Related papers: Density of Inertial Particles: Exactly Solvable 2D…
We analyze the dynamics of particles in two dimensions with constant speed and a stochastic switching angle dynamics defined by a correlated dichotomous Markov process (telegraph noise) plus Gaussian white noise. We study various cases of…
The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D…
We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…
Oscillatory flows have become an indispensable tool in microfluidics, inducing inertial effects for displacing and manipulating fluid-borne objects in a reliable, controllable, and label-free fashion. However, the quantitative description…
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…
We consider the 2D stochastic Navier-Stokes equations driven by noise that has the regularity of space-time white noise but doesn't exactly coincide with it. We show that, provided that the intensity of the noise is sufficiently weak at…
We study the stochastic dynamics of a two-dimensional particle assuming that the components of its position are two coupled random-acceleration processes evolving in a confining parabolic potential and are the subjects of independent…
We study the long time statistics of a two-dimensional Hamiltonian system in the presence of Gaussian white noise. While the original dynamics is known to exhibit finite time explosion, we demonstrate that under the impact of the stochastic…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
We show that uncorrelated Gaussian noise, despite its paradigmatic association with thermal equilibrium, can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle…
We prove that the densities of the finite dimensional projections of weak solutions of the Navier-Stokes equations driven by Gaussian noise are bounded and H\"older continuous, thus improving the results of Debussche and Romito…
The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…
In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H >…
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…
The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator of entanglement. We show that in order to witness this type of entanglement experimentally, strong limits…
Inertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor-Green (TG) flow and characterize particle dynamics as a function of the particle's Stokes number using dynamic mode…