Related papers: Rate-dependent bifurcation dodging in a thermoacou…
We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…
A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. (PRL 112:038101, 2014). They have computed the mean switching time for such a system using a continuous Fokker-Planck equation…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…
Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory…
The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…
Changes in the parameters of dynamical systems can cause the state of the system to shift between different qualitative regimes. These shifts, known as bifurcations, are critical to study as they can indicate when the system is about to…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
Using a nominally symmetric annular combustor, we present experimental evidence of a predicted spontaneous symmetry breaking and an unexpected explicit symmetry breaking in the neighborhood of the Hopf bifurcation, which separates…
In order to stabilize the behavior of noisy systems, confining it around a desirable state, an effort is required to suppress the intrinsic noise. This noise suppression task entails a cost. For the important case of thermal noise in an…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…