To better understand the capacity of Lagrangian Stochastic Models to simulate superdiffusive and subdiffusive tracer motion in oceanic turbulence, we examine their performance on a simple class of model velocity fields which support subdiffusive or superdiffusive regimes of tracer transport associated to power-law regions of the Lagrangian power spectrum. We focus on how well the Lagrangian Sto...

In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with cohomogeneity one. We characterize them as the only minimal Lagrangian submanifolds in CHn foliated by umbilical hypersurfaces of Lagrangian subspaces RHn of CHn. Several suitable generalizations of the above constructio...

My project addresses statistical and stochastic problems in the following fields: Lagrangian prediction (1), Lagrangian data assimilation (2), development and validation of Lagrangian stochastic models (LSM) (3). The long range scientific objectives of this study comprise rigorous determining limits of predictability for Lagrangian motion in semi-enclosed seas, littoral zones, and straits on ti...

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel’s theorem for frozen-in vo...

The main theorem of this paper asserts that the inclusion of the space of projective Lagrangian planes into the space of Lagrangian submanifolds of complex projective space induces an injective homomorphism of fundamental groups. We introduce three invariants of exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Polterovich for loops of Hamiltonian symplectomor...

The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the canonical embedding of the Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety of the Drinfel’d Lagrangian Grassmannian is generated by polynomials which gi...

In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of...

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vo...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of CP in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian knotting.