13,104 research outputs found
Nonlinear electrodynamics is skilled with knots
The aims of this letter are three-fold: First is to show that nonlinear
generalizations of electrodynamics support various types of knotted solutions
in vacuum. The solutions are universal in the sense that they do not depend on
the specific Lagrangian density, at least if the latter gives rise to a
well-posed theory. Second is to describe the interaction between probe waves
and knotted background configurations. We show that the qualitative behaviour
of this interaction may be described in terms of Robinson congruences, which
appear explicitly in the causal structure of the theory. Finally, we argue that
optical arrangements endowed with intense background fields could be the
natural place to look for the knots experimentally.Comment: 5 pages, 1 figur
Observer design for systems with an energy-preserving non-linearity
Observer design is considered for a class of non-linear systems whose
non-linear part is energy preserving. A strategy to construct convergent
observers for this class of non-linear system is presented. The approach has
the advantage that it is possible, via convex programming, to prove whether the
constructed observer converges, in contrast to several existing approaches to
observer design for non-linear systems. Finally, the developed methods are
applied to the Lorenz attractor and to a low order model for shear fluid flow
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