Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. <br/> According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. <br/> In particular, damage is obtained as limit of periodically distributed microfractures

Search for exotic contributions to atmospheric neutrino oscillations

The energy spectrum of neutrino-induced upward-going muons in MACRO was analysed in terms of relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant effect. The data disfavor these possibilities even at a sub-dominant level; stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter $|\Delta v| < 6 \times 10^{-24}$ at $\sin 2{\theta}_v$ = 0 and $|\Delta v| < 2.5 \div 5 \times 10^{-26}$ at $\sin 2{\theta}_v$ = $\pm$1. The limits can be re-interpreted as bounds on the Equivalence Principle violation parameters.Comment: Presented at the 29th I.C.R.C., Pune, India (2005

On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation

In the framework of toroidal Pseudodifferential operators on the flat torus $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$ we begin by proving the closure under composition for the class of Weyl operators $\mathrm{Op}^w_\hbar(b)$ with simbols $b \in S^m (\mathbb{T}^n \times \mathbb{R}^n)$. Subsequently, we consider $\mathrm{Op}^w_\hbar(H)$ when $H=\frac{1}{2} |\eta|^2 + V(x)$ where $V \in C^\infty (\Bbb T^n;\Bbb R)$ and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schr\"odinger equation. Moreover, we prove the convergence (in a weak sense) of the Wigner transform of the solution of the Schr\"odinger equation to the solution of the Liouville equation on $\Bbb T^n \times \Bbb R^n$ written in the measure sense. These results are applied to the study of some WKB type wave functions in the Sobolev space $H^{1} (\mathbb{T}^n; \Bbb C)$ with phase functions in the class of Lipschitz continuous weak KAM solutions (of positive and negative type) of the Hamilton-Jacobi equation $\frac{1}{2} |P+ \nabla_x v_\pm (P,x)|^2 + V(x) = \bar{H}(P)$ for $P \in \ell \Bbb Z^n$ with $\ell >0$, and to the study of the backward and forward time propagation of the related Wigner measures supported on the graph of $P+ \nabla_x v_\pm$

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension

We prove that if $t \mapsto u(t) \in \mathrm {BV}(\R)$ is the entropy solution to a $N \times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields $$u_t + f(u)_x = 0,$$ then up to a countable set of times $\{t_n\}_{n \in \mathbb N}$ the function $u(t)$ is in $\mathrm {SBV}$, i.e. its distributional derivative $u_x$ is a measure with no Cantorian part. The proof is based on the decomposition of $u_x(t)$ into waves belonging to the characteristic families $$u(t) = \sum_{i=1}^N v_i(t) \tilde r_i(t), \quad v_i(t) \in \mathcal M(\R), \ \tilde r_i(t) \in \mathrm R^N,$$ and the balance of the continuous/jump part of the measures $v_i$ in regions bounded by characteristics. To this aim, a new interaction measure \mu_{i,\jump} is introduced, controlling the creation of atoms in the measure $v_i(t)$. The main argument of the proof is that for all $t$ where the Cantorian part of $v_i$ is not 0, either the Glimm functional has a downward jump, or there is a cancellation of waves or the measure $\mu_{i,\mathrm{jump}}$ is positive

Search for nuclearites with the SLIM detector

We discuss the properties of cosmic ray nuclearites, from the point of view of their search with large nuclear track detector arrays exposed at different altitudes, in particular with the SLIM experiment at the Chacaltaya high altitude lab (5290 m a.s.l.). We present calculations concerning their propagation in the Earth atmosphere and discuss their possible detection with CR39 and Makrofol nuclear track detectors.Comment: 11 pages, 6 figure

Existence and approximation of probability measure solutions to models of collective behaviors

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm.Comment: 31 pages, 1 figur

Effect of beetroot (Beta vul-garis) extract on black angus burgers shelf life

Beef burgers are meat preparations with easy perishability. To ensure a longer shelf-life, the Regulation EU 1129/11 allows the use of some additives. However, health-conscious consumers prefer products which do not contain synthetic substances. Aim of the present study was to evaluate the effect of Red Beetroot (Beta vulgaris) integration on Black Angus made burgers shelf life. Red beet was prepared as powder and added to meat mixture as the same or in water solution. The study was split into 2 trials to assess the extract activity also in burgers vacuum-packaged stored. Burgers were analysed (up to 9 days at 4°C) in terms of sensory properties, microbiological profile, pH, aw and lipid oxidation (TBARS). At the end of storage, treated samples showed the highest values of redness and the lowest content of malondialdehyde, probably due to antioxidant properties of red beet towards myoglobin and lipid oxidation processes. Moreover, results highlighted that Red Beetroot activities were dose-dependent and intensified if dissolved in water. The aw values did not appear to be conditioned by extract integrations, unlike the pH that was lower in treated samples than control ones. Microbiological analyses identified beet-root as a potential antimicrobial substance, especially in high concentration. In conclusion, Beta vulgaris extract could be pro-posed as natural compound exploitable in beef burgers to preserve qualities and extend their shelf-life

Mass Transportation on Sub-Riemannian Manifolds

We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and uniqueness of the optimal transport map. We show the absolute continuity property of Wassertein geodesics, and we address the regularity issue of the optimal map. In particular, we are able to show its approximate differentiability a.e. in the Heisenberg group (and under some weak assumptions on the measures the differentiability a.e.), which allows to write a weak form of the Monge-Amp\`ere equation