50,169 research outputs found
Quasi regular concentric waves in heterogeneous lattices of coupled oscillators
We study the pattern formation in a lattice of coupled phase oscillators with
quenched disorder. In the synchronized regime concentric waves can arise, which
are induced and increase in regularity by the disorder of the system. Maximal
regularity is found at the edge of the synchronization regime. The emergence of
the concentric waves is related to the symmetry breaking of the interaction
function. An explanation of the numerically observed phenomena is given in a
one-dimensional chain of coupled phase oscillators. Scaling properties,
describing the target patterns are obtained.Comment: 4 pages, 3 figures, submitted to PR
Rigidity of frameworks on expanding spheres
A rigidity theory is developed for bar-joint frameworks in
whose vertices are constrained to lie on concentric -spheres with
independently variable radii. In particular, combinatorial characterisations
are established for the rigidity of generic frameworks for with an
arbitrary number of independently variable radii, and for with at most
two variable radii. This includes a characterisation of the rigidity or
flexibility of uniformly expanding spherical frameworks in .
Due to the equivalence of the generic rigidity between Euclidean space and
spherical space, these results interpolate between rigidity in 1D and 2D and to
some extent between rigidity in 2D and 3D. Symmetry-adapted counts for the
detection of symmetry-induced continuous flexibility in frameworks on spheres
with variable radii are also provided.Comment: 22 pages, 2 figures, updated reference
Quantum Interference Effects in Electronic Transport through Nanotube Contacts
Quantum interference has dramatic effects on electronic transport through
nanotube contacts. In optimal configuration the intertube conductance can
approach that of a perfect nanotube (). The maximum conductance
increases rapidly with the contact length up to 10 nm, beyond which it exhibits
long wavelength oscillations. This is attributed to the resonant cavity-like
interference phenomena in the contact region. For two concentric nanotubes
symmetry breaking reduces the maximum intertube conductance from to
. The phenomena discussed here can serve as a foundation for building
nanotube electronic circuits and high speed nanoscale electromechanical
devices
The Power of Poincar\'e: Elucidating the Hidden Symmetries in Focal Conic Domains
Focal conic domains are typically the "smoking gun" by which smectic liquid
crystalline phases are identified. The geometry of the equally-spaced smectic
layers is highly generic but, at the same time, difficult to work with. In this
Letter we develop an approach to the study of focal sets in smectics which
exploits a hidden Poincar\'e symmetry revealed only by viewing the smectic
layers as projections from one-higher dimension. We use this perspective to
shed light upon several classic focal conic textures, including the concentric
cyclides of Dupin, polygonal textures and tilt-grain boundaries.Comment: 4 pages, 3 included figure
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