Quantifying resonant activation like phenomenon in non-Markovian systems

Resonant activation is an effect of a noise-induced escape over a modulated potential barrier. The modulation of a energy landscape facilitates the escape kinetics and makes it optimal as measured by the mean first passage time. A canonical example of resonant activation is a Brownian particle moving in a time-dependent potential under action of Gaussian white noise. Resonant activation is observed not only in typical Markovian-Gaussian systems but also in far from equilibrium and far from Markovianity regimes. We demonstrate that using an alternative to the mean first passage time, robust measures of resonant activation, the signature of this effect can be observed in general continuous time random walks in modulated potentials even in situations when the mean first passage time diverges.Comment: 7 pages, 9 figure

Stationary states in 2D systems driven by bi-variate L\'evy noises

Systems driven by $\alpha$-stable noises could be very different from their Gaussian counterparts. Stationary states in single-well potentials can be multimodal. Moreover, a potential well needs to be steep enough in order to produce stationary states. Here, it is demonstrated that 2D systems driven by bi-variate $\alpha$-stable noises are even more surprising than their 1D analogs. In 2D systems, intriguing properties of stationary states originate not only due to heavy tails of noise pulses, which are distributed according to $\alpha$-stable densities, but also because of properties of spectral measures. Consequently, 2D systems are described by a whole family of Langevin and fractional diffusion equations. Solutions of these equations bear some common properties but also can be very different. It is demonstrated that also for 2D systems potential wells need to be steep enough in order to produce bounded states. Moreover, stationary states can have local minima at the origin. The shape of stationary states reflects symmetries of the underlying noise, i.e. its spectral measure. Finally, marginal densities in power-law potentials also have power-law asymptotics.Comment: 9 pages, 8 figure

Non-Gaussian, non-dynamical stochastic resonance

The archetypal system demonstrating stochastic resonance is nothing more than a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exist the optimal value of the noise intensity resulting in the "most" periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an $\alpha$-stable noise. We demonstrate that non-equilibrium $\alpha$-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.Comment: 5 pages, 6 figurure

Escape from bounded domains driven by multi-variate α\alpha-stable noises

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $\alpha$-stable L\'evy type noise from a 2-dimensional disk. For an appropriate choice of parameters the mean first passage time reveals non-trivial, non-monotonous dependence on the stability index $\alpha$ describing jumps' length asymptotics both for spherical and Cartesian L\'evy flights. Finally, we study escape from $d$-dimensional hyper-sphere showing that $d$-dimensional escape process can be used to discriminate between various types of multi-variate $\alpha$-stable noises, especially spherical and Cartesian L\'evy flights.Comment: 8 pages, 5 figure

Escape from hypercube driven by multi-variate

We explore properties of the escape kinetics from the d-dimensional hypercube driven by multi-variate α-stable noises. Using methods of stochastic dynamics we show complex dependence of the mean first passage time for the escape from the hypercube as a function of the hypercube dimension d. Finally, we show how the escape process can be used to quantify independence of components of multi-variate α-stable noises

Resonant activation in 2D and 3D systems driven by multi-variate Lévy noise

Resonant activation is one of the classical effects demonstrating the constructive role of noise. In resonant activation, the cooperative action of a barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatile systems for various types of barrier modulation process and noise type. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate α -stable noise. The strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index α results in the disappearance of the resonant activation

Non-equilibrium escape problems under Bivariate α\alpha-stable noises

Stochastic resonance is a prominent effect consisting in enhancement of a response of a physical system to deterministic driving in the presence of noise. It demonstrates a constructive role the noise may play in increasing the sensitivity of the system to weak signals, and emerges in different theoretical models and experimental situations. We consider this effect in a periodically modulated two-dimensional double-well potential under the influence of an isotropic α-stable noise, and discuss the performance of various measures used to describe the stochastic resonance in other setups

Operational and Meteorological Influence on the Utilized Biogas Composition at the Barycz Landfill Site in Cracow, Poland

International audienceThe aim of the present investigation was to determine time variation of biogas composition at the gas collection network on the ‘Barycz' landfill site in Cracow, Poland, as well as the influence of operational and meteorological conditions on the biogas composition. The study of biogas composition at selected gas wells and gas collectors was conducted using a portable IR landfill gas analyser. The methane concentration in biogas on the part of the landfill site currently in operation varied in the range 59-63% vol. and on the reclaimed part of the landfill, in the range 42-62% vol. It was found that biogas composition is significantly affected by operational conditions and meteorological parameters. For example, methane concentrations were more constant when the pressure in the installation was above the ambient atmosphere than when it was below, where fluctuations of 15% vol. were seen. Low air temperature, high precipitation and high atmospheric pressure, which lower the permeability of the outer layer of the landfill, result in higher quality of the biogas getting to the gas collection system