arXiv subjects

Giuseppe Alberti

Publications and source records attributed to Giuseppe Alberti.

10 recordsLinked to original sources

arXiv2023

A conjecture on demographic mortality at high ages

The study considers the model of an abstract organism, called Arbitrary Oscillator (ArbO), which is capable of making decisions at each timed step. These decisions are 'critical' since, randomly, their outcome can be 'fatal' for ArbO, thus bringing its life cycle to an end. If we impose limits on the total number of critical decisions using a fixed parameter TC (Total Cases), we can treat the statistical distribution of fatal events over a large number of ArbOs using statistical mechanics methods. This results in a mathematically definable asymmetric 'bell' distribution, which can be compared with demographic mortality curves (dx curves), with an appropriate choice of time scale (one step = five years). Our conjecture assumes that, as demographic longevity improves, i.e., with the lengthening of lifespan, the actual demographic curves will increasingly match the mathematical distribution curve of our ArbO. The statistical distribution of the ArbO was introduced by the author in a previous paper and is here recalled and formalized analytically and its characteristics are detailed. The above said conjecture is based on two case studies: mortality in the United States from 1900 to 2017 and mortality in Italy from 1974 to 2019. The conjecture, applied to both case studies, appears reasonable. Tables and comparison figures are provided to support this. Also, an attempt to predict demographic mortality behavior and limitations for the years to come is provided. Finally, the more general theme of the nature of human aging can also be related to our conjecture, since it can highlight the presence of an absolute limit on the number of 'critical' events (the TC parameter). As 'critical' events accumulate over time by aging, approaching the final limit value, the probability of death will tend toward one.

physics.soc-ph↗

arXiv2022

Fermi statistics method applied to model macroscopic demographic data

The study begins by considering an abstract object (cellular automaton) able of moving -- by arbitrary decision -- between two given fixed positions. That is, at each clock step, it can change position or remain stationary in its current position. This object, which we call an Arbitrary Oscillator (ArbO), cannot evolve indefinitely since it may encounter 'end-of-life' events, which are also random. If we place quantitative limits on the number of arbitrary events and impose that the life cycle of ArbO must end in any case, we can use Fermi statistics to find the most probable distribution of fatal events along the possible sequences of choices. This distribution is represented by a recursive function that can be calculated for each total number of possible 'life/death' choices, which we will call Total Cases (TC). By means of a time-scale adjustment, we have associated the distribution curves of ArbO 'fatal' events with the demographic mortality curves (dx and qx data) of populations in the case of Italy. To better study the properties of the statistical function thus found, we attempted a continuous transposition of the recursive equation, seeking solutions to the differential equation linkable with it. With a continuous analytical expression, the characteristics of this statistical distribution can be studied more effectively. Similarities and differences with demographic mortality curves have been highlighted, attempting to explain the latter as overlaps of curves with different TC parameters. Implications with life span and more general life cycle concepts are outlined. A correlation with a more recent study using a multi-omics approach is also pointed out. Key Words: Cellular Automata, Fermi Statistics, Logistic Distribution, Demographic Mortality, Lifespan

cond-mat.stat-mech↗

arXiv2019

Gravitational phase transitions and instabilities of self-gravitating fermions in general relativity

We discuss the occurrence of gravitational phase transitions and instabilities in a gas of self-gravitating fermions within the framework of general relativity. In the classical (nondegenerate) limit, the system undergoes a gravitational collapse at low energies $E N_{\rm OV}$, there can be a subsequent gravitational collapse below a lower critical energy $E<E''_c$ or a lower critical temperature $T<T'_c$ leading presumably to the formation of a black hole. The evolution of the system is different in the microcanonical and canonical ensembles. In the microcanonical ensemble, the system takes a "core-halo" structure. The core consists in a compact quantum object or a black hole while the hot halo is expelled at large distances. This is reminiscent of the red giant structure of low-mass stars or the implosion-explosion of massive stars (supernova). In the canonical ensemble, the system collapses as a whole towards a compact object or a black hole. This is reminiscent of the implosion of supermassive stars (hypernova).

gr-qc↗

arXiv2019

Caloric curves of classical self-gravitating systems in general relativity

We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter $ν=GNm/Rc^2$, called the compactness parameter, where $N$ is the particle number and $R$ the system's size. Typically, the caloric curves have the form of a double spiral. The "cold spiral", corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The "hot spiral'", corresponding to strongly relativistic configurations, is similar (but not identical) to the caloric curve of the ultrarelativistic self-gravitating black-body radiation. We introduce two types of normalization of energy and temperature in order to obtain asymptotic caloric curves describing respectively the cold and the hot spirals in the limit $ν\rightarrow 0$. As the number of particles increases, the cold and the hot spirals approach each other, merge at $ν'_S=0.128$, form a loop above $ν_S=0.1415$, reduce to a point at $ν_{\rm max}=0.1764$, and finally disappear. Therefore, the double spiral shrinks when the compactness parameter $ν$ increases, implying that general relativistic effects render the system more unstable. We discuss the nature of the gravitational collapse at low and high energies with respect to a dynamical (fast) or a thermodynamical (slow) instability.

