On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations

In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with rapidly oscillating coefficients and the limiting homogenized solution. As an application of our result, we obtain an error estimate for the solution of some particular linear transport equations

Entangling macroscopic diamonds at room temperature: Bounds on the continuous-spontaneous-localization parameters

A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experimental data are weaker than those coming from matter-wave interferometry and non-interferometric tests of collapse models.Comment: 7 pages, 3 figures, v2: close to the published version, LaTe

Biomolecular, histological, clinical, and radiological analyses of dental implant bone sites prepared using magnetic mallet technology: A pilot study in animals

Background. A new instrumentation exploiting magneto-dynamic technology (mallet) proposed for implant site preparation was investigated. Methods. In the tibias of three minipigs, two sites were prepared by mallet and two by drill technique. Primary stability (ISQ) was detected after implant positioning (T0) and at 14 days (T14). X-rays and computed tomography were performed. At T14, bone samples were utilized for histological and biomolecular analyses. Results. In mallet sites, histological evaluations evidenced a significant increase in the newly formed bone, osteoblast number, and a smaller quantity of fibrous tissue. These results agree with the significant BMP-4 augmentation and the positive trend in other osteogenic factors (biological and radiological investigations). Major, albeit IL-10-controlled, inflammation was present. For both techniques, at T14 a significant ISQ increase was evidenced, but no significant difference was observed at T0 and T14 between the mallet and drill techniques. In mallet sites, lateral bone condensation was observed on computed tomography. Conclusions. Using biological, histological, clinical, and radiological analyses, this study first shows that the mallet technique is effective for implant site preparation. Based on its ability to cause osseocondensation and improve newly formed bone, mallet technology should be chosen in all clinical cases of poor bone quality

Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

Track billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of of 3-dimensional billiards. Finally, we find that for some subclasses of track billiards, the mechanism generating hyperbolicity is not the defocusing one that requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.Comment: 7 figure

Carlo Cristini: un ricordo a più voci

Ricordo di Carlo Cristini quale ricercatore nell'ambito della psicologia dell'invecchiament