This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complexsteerable pyramid. We discuss the gain of Eulerian motion in a set of practical use cases: (i) action recognition, (ii) motion prediction in static images, (iii) motion transfer...

Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal character of Lagrangian particle coupling due to pressure effects makes the main obstacle to derive turbulence statistics from the three-dimensional Navier-Sto...

In this paper, we propose a new technique to visualize dense representations of time-dependent vector fields based on a Lagrangian-Eulerian Advection (LEA) scheme. The algorithm produces animations with high spatio-temporal correlation at interactive rates. With this technique, every still frame depicts the instantaneous structure of the flow, whereas an anima...

The surface flows on a droplet in an oscillating pressure field are simulated numerically by solving the Navier-Stokes equations using the Arbitrary Lagrangian-Eulerian and level set coupled method. Detailed transient flow fields in and around the droplet are calculated by performing parallel computations, and the flow phenomena in a thin layer around the droplet surface are discussed. The reci...

Recently Vlad et al. [Phys. Rev. E. 63, 066304 (2001)] applied the method of decorrelation trajectories to the transport of tracers in stochastic velocity fields with constant drift, and found that the average Lagrangian velocity is smaller than the Eulerian average. As this contradicts a theoretical result due to Lumley [in Mécanigue de la Turbulence, International Conference of the CNRS, Mars...

This paper deals with parameter identification for traffic models. Two fundamentally different approaches are presented, which are combined to the best advantage. With Eulerian sensing the sensors are spatially stationary, i.e. fixed in place, while with Lagrangian sensing the sensors move with the traffic flow as sensor-vehicles. We present a method to identify model parameters from both metho...

We investigate the effect of tracking errors on the accuracy and stability of Eulerian– Lagrangian methods (ELMS) for the solution of the transport equation. A combination of formal analysis and numerical experimentation demonstrates that the effect is severe. Even moderate tracking errors substantially affect the preservation of the zeroth, first and second moments of concentration (mass, phas...

Solid rocket motor flows depend strongly on alumina granulometry, which spreads up with coalescence. Solving droplet sizes in unsteady flows is a modeling and numerical challenge, specially when high loadings generate retrocoupling. As an alternative to Lagrangian approaches, the Eulerian Multi-Fluid model describes polydispersity with size-sorted droplet fluids called sections. A two size mome...

Energy-decreasing continuum flows of geometric order parameters are considered. The dynamics of pattern formation for an arbitrary geometric quantity is derived using a generalization of Darcy’s law based on the geometric nature of the order parameter. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanic...

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Λ to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times...