887 research outputs found
Geodesics in the space of measure-preserving maps and plans
We study Brenier's variational models for incompressible Euler equations.
These models give rise to a relaxation of the Arnold distance in the space of
measure-preserving maps and, more generally, measure-preserving plans. We
analyze the properties of the relaxed distance, we show a close link between
the Lagrangian and the Eulerian model, and we derive necessary and sufficient
optimality conditions for minimizers. These conditions take into account a
modified Lagrangian induced by the pressure field. Moreover, adapting some
ideas of Shnirelman, we show that, even for non-deterministic final conditions,
generalized flows can be approximated in energy by flows associated to
measure-preserving maps
Convex domains of Finsler and Riemannian manifolds
A detailed study of the notions of convexity for a hypersurface in a Finsler
manifold is carried out. In particular, the infinitesimal and local notions of
convexity are shown to be equivalent. Our approach differs from Bishop's one in
his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the
Riemannian case. Ours not only can be extended to the Finsler setting but it
also reduces the typical requirements of differentiability for the metric and
it yields consequences on the multiplicity of connecting geodesics in the
convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update
The type numbers of closed geodesics
A short survey on the type numbers of closed geodesics, on applications of
the Morse theory to proving the existence of closed geodesics and on the recent
progress in applying variational methods to the periodic problem for Finsler
and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of
variations in the large" by M. Mors
Atomic Configuration of Nitrogen Doped Single-Walled Carbon Nanotubes
Having access to the chemical environment at the atomic level of a dopant in
a nanostructure is crucial for the understanding of its properties. We have
performed atomically-resolved electron energy-loss spectroscopy to detect
individual nitrogen dopants in single-walled carbon nanotubes and compared with
first principles calculations. We demonstrate that nitrogen doping occurs as
single atoms in different bonding configurations: graphitic-like and
pyrrolic-like substitutional nitrogen neighbouring local lattice distortion
such as Stone-Thrower-Wales defects. The stability under the electron beam of
these nanotubes has been studied in two extreme cases of nitrogen incorporation
content and configuration. These findings provide key information for the
applications of these nanostructures.Comment: 25 pages, 13 figure
Metal–ferroelectric supercrystals with periodically curved metallic layers
Simultaneous manipulation of multiple boundary conditions in nanoscale heterostructures offers a versatile route to stabilizing unusual structures and emergent phases. Here, we show that a stable supercrystal phase comprising a three-dimensional ordering of nanoscale domains with tailored periodicities can be engineered in PbTiO3–SrRuO3 ferroelectric–metal superlattices. A combination of laboratory and synchrotron X-ray diffraction, piezoresponse force microscopy, scanning transmission electron microscopy and phase-field simulations reveals a complex hierarchical domain structure that forms to minimize the elastic and electrostatic energy. Large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO3 layers with curvatures up to 107 m−1. Our results show that multidomain ferroelectric systems can be exploited as versatile templates to induce large curvatures in correlated materials, and present a route for engineering correlated materials with modulated structural and electronic properties that can be controlled using electric fields
Photoluminescence investigations of 2D hole Landau levels in p-type single Al_{x}Ga_{1-x}As/GaAs heterostructures
We study the energy structure of two-dimensional holes in p-type single
Al_{1-x}Ga_{x}As/GaAs heterojunctions under a perpendicular magnetic field.
Photoluminescence measurments with low densities of excitation power reveal
rich spectra containing both free and bound-carrier transitions. The
experimental results are compared with energies of valence-subband Landau
levels calculated using a new numerical procedure and a good agreement is
achieved. Additional lines observed in the energy range of free-carrier
recombinations are attributed to excitonic transitions. We also consider the
role of many-body effects in photoluminescence spectra.Comment: 13 pages, 10 figures, accepted to Physical Review
On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of or . In the
-periodic case, we establish criteria for recurrence. In the more difficult
-periodic case, we establish some general results. For a particular
family of -periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
Symplectically degenerate maxima via generating functions
We provide a simple proof of a theorem due to Nancy Hingston, asserting that
symplectically degenerate maxima of any Hamiltonian diffeomorphism of the
standard symplectic 2d-torus are non-isolated contractible periodic points or
their action is a non-isolated point of the average-action spectrum. Our
argument is based on generating functions.Comment: 25 pages, thoroughly revised version, new titl
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