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We complement and extend our work on fluctuation relations arising in nonequilibrium systems in steady states driven by L\'evy noise [Phys. Rev. E 76, 020101(R) (2006)]. As a concrete example, we consider a particle subjected to a drag…
The behavior of non-spherical particles in a shear-flow is of significant practical and theoretical interest. These systems have been the object of numerous investigations since the pioneering work of Jeffery a century ago. His eponymous…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
We present a new form of intermittency, L\'evy on-off intermittency, which arises from multiplicative $\alpha$-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both…
This paper attempts to find a probability distribution for the white noise (rapidly fluctuating unbalanced force) in the Langevin Equation. Unbalanced force is the resultant impulse provided to the brownian particle by the colliding fluid…
We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by {\it white L\'evy noise} in a dynamical regime where inertial effects can safely be neglected. The…
The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently,…
We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative L\'evy noises in a steady-state nonequilibrium case. This solution shows that L\'evy flights suppress always a quasi-periodical motion…
Descriptions of complex physical or biological systems often include stochastic contributions, and these are commonly simulated using Wiener processes. In many cases however, non-Gaussian fluctuations may originate from non-Wiener processes…
A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt = -F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose amplitude e(q) depends on q itself. Such equations are ambiguous, and depend on the…
We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…
This study aims to examine the effect of L\'evy noise on the solutions of the nonlinear Schr\"odinger equation. An improved diversity of stochastic solutions is instinctively located discretely on certain conditions by applying the…
The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of…
The Langevin equation with a multiplicative L\'evy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed.…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network…
We consider a Hamiltonian lattice field model with two conserved quantities, energy and volume, perturbed by stochastic noise preserving the two previous quantities. It is known that this model displays anomalous diffusion of energy of…
We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped…
We examine deviations from Boltzmann-Gibbs statistics for partially equilibrated systems of finite size. We find that such systems are characterized by the Levy distribution whose non-extensivity parameter is related to the number of…