92,048 research outputs found
Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path
The optical path lengths travelled by rays across a wavefront essentially
determine the resulting phase front irrespective of the shape of a medium
according to the principle of equal optical path. Thereupon we propose a method
for the transformation between two arbitrary wavefronts by a slab, i.e. the
profile of the spatial separation between the two wavefronts is taken to be
transformed to a plane surface. Interestingly, for the mutual conversion
between planar and curved wavefronts, the method reduce to an inverse
transformation method in which it is the reversed shape of the desired
wavefront that is converted to a planar one. As an application, three kinds of
phase transformation are realized and it is found that the transformation on
phase is able to realize some important properties such as phase reversal or
compensation, focusing, and expanding or compressing beams, which are further
confirmed by numerical simulations. The slab can be applied to realizing
compact electromagnetic devices for which the values of the refractive index or
the permittivity and permeability can be high or low, positive or negative, or
near zero, depending on the choice of coordinate transformations.Comment: 8 pages, 6 figure
The enumeration of generalized Tamari intervals
Let be a grid path made of north and east steps. The lattice
, based on all grid paths weakly above and
sharing the same endpoints as , was introduced by Pr\'eville-Ratelle and
Viennot (2014) and corresponds to the usual Tamari lattice in the case
. Our main contribution is that the enumeration of intervals in
, over all of length , is given by . This formula was first obtained by Tutte(1963) for
the enumeration of non-separable planar maps. Moreover, we give an explicit
bijection from these intervals in to non-separable
planar maps.Comment: 19 pages, 11 figures. Title changed, originally titled "From
generalized Tamari intervals to non-separable planar maps (extended
abstract)", submitte
Conformal Anomalies in Noncommutative Gauge Theories
We calculate conformal anomalies in noncommutative gauge theories by using
the path integral method (Fujikawa's method). Along with the axial anomalies
and chiral gauge anomalies, conformal anomalies take the form of the
straightforward Moyal deformation in the corresponding conformal anomalies in
ordinary gauge theories. However, the Moyal star product leads to the
difference in the coefficient of the conformal anomalies between noncommutative
gauge theories and ordinary gauge theories. The (Callan-Symanzik)
functions which are evaluated from the coefficient of the conformal anomalies
coincide with the result of perturbative analysis.Comment: 17 pages, Latex, no figures, minor corrections and references added;
to appear in Phys. Rev.
Inverse problem in cylindrical electrical networks
In this paper we study the inverse Dirichlet-to-Neumann problem for certain
cylindrical electrical networks. We define and study a birational
transformation acting on cylindrical electrical networks called the electrical
-matrix. We use this transformation to formulate a general conjectural
solution to this inverse problem on the cylinder. This conjecture extends work
of Curtis, Ingerman, and Morrow, and of de Verdi\`ere, Gitler, and Vertigan for
circular planar electrical networks. We show that our conjectural solution
holds for certain "purely cylindrical" networks. Here we apply the grove
combinatorics introduced by Kenyon and Wilson.Comment: 22 pages, 15 figure
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