RESUMEN
This study explores the thermodynamic properties of doped graphene using an adapted electronic spectrum. We employed the one-electron tight-binding model to describe the hexagonal lattice structure. The dispersion relation for graphene is expressed in terms of the hopping energies using a compositional parameter that characterizes the different dopant atoms in the lattice. The focus of the investigation is on the impact of the compositions, specifically the presence of dopant atoms, on the energy spectrum, entropy, temperature, and specific heat of graphene. The numerical and analytical results reveal distinct thermodynamic behaviors influenced by the dopant composition, including topological transitions, inflection points in entropy, and specific heat divergences. In addition, the use of Boltzmann entropy and the revision of Nernst's theorem for doped graphene are introduced as novel aspects.
RESUMEN
Graphene consists of coupled direct/dual fermionic sub-systems and, consequently, the thermal properties of both are intrinsically correlated. The dual is characterized by negative temperatures, and its free energy keeps opposite sign concerning the direct. The growth of ripples in graphene becomes related to temperature rises with fractional spatial dimension ~2.19 at 300 °K. An analytical, and suitable, expression for ripples dimension as a function of temperature is presented. Further, internal energy, entropy, specific heat and free energy are evaluated as a function of temperature and dimension for both sub-systems. Free energy supports a simple, functional expression inversely proportional to ripples dimension.
RESUMEN
An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ(N)) from 0.01 to 0.1.