and 2 figures; one non postcript figure is available upon request; for any problem please write to [email protected]

Triggering the Formation of Halo Globular Clusters with Galaxy Outflows

We investigate the interactions of high-redshift galaxy outflows with low-mass virialized (Tvir < 10,000K) clouds of primordial composition. While atomic cooling allows star formation in larger primordial objects, such "minihalos" are generally unable to form stars by themselves. However, the large population of high-redshift starburst galaxies may have induced widespread star formation in these objects, via shocks that caused intense cooling both through nonequilibrium H2 formation and metal-line emission. Using a simple analytic model, we show that the resulting star clusters naturally reproduce three key features of the observed population of halo globular clusters (GCs). First, the 10,000 K maximum virial temperature corresponds to the ~ 10^6 solar mass upper limit on the stellar mass of GCs. Secondly, the momentum imparted in such interactions is sufficient to strip the gas from its associated dark matter halo, explaining why GCs do not reside in dark matter potential wells. Finally, the mixing of ejected metals into the primordial gas is able to explain the ~ 0.1 dex homogeneity of stellar metallicities within a given GC, while at the same time allowing for a large spread in metallicity between different clusters. To study this possibility in detail, we use a simple 1D numerical model of turbulence transport to simulate mixing in cloud-outflow interactions. We find that as the shock shears across the side of the cloud, Kelvin-Helmholtz instabilities arise, which cause mixing of enriched material into > 20% of the cloud. Such estimates ignore the likely presence of large-scale vortices, however, which would further enhance turbulence generation. Thus quantitative mixing predictions must await more detailed numerical studies.Comment: 21 pages, 11 figures, Apj in pres

On the second overtone stability among SMC Cepheids

We present a new set of Cepheid, full amplitude, nonlinear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical for Cepheids in the Small Magellanic Cloud (SMC) and stellar masses ranging from 3.25 to 4 solar masses. Predicted phi{21} Fourier parameters agree, within current uncertainties, with empirical data for pure first and second overtone variables as well as for first/second overtone (FO/SO) double-mode Cepheids collected by Udalski et al. (1999a,b) in the SMC. On the other hand, predicted I band amplitudes are systematically larger than the observed ones in the short period range. We also find, in agreement with empirical evidence, that the region within which both second and first overtones attain a stable limit cycle widens when moving toward lower luminosities. Moreover, predicted P{SO}/P{FO} and P{FO}/P{F} period ratios agree quite well with empirical period ratios for FO/SO and F/FO double-mode SMC Cepheids. Finnaly, current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators.Comment: 6 pages, 6 postscript figures, accepted for publication on MNRA

A robust approach for the determination of Gurson model parameters

Among the most promising models introduced in recent years, with which it is possible to obtain very useful results for a better understanding of the physical phenomena involved in the macroscopic mechanism of crack propagation, the one proposed by Gurson and Tvergaard links the propagation of a crack to the nucleation, growth and coalescence of micro-voids, which is likely to connect the micromechanical characteristics of the component under examination to crack initiation and propagation up to a macroscopic scale. It must be pointed out that, even if the statistical character of some of the many physical parameters involved in the said model has been put in evidence, no serious attempt has been made insofar to link the corresponding statistic to the experimental and macroscopic results, as for example crack initiation time, material toughness, residual strength of the cracked component (R-Curve), and so on. In this work, such an analysis was carried out in a twofold way: the former concerned the study of the influence exerted by each of the physical parameters on the material toughness, and the latter concerned the use of the Stochastic Design Improvement (SDI) technique to perform a "robust" numerical calibration of the model evaluating the nominal values of the physical and correction parameters, which fit a particular experimental result even in the presence of their "natural" variability