Systems of second-order ordinary differential equations admitting a Lagrangian formulation are deformed requiring that the extended Lagrangian preserves a fixed subalgebra of Noether symmetries of the original system. For the case of the simple Lie algebra sl(2,R), this provides non-linear systems with two independent constants of the motion quadratic in the velocities. In the case of scalar di...

Starting from a system of planar electrons in a strong magnetic field normal to the plane, interacting with perturbing electromagnetic fields, an effective Lagrangian for the fermions in the lowest Landau level (L.L.L.) has been derived. By choosing a suitable background electrostatic potential, an incompressible droplet of these electrons is constructed. The gauge invariant effective Lagrangia...

We present a method for applying 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 implicit and fully coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of surface tension force, which...

A method is proposed of constructing quantum correlators for a general gauge system whose classical equations of motion do not necessarily follow from the least action principle. The idea of the method is in assigning a certain BRST operator Ω̂ to any classical equations of motion, Lagrangian or not. The generating functional of Green’s functions is defined by the equation Ω̂Z(J) = 0 that is redu...

Dynamical systems described by equations of motion with the first-order time derivative (dissipative) terms of even and odd powers, and coefficients varying either in time or in space, are considered. Methods to obtain standard and nonstandard Lagrangians are presented and used to identify classes of equations of motion that admit a Lagrangian description. It is shown that there are two general...

I promised a second part. Here it is. I hesitated, because I don’t like being destructive, and unfortunately, to deal with the current state of affairs in quantum theory means just doing this: I show you that the current gauge theory is fundamentally ill-designed, along with it fall Weinberg model and Wightman theory. 1. Continuing with the Lagrangian Formalism Let me continue from where I left...

The aim of this study is to investigate the problems caused by discharge of polluted air from tunnels into the environment with a specific focus on residential areas. In city tunnels, portal or stacks, pollutant management is a big challenge. Nowadays, air quality management, particularly in urban tunnels, is considered as a part of the ventilation system design. The goal is to see the environm...

The vortex-wave system is a version of the vorticity equation governing the motion of 2D incompressible fluids in which vorticity is split into a finite sum of Diracs, evolved through an ODE, plus an L part, evolved through an active scalar transport equation. Existence of a weak solution for this system was recently proved by Lopes Filho, Miot and Nussenzveig Lopes, for p > 2, but their result...

Lagrangian theory provides a diverse set of tools for continuous motion analysis. Existing work shows the applicability of Lagrangian method for video analysis in several aspects. In this paper we want to utilize the concept of Lagrangian measures to detect violent scenes. Therefore we propose a local feature based on the SIFT algorithm that incooperates appearance and Lagrangian based motion m...