Related papers: Stochastic Flows and Marked Stable Processes
We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted H\"older norms using the Sobolev embedding theorem and the change of variable formula.…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha >…
We study the dissipative bi-stable Duffing oscillator with equal energy wells and observe fractal patterns in the parameter space of driving frequency, forcing amplitude, and damping ratio. Our numerical investigation reveals the Hausdorff…
We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…
We combine theory, numerical calculations, and experiments to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an…
In this note we study the asymptotic mean-square stability for two-step schemes applied to a scalar stochastic differential equation (sde) and applied to systems of sdes. We derive necessary and sufficient conditions for the asymptotic…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those…
In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite…
In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…
Steep slope streams show large fluctuations of sediment discharge across several time scales. These fluctuations may be inherent to the internal dynamics of the sediment transport process. A probabilistic framework thus seems appropriate to…
This study is concerned with the statistics of vertical turbulent channel flow laden with inertial particles for two different volume concentrations ($\Phi_{V} = 3 \times 10^{-6}$ and $\Phi_{V} = 5 \times 10^{-5}$) at a Stokes number of…
We investigate channel-confined, nematic liquid crystals using the Beris-Edwards model of nematohydrodynamics. Using strong homeotropic anchoring at the walls, we find multistability i.e. multiple coexisting states where the uniform nematic…
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…
Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X,\mathbb{R})$ (with $d<n$) are stable under perturbations of the distributions of…
We report the presence of traveling Elastic Waves in experiments featuring a shear flow in the very low Reynolds number regime (Re < 0.1) with no external curvatures or internal perturbations in the channel design. The classic…