Related papers: The exact geostrophic streamfunction for neutral s…
Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…
We prove a quantitative version of the non-uniform hyperbolicity of the Teichm\"uller geodesic flow. Namely, at each point of any Teichm\"uller flow line, we bound the infinitesimal spectral gap for variations of the Hodge norm along the…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We consider a process on $\mathbb{T}^2$, which consists of fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the graph naturally associated to the structure…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In…
I present a new framework for modeling the dynamics of tidal streams. The framework consists of simple models for the initial action-angle distribution of tidal debris, which can be straightforwardly evolved forward in time. Taking…
We study the computation of the flow of water on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinuous when there is no loss of mass. In case we are losing…
The equations for geodesic flow on the ellipsoid are well known, and were first solved by Jacobi in 1838 by separating the variables of the Hamilton-Jacobi equation. In 1979 Moser investigated the case of the general ellipsoid with distinct…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
We present a differential geometric framework for the motion of a non-Brownian particle in the presence of fixed obstacles in a quiescent fluid, in the deterministic Stokesian regime. While the Helmholtz Minimum Dissipation Theorem suggests…
Ocean mesoscale eddies enhance meridional buoyancy transport, notably in the Antarctic Circumpolar Current where they contribute to setting the deep stratification of the neighboring ocean basins. The much-needed parameterization of this…
An elliptic Newton flow is a dynamical system that can be interpreted as a continuous version of Newton's iteration method for finding the zeros of an elliptic function f. Previous work focusses on structurally stable flows (i.e., the phase…
We address unsupervised optical flow estimation for ego-centric motion. We argue that optical flow can be cast as a geometrical warping between two successive video frames and devise a deep architecture to estimate such transformation in…
Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. Results show the existence of concentration polarization layers on the surfaces of the…
In the context of subaqueous ripple and dune formation, we present here a Reynolds averaged calculation of the turbulent flow over a topography. We perform a weakly non-linear expansion of the velocity field, sufficiently accurate to…
In this paper we provide a bridge between classical results concerning discrete dynamical systems and dynamical systems governed by nonsmooth vector fields. In fact, we obtain a set of piecewise smooth vector field trajectories where the…