On a characterization of Dilworth truncations of combinatorial geometries

A combinatorial geometry being given, a Dilworth structure is defined to be a family of point subsets for which properties (1_d), (2_d), (3_d) in sect.2 hold. Let T^d(G) denote Dilworth truncation of a geometry G. It is possible to associa te with T^d(G) a Dilworth structure D(G) (see sect.2). It will be proved that a one-to-one and onto corresponden ce exists between Dilworth structures S of a connected geo metry K and those geometries G such that T^d(G)=K and D(G)=S.     

High-performance guided-wave asynchronous heralded single-photon source

We report on a guided-wave asynchronous heralded single-photon source based on the creation of nondegenerate photon pairs by spontaneous parametric downconversion in a periodically poled lithium niobate wave-guide. We show that, by use of the signal photon at 1310 nm as a trigger, a gated detection process permits announcement of the arrival of single photons at 1550 nm at the output of a single-mode optical fiber with a high probability of 0.37. At the same time the multiphoton emission probability is reduced by a factor of 10 compared with Poissonian light sources. Furthermore, the model we have developed to calculate those figures of merit is shown to be accurate. This study can therefore serve as a paradigm for the conception of new quantum communication and computation networks.     

Possible one-dimensional 3He quantum fluid formed in nanopores

Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK.     

Continuously tunable 1 byte delay in coupled-resonator optical waveguides

A reconfigurable coupled-resonator optical waveguide made of a few directly coupled ring resonators is employed to control the delay of data streams modulated at tens of gigabits per second. A delay of 8 bit lengths (1 optical byte) with a small pulse broadening and 1 dB/bit fractional loss is achieved by using only eight rings. The limiting role of waveguide loss and spurious backreflections is experimentally investigated. The high storage efficiency (1 bit/ring) of the device enables an easy, reliable, hitless, and relatively low-power-consuming management of the delay. A higher storage efficiency is demonstrated to be associated to an unavoidable higher pulse distortion.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

Modules Over the Noncommutative Torus and Elliptic Curves

Using the Weil–Brezin–Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely generated projective modules over the algebra A _θ of the noncommutative torus. We show that such A _θ -modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve E _τ , under the condition that the deformation parameter θ and the modular parameter τ satisfy a non-trivial relation.     

Shape reconstruction of metallic objects from intensity scattered field data only

We address an inverse scattering problem using only amplitude information of the scattered field. In particular, we are concerned with the reconstruction of the shape of a metallic planar obstacle, located in a known plane (aperture plane), starting from the knowledge of the intensity of the scattered field over two measurement planes in near zone and parallel to the aperture plane, when a single-frequency incident plane wave is exploited. The formulation of the inverse scattering problem is given under the physical optics approximation, and thus the resulting phase retrieval problem is quadratic. This allows us to apply some phase retrieval techniques already developed for antenna diagnostics. Reconstruction results with synthetic data indicate the feasibility of the proposed approach.     

Acoustic emission localization in complex dissipative anisotropic structures using a one-channel reciprocal time reversal method

This paper presents an imaging method for the localization of the impact point in complex anisotropic structures with diffuse field conditions, using only one passive transducer. The proposed technique is based on the reciprocal time reversal approach (inverse filtering) applied to a number of waveforms stored into a database containing the experimental Green's function of the structure. Unlike most acoustic emission monitoring systems, the present method exploits the benefits of multiple scattering, mode conversion, and boundaries reflections to achieve the focusing of the source with high resolution. Compared to a standard time reversal approach, the optimal refocusing of the back propagated wave field at the impact point is accomplished through a "virtual" imaging process. The robustness of the inverse filtering technique is experimentally demonstrated on a dissipative stiffened composite panel and the source position can be retrieved with a high level of accuracy in any position of the structure. Its very simple configuration and minimal processing requirements make this method a valid alternative to the conventional imaging Structural Health Monitoring systems for the acoustic emission source localization.