Quantifying a resonant-activation-like phenomenon in non-Markovian systems

Szczepaniec, Krzysztof; Dybiec, Bartłomiej

doi:10.1103/physreve.89.042138

Cited by 3 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 2(b) shows a well pronounced minimum of the mean absorption time for v = 5 and v = 10. The minimum is qualitatively equivalent to that in so called resonant activation problems [32][33][34][35][36][37][38][39][40][41][42][43]. In fact, the minimum of τ can be linked with the maximum of Δ.…”

Section: Discussionmentioning

confidence: 95%

Absorbed driven diffusion can provide positive heat and work output

Chvosta¹

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We investigate overdamped Brownian motion in a fluctuating potential on a one-dimensional interval bordered by absorbing boundaries. The potential switches randomly between the ∨-shaped and the ∧-shaped form and is symmetric with respect to the origin. We derive exact expressions describing the absorption process, dynamics and stochastic energetics of the particle. The mean absorption time can exhibit a pronounced minimum as the function of the potential switching rate. Moreover, there exists a parameter region where both the output work and the released heat are positive. We give a plausible explanation for this phenomenon based on typical statistical features of absorbed trajectories. The presented analytical method can be generalized to other models based on dichotomous switching between two potential shapes.

show abstract

Section: Discussionmentioning

confidence: 95%

Absorbed driven diffusion can provide positive heat and work output

Chvosta¹

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Therefore, resonant activation can be quantified by some of measures which characterize width or location of the first passage time density [31]. Changes in the efficiency of the escape kinetics affects characteristics of the first passage time density.…”

Section: Resultsmentioning

confidence: 99%

“…Resonant activation is the property of the system at hand but its presence affects the shape of the first passage time density. Therefore, resonant activation can be quantified by some of measures which characterize width or location of the first passage time density [31]. Changes in the efficiency of the escape kinetics affects characteristics of the first passage time density.…”

Section: Resultsmentioning

confidence: 99%

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

Szczepaniec¹,

Dybiec

2014

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

Resonant activation is one of classical effects demonstrating constructive role of noise. In resonant activation cooperative action of 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 versatilities of systems for various types of barrier modulation processes and noise types. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate α-stable noises. 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.

show abstract

“…However, if the asymptotics of the waiting time distribution has power-law tails, w(t) ∝ t −1−β with 0 < β < 1, the mean first passage time diverges. Instead, one can simply characterise the first passage time statistics by a median location or an interquantile width [21]. Alternatively, one may introduce fractional moments of p F P (t),…”

Section: Random Walk With a Position-dependent Waiting Time And Tmentioning

confidence: 99%

“…The escape problem is well-known in the Gaussian case [17]; it was also discussed for the Lévy flights when trajectories are discontinuous and the boundary conditions nonlocal which results in a nontrivial leapover statistics [18]. The escape problem for the Lévy flights was studied both for a free particle [19] and in the presence of an external deterministic force [20,21]. It was demonstrated in the field of the disordered systems that the first passage time statistics may be different for the annealed and quenched disorder [22].…”

Section: Introductionmentioning

confidence: 99%

Escape process in systems characterized by stable noises and position-dependent resting times

Srokowski

2016

Phys. Rev. E

View full text Add to dashboard Cite

Stochastic systems characterized by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position dependent and obeys a power-law form attributed to the underlying self-similar structure. Both the one- and two-dimensional cases are analyzed. The random walk description involves a position-dependent waiting time distribution. On the other hand, the stochastic dynamics is formulated in terms of the subordination technique where the random time generator is position dependent. The first passage time problem is addressed by evaluating a first passage time density distribution and an escape rate. The influence of the medium nonhomogeneity on those quantities is demonstrated; moreover, the dependence of the escape rate on the stability index and the memory parameter is evaluated. Results indicate essential differences between the Gaussian case and the case involving Lévy flights.

show abstract

Quantifying a resonant-activation-like phenomenon in non-Markovian systems

Cited by 3 publications

References 41 publications

Absorbed driven diffusion can provide positive heat and work output

Absorbed driven diffusion can provide positive heat and work output

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

Escape process in systems characterized by stable noises and position-dependent resting times

Contact Info

Product

Resources

About