[1] In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the L...

Minimal Lagrangian submanifolds of a Kähler manifold represent a very interesting class of submanifolds as they are Lagrangian with respect to the symplectic structure of the ambient space, while minimal with respect to the Riemannian structure. In this paper we study minimal Lagrangian immersions of the universal cover of closed surfaces (of genus g ≥ 2) in CH, with prescribed data (σ, tq), wh...

Permanent magnet machines with both magnetic saturation and saliency effects can be directly described via Euler-Lagrangian formulation with complex currents. The Lagrangian is the sum of a mechanical kinetic energy and a magnetic Lagrangian. This second term is expressed in terms of rotor angle, complex stator and rotor magnetizing currents. Via simple modification of magnetic Lagrangian we de...

We propose a Lagrangian function, which combines Landau-Ginzburg term and Chern-Simons term, for describing the competition between disorder and superconductivity. To describe the normal-to-superconducting transition in the thin superconducting films, we apply Wilson's renormalization group methods into this Lagrangian function. Finally, we obtain a scaling law between critical temperature (Tc)...

The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This ...

This paper suggests an inverse optimal proportional–integral–derivative (PID) control design method to track trajectories in Lagrangian systems. The inverse optimal PID controller exists if and only if the Lagrangian system is extended disturbance input-to-state stable. First, we find the Lyapunov function and the control law that satisfy the extended disturbance input-to-state stability by usi...

The study of singular Lagrangian and Legendrian varieties was initiated about twenty-five years ago by Arnold when he was investigating singularities in the variational problem of obstacle bypassing [1]. The first examples of such varieties, open swallowtails, were related to the discriminants of the non-crystallographic Coxeter groups [8, 14]. Incorporating these examples into a general contex...

The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems, observability and invariant differential forms. The approach is applicable to non-degenerate optimal control systems with smooth integral cost function. The cost functi...

Abstract: The divergence function in information geometry, and the discrete Lagrangian in discrete 1 geometric mechanics each induce a differential geometric structure on the product manifold QˆQ. 2 We aim to investigate the relationship between these two objects, and the fundamental role that 3 duality, in the form of Legendre transforms, play in both fields. By establishing an analogy between...

We analyze characteristics of drifter trajectories from the Adriatic Sea with recently introduced nonlinear dynamics techniques. We discuss how in quasienclosed basins, relative dispersion as function of time, a standard analysis tool in this context, may give a distorted picture of the dynamics. We further show that useful information may be obtained by using two related nonasymptotic indicato...