3,762 research outputs found
Stationary Closed Strings in Five-dimensional Flat Spacetime
We investigate stationary rotating closed Nambu-Goto strings in
five-dimensional flat spacetime. The stationary string is defined as a
worldsheet that is tangent to a timelike Killing vector. Nambu-Goto equation of
motion for the stationary string is reduces to the geodesic equation on the
orbit space of the isometry group action generated by the Killing vector. We
take a linear combination of a time-translation vector and space-rotation
vectors as the Killing vector, and explicitly construct general solutions of
stationary rotating closed strings in five-dimensional flat spacetime. We show
a variety of their configurations and properties.Comment: 22 pages, 17 figure
Non-perturbative Fermion Propagator for the Massless Quenched QED3
For massless quenched QED in three dimensions, we evaluate a non-perturbative
expression for the fermion propagator which agrees with its two loop
perturbative expansion in the weak coupling regime. This calculation is carried
out by making use of the Landau-Khalatnikov-Fradkin transformations. Any
improved construction of the fermion-boson vertex must make sure that the
solution of the Schwinger-Dyson equation for the fermion propagator reproduces
this result. For two different gauges, we plot the fermion propagator against
momentum. We then make a comparison with a similar plot, using the earlier
expression for the fermion propagator, which takes into account only the one
loop result.Comment: 11 pages, 3 figures, to appear in Phys. Lett.
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
We show that, near periodic orbits, a class of hybrid models can be reduced
to or approximated by smooth continuous-time dynamical systems. Specifically,
near an exponentially stable periodic orbit undergoing isolated transitions in
a hybrid dynamical system, nearby executions generically contract
superexponentially to a constant-dimensional subsystem. Under a non-degeneracy
condition on the rank deficiency of the associated Poincare map, the
contraction occurs in finite time regardless of the stability properties of the
orbit. Hybrid transitions may be removed from the resulting subsystem via a
topological quotient that admits a smooth structure to yield an equivalent
smooth dynamical system. We demonstrate reduction of a high-dimensional
underactuated mechanical model for terrestrial locomotion, assess structural
stability of deadbeat controllers for rhythmic locomotion and manipulation, and
derive a normal form for the stability basin of a hybrid oscillator. These
applications illustrate the utility of our theoretical results for synthesis
and analysis of feedback control laws for rhythmic hybrid behavior
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