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While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
Thermally-driven atmospheric escape evolves from an organized outflow (hydrodynamic escape) to escape on a molecule by molecules basis (Jeans escape) with increasing Jeans parameter, the ratio of the gravitational to thermal energy of…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
We use (nonconservative) dynamical semigroups to investigate the decay law of a quantum unstable system weakly coupled with a large environment. We find that the deviations from the classical exponential law are small and can be safely…
The dynamics is studied of an infinite continuum system of jumping and coalescing point particles. In the course of jumps, the particles repel each other whereas their coalescence is free. As the equation of motion we take a kinetic…
The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
The review aims to give an overview of atmospheric escape processes from exoplanets. I briefly discuss the physics of various escape processes responsible for atmospheric escape across different types of exoplanets. Transmission…
We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools…
From sport and science production to everyday life, higher-level pursuits demand collaboration. Despite an increase in the number of data-driven studies on human behavior, the social dynamics of collaborative problem solving are still…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough…
Exoplanets with substantial Hydrogen/Helium atmospheres have been discovered in abundance, many residing extremely close to their parent stars. The extreme irradiation levels these atmospheres experience causes them to undergo hydrodynamic…
We compute for an archetypical glass-forming system the excess of particle mobility distributions over the corresponding distribution of dynamic propensity, a quantity that measures the tendency of the particles to be mobile and reflects…
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We…
Transmission spectroscopy is a key technique in the characterization of exoplanet atmospheres and has been widely applied to planets undergoing hydrodynamic escape. While a robust analytic theory exists for transmission spectra of…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…