Related papers: Lagrangian descriptors and their applications to d…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems,…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
Both orbital and rotational dynamics employ the method of variation of parameters. We express, in a non-perturbed setting, the coordinates (Cartesian, in the orbital case, or Eulerian in the rotation case) via the time and six adjustable…
Accurate prediction of Lagrangian trajectories in turbulent flow remains challenging due to limited temporal information in transport functions. This paper shows that surrounding coherent motions sharing the same dynamics carry enough…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
The Author shows how to construct a class of Lagrangians for relativistic dynamical systems described by position and a single spinor. One arrives to it by imposing three requirements: 1) Hamilton action should be reparametrization…
It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…
This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter $\Omega$, with either a zero cosmological constant, $\Lambda = 0$, or with a non-zero cosmological…
A temporal complex network-based approach is proposed as a novel formulation to investigate turbulent mixing from a Lagrangian viewpoint. By exploiting a spatial proximity criterion, the dynamics of a set of fluid particles is geometrized…
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is…
Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two-…
Chiral perturbation theory is extended to nonrelativistic systems with spontaneously broken symmetry. In the effective Lagrangian, order parameters associated with the generators of the group manifest themselves as effective coupling…
We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
We present two types of relativistic Lagrangians for the Lorentz-Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends…