Derivation and analytical solutions of a non-linear diffusion equation applied to non-constant heat conductivity and ionic diffusion in glasses.

This paper derives a non-linear diffusion equation discussing two possible applications: the ionic diffusion in glasses and temperature-dependent conductivity in semiconductors. The first equation is a logarithmic diffusion derived formally from the continuity of ion concentration, but the latter is a more phenomenological example. A power-law ansatz with time-dependent parameters maximizes a non-standard entropy and gives a set of coupled motion equations we can solve analytically.

Analyzing the 2019 Chilean social outbreak: Modelling Latin American economies.

In this work, we propose a quantitative model for the 2019 Chilean protests. We utilize public data for the consumer price index, the gross domestic product, and the employee and per capita income distributions as inputs for a nonlinear diffusion-reaction equation, the solutions to which provide an in-depth analysis of the population dynamics. Specifically, the per capita income distribution stands out as a solution to the extended Fisher-Kolmogorov equation.

Solving Equations of Motion by Using Monte Carlo Metropolis: Novel Method Via Random Paths Sampling and the Maximum Caliber Principle.

A permanent challenge in physics and other disciplines is to solve Euler-Lagrange equations. Thereby, a beneficial investigation is to continue searching for new procedures to perform this task. A novel Monte Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems.

Discontinuous spirals of stability in an optically injected semiconductor laser.

We report a new kind of discontinuous spiral with stable periodic orbits in the parameter space of an optically injected semiconductor laser model, which is a combination of the intercalation of fish-like and cuspidal-like structures (the two normal forms of complex cubic dynamics). The spiral has a tridimensional structure that rolls up in at least three directions. A turn of approximately 2π radians along the spiral and toward the center increases the number of peaks in the laser intensity by one, which does not occur when traversing the discontinuities.

Tricorn-like structures in an optically injected semiconductor laser.

This study reports the existence of tricorn-like structures of stable periodic orbits in the parameter plane of an optically injected semiconductor laser model (a continuous-time dynamical system). These tricorns appear inside tongue-like structures that are created through simple Shi'lnikov bifurcations. As the linewidth enhancement factor-α of the laser increases, these tongues invade the laser locking zone and extends over the zone of stable period-1 orbits.

Publisher's Note: Dynamics and thermodynamics of systems with long-range dipole-type interactions [Phys. Rev. E 95, 022110 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.

Dynamics and thermodynamics of systems with long-range dipole-type interactions.

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.