— We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [6].

H-minimal Lagrangian submanifolds in general Kähler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with negative first Chern class.

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of...

In this paper we introduce harmonic Lagrangian submanifolds in general Kähler manifolds, which generalize special Lagrangian submanifolds in Calabi-Yau manifolds. We will use the deformation theory of harmonic Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with negative first Chern class.

Lagrangian curves in R entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R and determ...

In this article, we present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The is “block-based,” in which vectors of primal and dual variables are partitioned into blocks, each updated only by single processor. We consider four behaviors that could be asynchronous: 1) updates to variables; 2) 3) communications 4) variables. show any amount asynchrony ...

Abstract Handling stress constraints is an important topic in topology optimization. In this paper, we introduce interpretation of stresses as optimization variables, leading to augmented Lagrangian formulation. This formulation takes two sets i.e., auxiliary variable per element, addition a density conventional density-based approaches. The related the actual (i.e., computed by its definition)...

Lagrangian analysis is becoming increasingly important to better understand the ocean's biological and biogeochemical cycles. Yet, biologists chemists often lack technical skills required set up such analyses. Here, we present a new product of pre-computed ocean Lagrangian trajectories (OLTraj) targeting non-expert users, demonstrate how use it by means worked examples. OLTraj based on s...