Modelling the Kinked Jet of the Crab Nebula

We investigate the dynamical propagation of the South-East jet from the Crab pulsar interacting with supernova ejecta by means of three-dimensional relativistic MHD numerical simulations with the PLUTO code. The initial jet structure is set up from the inner regions of the Crab Nebula. We study the evolution of hot, relativistic hollow outflows initially carrying a purely azimuthal magnetic field. Our jet models are characterized by different choices of the outflow magnetization ($\sigma$ parameter) and the bulk Lorentz factor ($\gamma_{j}$). We show that the jet is heavily affected by the growth of current-driven kink instabilities causing considerable deflection throughout its propagation length. This behavior is partially stabilized by the combined action of larger flow velocities and/or reduced magnetic field strengths. We find that our best jet models are characterized by relatively large values of $\sigma$ ($\gtrsim 1$) and small values of $\gamma_{j}\simeq 2$. Our results are in good agreement with the recent X-ray (\textit{Chandra}) data of the Crab Nebula South-East jet indicating that the jet changes direction of propagation on a time scale of the order of few years. The 3D models presented here may have important implications in the investigation of particle acceleration in relativistic outflows.Comment: 15 pages, 20 figure

Geometry of contours and Peierls estimates in d=1 Ising models

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.Comment: 28 pages, 3 figure

On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

Piezoelectric Resonant Sensors with Contactless Interrogation for Mass-Sensitive and Acoustic-Load Detection

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Sensors and energy harvesters based on piezoelectric thick films

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Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Solving the solar neutrino problem with kamLAND and BOREXINO

We analyze the expected signals of two future neutrino experiments, kamLAND and BOREXINO. We show that with just these experiments, we will hopefully be able to determine which of the existing solutions to the solar neutrino problem is the real solution. We also analyze existing solar neutrino data and determine the best-fit points in the oscillation-parameter space finding that with the inclusion of SNO-charged current, the global-rates analysis gives a favored LMA solution with a goodness of fit (g.o.f) of just 32.63%, whereas the g.o.f of the SMA solution is 9.83%. Nonetheless, maximal and quasi-maximal mixing is not favored. If we include the Superkamiokande spectrum in our \chi^2 analysis, we obtain a LMA solution with a g.o.f. of 84.38%.Comment: 4 pages, 5 figures, Talk given at 37th Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs, France, 9-16 Mar 200

The solar neutrino puzzle: present situation and future scenarios

We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated phenomenological analysis of all the available data and we comment on different possible future scenarios.Comment: 22 pp. Expanded version of the contribution to appear in the Proceedings of ``Les Rencontres de Physique de la Vallee d'Aoste'', February 200