Related papers: Vlasov's beams and multivector Grassmann Statics
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
The foundations of gyrokinetic theory are reviewed with an emphasis on the applications of Lagrangian and Hamiltonian methods used in the derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. These reduced dynamical equations…
We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear…
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface…
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the…
A semiclassical linear response theory based on the Vlasov equation is reviewed. The approach discussed here differs from the classical one of Vlasov and Landau for the fact that the finite size of the system is explicitly taken into…
This paper studies geometric engineering, in the simplest possible case of rank one (Abelian) gauge theory on the affine plane and the resolved conifold. We recall the identification between Nekrasov's partition function and a version of…
A Batalin-Vilkovisky formalism is most general framework to construct consistent quantum field theories. Its mathematical structure is called {\it a Batalin-Vilkovisky structure}. First we explain rather mathematical setting of a…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
The nonlinear Vlasov equation contains the full nonlinear dynamics and collective effects of a given Hamiltonian system. The linearized approximation is not valid for a variety of interesting systems, nor is it simple to extend to higher…
We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated problems, from Real Algebraic Geometry to sub-Riemannian Geometry.
This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants…
On a basis of theory of Riemann extension of the space of constant affine connection associated with the R\"ossler system of equations relations between its parameters are investigated.
We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized…
In this paper a construction of affine exterior algebra of Grassmann, with a special attention to the revisitation of this subject operated by Peano and his School, is examined from a historical viewpoint. Even if the exterior algebra over…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the…
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…