1,449 research outputs found
The Geometry of Non-Ideal Fluids
Arnold showed that the Euler equations of an ideal fluid describe geodesics
on the Lie algebra of incompressible vector fields. We generalize this to
fluids with dissipation and Gaussian random forcing. The dynamics is determined
by the structure constants of a Lie algebra, along with inner products defining
kinetic energy, Ohmic dissipation and the covariance of the forces. This allows
us to construct tractable toy models for fluid mechanics with a finite number
of degrees of freedom. We solve one of them to show how symmetries can be
broken spontaneously.In another direction, we derive a deterministic equation
that describes the most likely path connecting two points in the phase space of
a randomly forced system: this is a WKB approximation to the
Fokker-Plank-Kramer equation, analogous to the instantons of quantum theory.
Applied to hydrodynamics, we derive a PDE system for Navier-Stokes instantons.Comment: Talk at the Quantum Theory and Symmetries 6 Conference at the
University of Kentuck
Two Dimensional Quantum Chromodynamics on a Cylinder
We study two dimensional Quantum Chromodynamics with massive quarks on a
cylinder in a light--cone formalism. We eliminate the non--dynamical degrees of
freedom and express the theory in terms of the quark and Wilson loop variables.
It is possible to perform this reduction without gauge fixing. The fermionic
Fock space can be defined independent of the gauge field in this light--cone
formalism.Comment: 8 pages, UR-128
- …