Related papers: Noise-Induced Order in Extended Systems: A Tutoria…
We present a study of disorder origination and growth inside an ordered phase processes induced by the presence of multiplicative noise within mean-field approximation. Our research is based on the study of solutions of the nonlinear…
The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
We discuss fluctuation-induced forces in a system described by a continuous Landau-Ginzburg model with a quenched disorder field, defined in a $d$-dimensional slab geometry $\mathbb R^{d-1}\times[0,L]$. A series representation for the…
Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger,…
Noise is often used in the study of open systems, such as in classical Brownian motion and in Quantum Dynamics, to model the influence of the environment. However generalising results from G\"{o}del and Chaitin in mathematics suggests that…
In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal…
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…
We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…
The dynamics of non-equilibrium spatially extended systems are often dominated by fluctuations, due to e.g.\ deterministic chaos or to intrinsic stochasticity. This reflects into generic scale invariant or kinetic roughening behavior that…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
Exceptional points, a remarkable phenomenon in physical systems, have been exploited for sensing applications. It has been demonstrated recently that it can also utilize as sensory threshold in which the interplay between exceptional-point…
The term active nematics designates systems in which apolar elongated particles spend energy to move randomly along their axis and interact by inelastic collisions in the presence of noise. Starting from a simple Vicsek-style model for…
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…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…