882 research outputs found
Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures
This paper presents an approach to a time-dependent variant of the concept of
vector field topology for 2-D vector fields. Vector field topology is defined
for steady vector fields and aims at discriminating the domain of a vector
field into regions of qualitatively different behaviour. The presented approach
represents a generalization for saddle-type critical points and their
separatrices to unsteady vector fields based on generalized streak lines, with
the classical vector field topology as its special case for steady vector
fields. The concept is closely related to that of Lagrangian coherent
structures obtained as ridges in the finite-time Lyapunov exponent field. The
proposed approach is evaluated on both 2-D time-dependent synthetic and vector
fields from computational fluid dynamics
Aspects of hot Galilean field theory
We reconsider general aspects of Galilean-invariant thermal field theory.
Using the proposal of our companion paper, we recast non-relativistic
hydrodynamics in a manifestly covariant way and couple it to a background
spacetime. We examine the concomitant consequences for the thermal partition
functions of Galilean theories on a time-independent, but weakly curved
background. We work out both the hydrodynamics and partition functions in
detail for the example of parity-violating normal fluids in two dimensions to
first order in the gradient expansion, finding results that differ from those
previously reported in the literature. As for relativistic field theories, the
equality-type constraints imposed by the existence of an entropy current appear
to be in one-to-one correspondence with those arising from the existence of a
hydrostatic partition function. Along the way, we obtain a number of useful
results about non-relativistic hydrodynamics, including a manifestly
boost-invariant presentation thereof, simplified Ward identities, the
systematics of redefinitions of the fluid variables, and the positivity of
entropy production.Comment: 65 pages, 1 figur
A Generalization of the Bargmann's Theory of Ray Representations
The paper contains a complete theory of factors for ray representations
acting in a Hilbert bundle, which is a generalization of the known Bargmann's
theory. With the help of it we have reformulated the standard quantum theory
such that the gauge freedom emerges naturally from the very nature of quantum
laws. The theory is of primary importance in the investigations of covariance
(in contradistinction to symmetry) of a quantum theory which possesses a
nontrivial gauge freedom. In that case the group in question is not any
symmetry group but it is a covariance group only - that case which has not been
deeply investigated. It is shown on the paper that the factor of its
representation depends on space and time when the system in question possesses
a gauge freedom. In the nonrelativistic theories the factor depends on the time
only. In the relativistic theory the Hilbert bundle is over the spacetime in
the nonrelativistic one it is over the time.
We explain two applications of this generalization: in a theory of a quantum
particle in the nonrelativistic limit and in the quantum electrodynamics.Comment: 37 pages, LateX, revised version, submitted to Comm. Math. Phy
Vortex-antivortex proliferation from an obstacle in thin film ferromagnets
Magnetization dynamics in thin film ferromagnets can be studied using a
dispersive hydrodynamic formulation. The equations describing the
magnetodynamics map to a compressible fluid with broken Galilean invariance
parametrized by the longitudinal spin density and a magnetic analog of the
fluid velocity that define spin-density waves. A direct consequence of these
equations is the determination of a magnetic Mach number. Micromagnetic
simulations reveal nucleation of nonlinear structures from an impenetrable
object realized by an applied magnetic field spot or a defect. In this work,
micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an
obstacle. Their interaction establishes either ordered or irregular
vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds
unity (supersonic flow), a Mach cone and periodic wavefronts are observed,
which can be well-described by solutions of the steady, linearized equations.
These results are reminiscent of theoretical and experimental observations in
Bose-Einstein condensates, and further supports the analogy between the
magnetodynamics of a thin film ferromagnet and compressible fluids. The
nucleation of nonlinear structures and vortex-antivortex complexes using this
approach enables the study of their interactions and effects on the stability
of spin-density waves.Comment: 23 pages, 7 figure
Non-Relativistic Maxwell Chern-Simons Gravity
We consider a non-relativistic (NR) limit of -dimensional Maxwell
Chern-Simons (CS) gravity with gauge algebra [Maxwell] . We obtain a finite NR CS gravity with a degenerate invariant bilinear
form. We find two ways out of this difficulty: To consider i) [Maxwell]
, which does not contain Extended Bargmann gravity (EBG); or, ii)
the NR limit of [Maxwell] , which is a
Maxwellian generalization of the EBG.Comment: 19 pages, 1 table, subsection 3.3 added, abstract and references
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