A simple procedure to tighten the Lagrangian bounds is proposed. The approach is interpreted in two ways. First, it can be seen as a reformulation of the original problem aimed to split the resulting Lagrangian problem into two subproblems. Second, it can be considered as a search for a tighter estimation of the penalty term arising in the Lagrangian problem. The new bounds are illustrated by a...

Atmospheric dispersion is a topic of great importance especially in relation to pollutant transport. Two different approaches, known as the Eulerian and the Lagrangian frameworks, are used to describe this process. In the Eulerian framework, statistical properties are calculated in a fixed reference frame. This approach is most commonly used in field experiments as well as in laboratory experim...

This paper presents a complete derivation and implementation of the Arbitrary Lagrangian Eulerian (ALE) formulation for the simulation of nonlinear static and dynamic problems in solid mechanics. While most of the previous work done on ALE for dynamic applications was mainly based on operator split and explicit calculations, this work derives the quasi-static and dynamic ALE equations in its si...

We present a novel and efficient technique to extract Lagrangian coherent structures in two-dimensional time-dependent vector fields. We show that this can be achieved by employing bifurcation line extraction in the space-time representation of the vector field, and generating space-time bifurcation manifolds therefrom. To show the utility and applicability of our approach, we provide an evalua...

A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for the disadvantage of non-Lagrangian structures in presenting a correspondence between symmetries and conservation laws. Applications are made for the...

We first write down a very general description of nonlinear classical electrodynamics, making use of generalized constitutive equations and constitutive tensors. Our approach includes non-Lagrangian as well as Lagrangian theories, allows for electromagnetic fields in the widest possible variety of media (anisotropic, piroelectric, chiral and ferromagnetic), and accommodates the incorporation of...

In the revised version, we emphasized new results from EOF analysis and Lagrangian approach. Following sentence is added in the abstract: “The EOF analysis indicated that these diurnal variations over the African continent seem to be closely related to continental-scale daytime solar heating and topography. On the other hand, advection effect on the diurnal variation appeared to be minor becaus...

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...