We propose a notion of a pluri-Lagrangian problem, which should be understood as an analog of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistica...

In this paper, we examine the question of the boundary controllability of the one-dimensional nonisentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian coordinates and the one in Lagrangian coordinates. We obtain for both systems a result of controllability toward constant states (with the limitation γ < 5 3 on the...

We demonstrate that the supersymmetry can be dynamically broken even in theories without a Lagrangian. The example we study is the four-dimensional SUðNÞ gauge theory coupled to a strongly coupled superconformal theory, called TN , which does not have a Lagrangian description at present. Such a theory without Lagrangians can be analyzed due to the supersymmetry and duality. The model is a direc...

The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 = LτA1. We use this result ...

We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension ...

A new model of bosonic strings is considered. An action of the model is the sum of the standard string action and a term describing an interaction of a metric with a linear (affine) connection. The Lagrangian of this interaction is an arbitrary analytic function f (R) of the scalar curvature. This is a classically integrable model. The space of classical solutions of the theory consists from se...

The rst law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial in nity, of a stationary, axisymmetric black hole, in a di eomorphism invariant Lagrangian theory of gravity. The original statement of the rst law given by Bardeen, Carter and Hawking for an Einstein-perfect uid system contained, in addition, volume in...

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Mor...

The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n)⋉Symm(n). We give a Lagrangian derivation of the corresponding equations of motion, and introduce a discrete time analog of this system. The construction is based on the discrete time Lagrangian mechanics on Lie groups, accompanied wi...

In this paper, the Stability Augmentation System (SAS) is designed to improve the stability while Parallel Evolutionary Optimization based on Lagrangian I1 (PEvolian 11) is successfully applied to satisfy several constraints and to minimize the rising time. A controller to stabilize F-16 aircraft flying with a steady state around the altitude of 25,OOOft is described. The nonlinear pitching mot...