23 research outputs found
Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
The famous question of Mark Kac "Can one hear the shape of a drum?"
addressing the unique connection between the shape of a planar region and the
spectrum of the corresponding Laplace operator can be legitimately extended to
scattering systems. In the modified version one asks whether the geometry of a
vibrating system can be determined by scattering experiments. We present the
first experimental approach to this problem in the case of microwave graphs
(networks) simulating quantum graphs. Our experimental results strongly
indicate a negative answer. To demonstrate this we consider scattering from a
pair of isospectral microwave networks consisting of vertices connected by
microwave coaxial cables and extended to scattering systems by connecting leads
to infinity to form isoscattering networks. We show that the amplitudes and
phases of the determinants of the scattering matrices of such networks are the
same within the experimental uncertainties. Furthermore, we demonstrate that
the scattering matrices of the networks are conjugated by the, so called,
transplantation relation.Comment: 3 figures; Physical Review Letters, 201
Kontynentalizm termiczny w Europie
Five indices of thermal continentality were computed for 84 stations in Europe and shown in the
maps. The thermal continentality in Europe is spatially variable and increases eastward and southward from
the northwestern shores towards Asia. Continental features are distinct in the interior of the Iberian Peninsula
and in the northeastern part of the Scandinavian Peninsula, despite their small distance from the Atlantic
Ocean. Most continentality indices (Chromowâs, Ewertâs, Conradâs, Johansson-Ringlebâs) reveal a similar spatial
pattern of thermal continentality in Europe, and they allow the continent to be divided into a western and
eastern part along meridian 20â25°E. Marszâs index, which takes into consideration the level of oceanity, indicates
a narrow zone along the northwestern shore as oceanic and the remaining part of Europe as continental.617118213Badania Fizjograficzn
Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
We present the results of experimental and numerical study of the
distribution of the reflection coefficient P(R) and the distributions of the
imaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix for
irregular fully connected hexagon networks (graphs) in the presence of strong
absorption. In the experiment we used microwave networks, which were built of
coaxial cables and attenuators connected by joints. In the numerical
calculations experimental networks were described by quantum fully connected
hexagon graphs. The presence of absorption introduced by attenuators was
modelled by optical potentials. The distribution of the reflection coefficient
P(R) and the distributions of the reaction K matrix were obtained from the
measurements and numerical calculations of the scattering matrix S of the
networks and graphs, respectively. We show that the experimental and numerical
results are in good agreement with the exact analytic ones obtained within the
framework of random matrix theory (RMT).Comment: 15 pages, 8 figure
Isoscattering strings of concatenating graphs and networks
Abstract We identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for n â â . The theoretical predictions are confirmed experimentally using n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the 2 n Ă 2 n scattering matrices S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac âCan one hear the shape of a drum?â, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks