Potentially this paper contains some results that may be of interest to NPG, but not in its present form. The main issue is that the authors describe the method of Lagrangian descriptors in a variety of misleading and wrong ways, and they also have neglected to mention a large amount of relevant literature. The authors develop a new Lagrangian descriptor based on integrating the magnitude of th...

We describe a class of mechanical systems for which the “method of controlled Lagrangians” provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled Lagrangian approach involves making modifications to the Lagrangian for the uncontrolled system such that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the close...

A Poincaré gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under gen...

The aim of this study is to combine four fundamental forces in a single equation. Dirac equation is written by putting the Yukawa potential as a representation of the strong and gravitational forces. The ordinary terms seen in the Dirac Equation are treated as the representations of the electromagnetic forces. The Lagrangian of the weak local interaction of the charged particles is converted to...

A second order family of special Lagrangian submanifolds of C m is a family characterized by the satisfaction of a set of pointwise conditions on the second fundamental form. For example, the set of ruled special Lagrangian submanifolds of C 3 is characterized by a single algebraic equation on the second fundamental form. While the ‘generic’ set of such conditions turns out to be incompatible, ...

We argue that the string theory dual to a certain sector of the four-dimensional Yang-Mills theory at large-N is the A-model wrapping N Lagrangian Dbranes on the twistor space of the complex two-dimensional projective space, with a certain flux and Wilson loop background, by finding that the targetspace beta function of this A-model coincides with the large-N beta function of the Yang-Mills the...

Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). In principle, the kinetic description is valid from the dilute (non-collisional) to the dense limit. However, its numerical solution in multi-dimensional systems is intractable due to the large numbe...

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...

We present a manifestly SO(8) invariant non-linear Lagrangian for describing the non-abelian dynamics of the bosonic degrees of freedom of N coinciding M2 branes in flat spacetime. The theory exhibits a gauge symmetry structure of the BF type (semidirect product of SU(N) and translations) and at low energies it reduces exactly to the bosonic part of the Lorentzian BaggerLambert Lagrangian for g...

In second order Lagrangian systems bifurcation branches of periodic solutions preserve certain topological invariants. These invariants are based on the observation that periodic orbits of a second order Lagrangian lie on 3-dimensional (non-compact) energy manifolds and the periodic orbits may have various linking and knotting properties. The main ingredients to define the topological invariant...