abstract

In this paper, we have introduced two versions of the jerk model. These versions are commensurate fractional and distributed orders. They appear in several applications of physics and engineering, e.g. , laser physics, damped harmonic oscillators, and secure communications. The sufficient condition for the existence and uniqueness of the solution of commensurate fractional-order (CFO) jerk model is studied. We state and prove a theorem to test the dependence of the solutions of the CFO jerk model on initial conditions. The dynamics of the three versions of the jerk model are investigated. Using the largest Lyapunov exponent (LLE), we determine the values of the parameters at which these proposed versions have chaotic solutions. The linear feedback control is used to stabilize the chaotic solutions of these versions. Numerical simulations are used to show the chaotic solutions after control.

abstract

We analyze the evolution of the mass density contrast in spherical perturbations of flat Friedman–Lemaître–Robertson–Walker cosmologies. Both dark matter and dark energy are included. In the absence of dark energy, the evolution equation coincides with that obtained by Bonnor within the “Newtonian cosmology”.

abstract

In this article, we present a stationary metric ansatz to describe a rotating traversable wormhole in the presence of the topological defect produced by a global monopole charge. This particular rotating space-time is referred to as the topologically charged rotating Schwarzschild–Klinkahmer wormhole. Our study involves the analysis of geodesic motion for test particles and photon rays in the context of this topologically charged rotating traversable wormhole. We aim to analyze the effects of global monopole charge and other parameters on the outcomes of this investigation. Additionally, we explore the matter–energy distribution within this rotating wormhole, considering it as a non-vacuum solution of Einstein’s field equation. Notably, we demonstrate that the energy density of the matter content satisfies the criteria of the weak energy condition.

abstract

We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic) spin-\(1/2\) fermions interacting through a short-range spin-independent repulsive binary interaction potential. We show how to obtain a systematic expansion of the system’s free energy depending on the densities \(n_+\) and \(n_-\) of spin-up and spin-down fermions. In this paper, we truncate this expansion at the second order and determine, by numerically minimizing the free energy, the equilibrium proportions of \(n_+\) and \(n_-\) (that is, the system’s polarization) as functions of the temperature, the system’s overall density \(n=n_++n_-\), and the strength of the interaction.