arXiv subjects

Vincent Ervin

Publications and source records attributed to Vincent Ervin.

4 recordsLinked to original sources

arXiv1999

Escape Probability and Mean Residence Time in Random Flows with Unsteady Drift

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 develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.

chao-dyn↗

arXiv1999

On the Stochastic Kuramoto-Sivashinsky Equation

In this article we study the solution of the Kuramoto-Sivashinsky equation (for surface erosion or surface growth) on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time and depends continuously on the initial data.

math.DS↗

arXiv1998

Dynamics of a Nonlocal Kuramoto-Sivashinsky Equation

In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal attractors'' parameterized by the mean value of the initial data. The dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain.

math.DS↗

arXiv1998

Trajectory and Attractor Convergence for a Nonlocal Kuramoto-Sivashinsky Equation

The nonlocal Kuramoto-Sivashinsky equation arises in the modeling of the flow of a thin film of viscous liquid falling down an inclined plane, subject to an applied electric field. In this paper, the authors show that, as the coefficient of the nonlocal integral term goes to zero, the solution trajectories and the maximal attractor of the nonlocal Kuramoto-Sivashinsky equation converge to those of the usual Kuramoto-Sivashinsky equation.

math.DS↗