Abatement of thermal noise due to internal damping in 2D oscillators with rapidly rotating test masses

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.     

Extreme value statistics distributions in spin glasses

We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model, both with Gaussian and binary couplings, the distribution of the pseudocritical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like Fe(0.5)Mn)0.5)TiO(3) or Eu(0.5)Ba(0.5)MnO(3), its pseudocritical point distribution should be a priori experimentally accessible.     

Holographic watermarking for authentication of cut images

A watermarking technique, with a Computer Generated Hologram (CGH) coding system of the mark, is introduced and tested. The CGH watermarking can be used to authenticate parts of the original image. The hologram of the mark is embedded in the spatial domain by a blind additive embedding technique. The use of holography allows authenticating cuts of the original image, is the major novelty of this paper. The proposed methodology is characterized as an authentication technique, since it does not rely on the original image to decide whether the watermarked image has been altered or not and at the same time it is able to detect and localize any possible malicious change. Asymmetric cryptography is used to hide the hash information in an unambiguous way (non-repudiation property).     

Comparison of confinement characters between porous silicon and silicon nanowires

Confinement character and its effects on photoluminescence (PL) properties are theoretically investigated and compared between porous silicon (p-Si) and silicon nanowires (Si-NWs). The method is based on the application of the tight-binding technique using the minimal sp³-basis set, including the second-nearest-neighbor interactions. The results show that the quantum confinement (QC) is not entirely controlled by the porosity, rather it is mainly affected by the average distance between pores (d). The p-Si is found to exhibit weaker confinement character than Si-NWs. The confinement energy of charge carriers decays against d exponentially for p-Si and via a power-law for Si-NWs. This latter type of QC is much stronger and is somewhat similar to the case of a single particle in a quantum box. The excellent fit to the PL data demonstrates that the experimental samples of p-Si do exhibit strong QC character and thus reveals the possibility of silicon clustering into nano-crystals and/or nanowires. Furthermore, the results show that the passivation of the surface dangling bonds by the hydrogen atoms plays an essential role in preventing the appearance of gap states and consequently enhances the optical qualities of the produced structures. The oscillator strength (OS) is found to increase exponentially with energy in Si-NWs confirming the strong confinement character of carriers. Our theoretical findings suggest the existence of Si nanocrystals (Si-NCs) of sizes 1-3 nm and/or Si-NWs of cross-sectional sizes in the 1-3 nm range inside the experimental p-Si samples. The experimentally-observed strong photoluminescence from p-Si should be in favor of an exhibition of 3D-confinement character. The favorable comparison of our theoretical results with the experimental data consolidates our above claims.     

A general framework for the construction of piecewise-polynomial local interpolants of minimum degree

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, the proposed construction is extended to handle open sets of data and to the case of multiple knots.     

Myers-Type Theorems and Some Related Oscillation Results

In this paper we study the behavior of solutions of a second-order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers-type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the study of spectral properties of Schr?dinger operators on complete manifolds.