RESUMO
A physical model, based on energy balances, is proposed to describe the fractures in solid structures such as stelae, tiles, glass, and others. We applied the model to investigate the transition of the Rosetta Stone from the original state to the final state with three major fractures. We consider a statistical corner-breaking model with cutting rules. We obtain a probability distribution as a function of the area and the number of vertices. Our generic results are consistent with the current state of the Rosetta Stone and, additionally, predictions related to a fourth fracture are declared. The loss of information on such heritage pieces is considered through entropy production. The explicit quantification of this concept in information theory stays examined.
Assuntos
Modelos Estatísticos , EntropiaRESUMO
We found that the rare distribution of velocities in quasisteady states of the dipole-type Hamiltonian mean-field model can be explained by the Cairns-Tsallis distribution, which has been used to describe nonthermal electron populations of some plasmas. This distribution gives us two interesting parameters which allow an adequate interpretation of the output data obtained through molecular dynamics simulations, namely, the characteristic parameter q of the so-called nonextensive systems and the α parameter, which can be seen as an indicator of the number of particles with nonequilibrium behavior in the distribution. Our analysis shows that fit parameters obtained for the dipole-type Hamiltonian mean-field simulated system are ad hoc with some nonthermality and nonextensivity constraints found by different authors for plasma systems described through the Cairns-Tsallis distribution.
RESUMO
A Hamiltonian mean field model, where the potential is inspired by dipole-dipole interactions, is proposed to characterize the behavior of systems with long-range interactions. The dynamics of the system remains in quasistationary states before arriving at equilibrium. The equilibrium is analytically derived from the canonical ensemble and coincides with that obtained from molecular dynamics simulations (microcanonical ensemble) at only long time scales. The dynamics of the system is characterized by the behavior of the mean value of the kinetic energy. The significance of the results, compared to others in the recent literature, is that two plateaus sequentially emerge in the evolution of the model under the special considerations of the initial conditions and systems of finite size. The first plateau decays to a different second one before the system reaches equilibrium, but the dynamics of the system is expected to have only one plateau when the thermodynamics limit is reached because the difference between them tends to disappear as N tends to infinity. Hence, the first plateau is a type of quasistationary state the lifetime of which depends on a power law of N and the second seems to be a true quasistationary state as reported in the literature. We characterize the general behavior of the model according to its dynamics and thermodynamics.