71 research outputs found
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 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 for natural diffusions on post-critically finite self-similar sets
and that 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
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