Dynamics of f(R) gravity models and asymmetry of time

We solve the field equations of modified gravity for [Formula: see text] model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase-space analysis of [Formula: see text] models, both with and without the effects of radiation. The stability of these points is studied against the perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analyzing the dynamics of the system during the radiation, matter and acceleration-dominated phases of the universe. Certain linear and quadratic forms of [Formula: see text] are determined from the geometrical and physical considerations and the behavior of the scale factor is found for those forms. Further, we also determine the Hubble parameter [Formula: see text], the Ricci scalar [Formula: see text] and the scale factor [Formula: see text] for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the [Formula: see text] gravity in the Einstein frame that may lead to an arrow of time at a classical level.

Forecasting of Electricity Demand by Hybrid ANN-PSO Models

Developing economies need to invest in energy projects. Because the gestation period of the electric projects is high, it is of paramount importance to accurately forecast the energy requirements. In the present paper, the future energy demand of the state of Tamil Nadu in India, is forecasted using an artificial neural network (ANN) optimized by particle swarm optimization (PSO) and by General Algorithm (GA). Hybrid ANN Models have the potential to provide forecasts that perform well compared to the more traditional modelling approaches. The forecasted results obtained using the hybrid ANN-PSO models are compared with those of the ARIMA, hybrid ANN-GA, ANN-BP and linear models. Both PSO and GA have been developed in linear and quadratic forms and the hybrid ANN models have been applied to five-time series. Amongst all the hybrid ANN models, ANN-PSO models are the best fit models in all the time series based on RMSE and MAPE.