419 research outputs found
On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows
We show that if a sequence of Hamiltonian flows has a limit, and if the
generating Hamiltonians of the sequence have a limit, then this limit is
uniquely determned by the limiting flow. This answers a question by Y.G.
Oh.Comment: 11 page
Symplectic capacity and short periodic billiard trajectory
We prove that a bounded domain in with smooth boundary has a
periodic billiard trajectory with at most bounce times and of length less
than , where is a positive constant which depends only on
, and is the supremum of radius of balls in . This
result improves the result by C.Viterbo, which asserts that has a
periodic billiard trajectory of length less than C'_n \vol(\Omega)^{1/n}. To
prove this result, we study symplectic capacity of Liouville domains, which is
defined via symplectic homology.Comment: 32 pages, final version with minor modifications. Published online in
Mathematische Zeitschrif
Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations
We consider a wireless sensor network, sampling a bandlimited field,
described by a limited number of harmonics. Sensor nodes are irregularly
deployed over the area of interest or subject to random motion; in addition
sensors measurements are affected by noise. Our goal is to obtain a high
quality reconstruction of the field, with the mean square error (MSE) of the
estimate as performance metric. In particular, we analytically derive the
performance of several reconstruction/estimation techniques based on linear
filtering. For each technique, we obtain the MSE, as well as its asymptotic
expression in the case where the field number of harmonics and the number of
sensors grow to infinity, while their ratio is kept constant. Through numerical
simulations, we show the validity of the asymptotic analysis, even for a small
number of sensors. We provide some novel guidelines for the design of sensor
networks when many parameters, such as field bandwidth, number of sensors,
reconstruction quality, sensor motion characteristics, and noise level of the
measures, have to be traded off
Deformations of symplectic cohomology and exact Lagrangians in ALE spaces
We prove that the only exact Lagrangian submanifolds in an ALE space are
spheres. ALE spaces are the simply connected hyperkahler manifolds which at
infinity look like C^2/G for any finite subgroup G of SL(2,C). They can be
realized as the plumbing of copies of the cotangent bundle of a 2-sphere
according to ADE Dynkin diagrams. The proof relies on symplectic cohomology.Comment: 35 pages, 3 figures, minor changes and corrected typo
Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation
Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact
and connected manifold and let u be a semi-concave function defined on M. If E
(u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian
flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact
Lagrangian Lipschitz graph. This provides a geometric
interpretation/explanation of a regularization tool that was introduced by
P.~Bernard to prove the existence of C 1,1 subsolutions
Reconstruction of Multidimensional Signals from Irregular Noisy Samples
We focus on a multidimensional field with uncorrelated spectrum, and study
the quality of the reconstructed signal when the field samples are irregularly
spaced and affected by independent and identically distributed noise. More
specifically, we apply linear reconstruction techniques and take the mean
square error (MSE) of the field estimate as a metric to evaluate the signal
reconstruction quality. We find that the MSE analysis could be carried out by
using the closed-form expression of the eigenvalue distribution of the matrix
representing the sampling system. Unfortunately, such distribution is still
unknown. Thus, we first derive a closed-form expression of the distribution
moments, and we find that the eigenvalue distribution tends to the
Marcenko-Pastur distribution as the field dimension goes to infinity. Finally,
by using our approach, we derive a tight approximation to the MSE of the
reconstructed field.Comment: To appear on IEEE Transactions on Signal Processing, 200
Interface superconductivity: History, developments and prospects
The concept of interface superconductivity was introduced over 50 years ago. Some of the greatest physicists of that time wondered whether a quasi-two-dimensional (2D) superconductor can actually exist, what are the peculiarities of 2D superconductivity, and how does the reduced dimensionality affect the critical temperature (Tc). The discovery of high-temperature superconductors, which are composed of coupled 2D superconducting layers, further increased the interest in reduced dimensionality structures. In parallel, the advances in experimental techniques made it possible to grow epitaxial 2D structures with atomically flat surfaces and interfaces, enabling some of the experiments that were proposed decades ago to be performed finally. Now we know that interface superconductivity can occur at the junction of two different materials (metals, insulators, semiconductors). This phenomenon is being explored intensely; it is also exploited as a means to increase Tc or to study quantum critical phenomena. This research may or may not produce a superconductor with a higher Tc or a useful superconducting electronic device but it will likely bring in new insights into the physics underlying high-temperature superconductivity
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