For a double-well potential consisting of a truncated quartic potential and a truncated harmonic potential, the inter-well escape rates of Lévy particles are investigated numerically, and analytically for the Cauchy case, with focus on the former. The escape rate of Lévy particles from the...

Escape rate in the low-to-intermediate damping connecting the low damping with the intermediate damping is established for the power-law distribution on the basis of flux over population theory. We extend the escape rate in the low damping to the low-to-intermediate damping, and get an...

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel’nikov and Meshkov [V.I. Mel’nikov, S.V. Meshkov, J. Chem. Phys. 85 (1986) 1018] is applied to the inertial rotational Brownian motion of a fixed...

We consider the Bhatnagar–Gross–Krook (BGK) model for the dynamics of a particle in the phase space. Namely, the particle follows Newtonian trajectories that are randomly interrupted by collisions which thermalize its velocity. For this collisional model, we analyze the activationless escape...

The problem of escape of a particle by diffusion from a parabolic potential well across a parabolic barrier adjacent to free space is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the...

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from...

Kramers escape rate in the overdamped systems is restudied for the power-law distribution. By using the mean first passage time, we derive the escape rate with the power-law distribution and obtain the Kramers’ infinite barrier escape rate in this case. We show that the escape rate with the...

We introduce two new measures of network robustness and apply them to four different strategies. The measures are independent from the number of nodes in the network and have the strong potential to cover a large portfolio of applications. Using the Monte-Carlo methods, we demonstrate how to...

For the multi-agent spatial Parrondo’s games, the available theoretical analysis methods based on the discrete-time Markov chain were assumed that the losing and winning states of an ensemble of N players were represented to be the system states. The number of system states was 2N types....

A new approach to determine the stability of multiple access network control schemes is presented. A “busy” network (the precise meaning of the term “busy” will be presented in the text) is modelled as a switched single-server hybrid dynamical system whose switching laws are stochastic...