gr-qc↗

arXiv2019

On the dynamical instability of self-gravitating systems

We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition $<γ> \geq 4/3$ of the isotropic regime. Also, we discuss some applications of the criterion.

gr-qc↗

arXiv2019

Gravitational phase transition of self-gravitating systems of fermions in General Relativity

The Thomas-Fermi model is extended at finite temperature, to describe the gravitational phase transition occurring in massive fermionic systems in a general-relativistic framework. It is shown that, when a nondegenerate fermionic gas (for $N < N_{OV}$, where $N_{OV}$ is the Oppenheimer-Volkoff limit) is cooled down below a critical temperature, a condensed phase emerges and the gravitational collapse is prevented by quantum mechanics. If $N > N_{OV}$, by contrast, the system is destined to collapse towards a Black Hole because no equilibrium states exist.

gr-qc↗

arXiv2019

A General Criterion for the Dynamical Stability of Anisotropic Newtonian Systems

The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $γ$. The result has general validity and can be applied to several physical situations. Configurations that cannot exist in the isotropic regime can exist in the anisotropic one. Some applications of the criterion are also included.

gr-qc↗

arXiv2018

Caloric curves of self-gravitating fermions in general relativity

We study the nature of phase transitions between gaseous and condensed states in the self-gravitating Fermi gas at nonzero temperature in general relativity. The condensed states can represent compact objects such as white dwarfs, neutron stars, or dark matter fermion balls. The caloric curves depend on two parameters: the system size $R$ and the particle number $N$. When $N N_{\rm OV}$, there is no equilibrium state below a critical energy and below a critical temperature. In that case, the system is expected to collapse towards a black hole. We plot the caloric curves of the general relativistic Fermi gas, study the different types of phase transitions that occur in the system, and determine the phase diagram in the $(R,N)$ plane. The nonrelativistic results are recovered for $N\ll N_{\rm OV}$ and $R\gg R_{\rm OV}$ with $NR^3$ fixed. The classical results are recovered for $N\gg N_{\rm OV}$ and $R\gg R_{\rm OV}$ with $N/R$ fixed. We highlight a situation of physical interest where a gaseous Fermi gas, by cooling, first undergoes a phase transition towards a compact object (white dwarf, neutron star, dark matter fermion ball), then collapses into a black hole. This situation occurs in the microcanonical ensemble when $N_{\rm OV}<N<3.73\, N_{\rm OV}$. We also relate the phase transitions from a gaseous state to a core-halo state in the microcanonical ensemble to the onset of red-giant structure and to the supernova phenomenon.

gr-qc↗

arXiv2015

Self-Gravitating Relativistic Models of Fermions with Anisotropy and Cutoff Energy in their Distribution Function

In this paper we study the equilibrium configurations of anisotropic self-gravitating fermions, by extending to general relativity the solutions obtained in a previous paper. This treatment also generalizes to anisotropic systems the relativistic self-gravitating Fermi gas model, by considering different degrees of anisotropy. We discuss some important characteristics of the models and the obtained density profiles, and generalize the relation between the anisotropy and the mass of particles in the relativistic regime. These relativistic models may also be applied to the study of superdense neutron stars with anisotropic pressure or super-Chandrasekhar white dwarfs generated by the presence of a magnetic field.

astro-ph.GA↗

arXiv2014

Self-gravitating Newtonian models of fermions with anisotropy and cutoff energy in their distribution function

Systems of self-gravitating fermions constitute a topic of great interest in astrophysics, due to the wide field of applications. In this paper, we consider the gravitational equilibrium of spherically symmetric Newtonian models of collisionless semidegenerate fermions. We construct numerical solutions by taking into account the effects of the anisotropy in the distribution function and considering the prevalence of tangential velocity. In this way, our models generalize the solutions obtained for isotropic Fermi-Dirac statistics. We also extend the analysis to equilibrium configurations in the classical regime and in the fully degenerate limit, recovering, for different levels of anisotropy, hollow equilibrium configurations obtained in Maxwellian regime. Moreover, in the limit of full degeneracy, we find a direct expression relating the anisotropy with the mass of the particles composing the system.

astro-ph.CO↗