To assess the impact of dynamical formulation on climate simulations, a semi-Lagrangian and an Eulerian dynamical core have been used for 5-yr climate simulations with the same physical parameterizations. The comparison of the climate simulations is focused on various eddy statistics (the study of time-mean states from the simulations has been published in a previous paper). Significant differe...

We show that weak (Eulerian) solutions for the Semi-Geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove ...

The study of low energy hadron physics in QCD is a long standing difficult problem due to its nonperturbative nature. For low lying pseudoscalar mesons, a widely used approach is the theory of effective chiral Lagrangian based on the consideration of the global symmetry of the system and the momentum expansion without dealing with the nonperturbative dynamics of QCD [1] [2]. In the chiral Lagra...

We develop the non-di erentiable embedding theory of di erential operators and Lagrangian systems using a new operator on non-di erentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-di erentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. First, we extend the characteristics method to the non-di erentiabl...

It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This i...

A complete analysis of the consequences of introducing a set of holonomic gauge fixing constraints (to fix the dynamics) into a singular Lagrangian is performed. It is shown in general that the dynamical system originated from the reduced Lagrangian erases all the information regarding the first class constraints of the original theory, but retains its second class. It is proved that even thoug...

Lagrangian systems with ideal nonholonomic constraints can be expressed as implicit index 2 differential-algebraic equations (DAEs) and can be derived from the Lagrange-d’Alembert principle. We define a new nonholonomically constrained discrete Lagrange-d’Alembert principle based on a discrete Lagrange-d’Alembert principle for forced Lagrangian systems. Nonholonomic constraints are considered a...

We consider a special class of Lagrangians that play a fundamental role in the theory of second order Lagrangian systems: Twist systems. This subclass of Lagrangian systems is deened via a convenient monotonicity property that such systems share. This monotonicity property (Twist property) allows a nite dimensional reduction of the variational principle for nding closed characteristics in xed e...