Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to solutions of the PDE, considering both Taylor and Legendre series. Our results considerably improve on previously known estimates of this type, in particular taking into account structural features of the affine parametrization of the coefficient. Moreover, the results carry over to more general Jacobi polynomial expansions. We demonstrate that the new bounds are sharp in certain model cases and we illustrate them by numerical experiments

Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

Elliptic partial differential equations with diffusion coefficients of lognormal form, that is $a=exp(b)$, where $b$ is a Gaussian random field, are considered. We study the $\ell^p$ summability properties of the Hermite polynomial expansion of the solution in terms of the countably many scalar parameters appearing in a given representation of $b$. These summability results have direct consequences on the approximation rates of best $n$-term truncated Hermite expansions. Our results significantly improve on the state of the art estimates available for this problem. In particular, they take into account the support properties of the basis functions involved in the representation of $b$, in addition to the size of these functions. One interesting conclusion from our analysis is that in certain relevant cases, the Karhunen-Lo\`eve representation of $b$ may not be the best choice concerning the resulting sparsity and approximability of the Hermite expansion

Excitation of longitudinal coupled-bunch oscillations with the wide-band cavity in the CERN PS

Longitudinal coupled-bunch oscillations in the CERN Proton Synchrotron have been studied in the past years and they have been recognized as one of the major challenges to reach the high brightness beam required by the High Luminosity LHC project. In the frame of the LHC Injectors Upgrade project in 2014 a new wide-band Finemet cavity has been installed in the Proton Synchrotron as a part of the coupled-bunch feedback system. To explore the functionality of the Finemet cavity during 2015 a dedicated measurement campaign has been performed. Coupled-bunch oscillations have been excited with the cavity around each harmonic of the revolution frequency with both a uniform and nominal filling pattern. In the following the measurements procedure and results are presented

Longitudinal and Quadrupolar Coupling Impedance of an Elliptical Vacuum Chamber With Finite Conductivity in Terms of Mathieu Functions

The resistive wall impedance of an elliptical vacuum chamber in the classical regime with infinite thickness is known analytically for ultra-relativistic beams by means of the Yokoya form factors. Starting from the longitudinal electric field of a point charge moving at arbitrary speed in an elliptical vacuum chamber, which we express in terms of Mathieu functions, in this paper we take into account the finite conductivity of the beam pipe walls and evaluate the longitudinal and quadrupolar impedance for any beam velocity. We also obtain that the quadrupolar impedance of a circular pipe is different from zero, approaching zero only for ultra-relativistic particles. Even if some of the results, in particular in the ultrarelativistic limit, are already known and expressed in terms of form factors, this approach is the first step towards the calculation of the general problem of a multi-layer vacuum chamber with different conductivities and of elliptic cross section

“Uomini e topi” di John Steinbeck o dell’impossibile redenzione

Leggendo le opere di John Steinbeck è possibile riconoscere personaggi o vicende modellati su personaggi o vicende biblici. A partire da questa osservazione l'autore dell'articolo mette in luce, nel racconto intitolato Uomini e topi, alcuni dati che riguardano il tempo della fabula, che riguardano il numero dei personaggi e, in particolare, le caratteristiche di uno dei due protagonisti, Lennie. Tali elementi autorizzano a considerare la vicenda dei due braccianti come una libera riscrittura degli ultimi tre giorni della vicenda di Cristo. Il brutale abbassamento della figura di Lennie/Cristo e il suo ribaltamento sull'asse dei valori positivo-negativo, portano alla conclusione che il pessimismo di Steinbeck, come si manifesta a questa lettura, non contempla possibilità di redenzione

Design and optimization of a compact laser-driven proton beamline

Laser-accelerated protons, generated by irradiating a solid target with a short, energetic laser pulse at high intensity (I > 1018W·cm-2), represent a complementary if not outperforming source compared to conventional accelerators, due to their intrinsic features, such as high beam charge and short bunch duration. However, the broadband energy spectrum of these proton sources is a bottleneck that precludes their use in applications requiring a more reduced energy spread. Consequently, in recent times strong effort has been put to overcome these limits and to develop laser-driven proton beamlines with low energy spread. In this paper, we report on beam dynamics simulations aiming at optimizing a laser-driven beamline - i.e. a laser-based proton source coupled to conventional magnetic beam manipulation devices - producing protons with a reduced energy spread, usable for applications. The energy range of investigation goes from 2 to 20 MeV, i.e. the typical proton energies that can be routinely obtained using commercial TW-power class laser systems. Our beamline design is capable of reducing the energy spread below 20%, still keeping the overall transmission efficiency around 1% and producing a proton spot-size in the range of 10 mm2. We briefly discuss the results in the context of applications in the domain of Cultural Heritage

Lo spazio diacronico. Elementi di riflessione sull’uso del suolo attraverso i secoli

Si sottolinea l'importanza dello spazio reale ancora oggi, mentre siamo travolti dallo spazio virtuale. Lo spazio ha e ha sempre avuto rapporti con la politica, l'amministrazione, l'economia, ecc. Le fonti storiche e i dati archeologici forniscono alcuni esempi di come i popoli antichi hanno utilizzato lo spazio. Esempi riguardano l'antica città di Roma ma anche la campagna italiana. In ogni caso va sottolineato il ruolo chiave svolto dalle caratteristiche del territorio negli usi urbani e rurali. È necessario ricordare che le considerazioni sullo spazio non possono dimenticare le tre dimensioni, ignorare ciò può portare allle false ricostruzioni archeologiche di edifici antichi e di città

Posizionarsi nel mondo : del lavoro artigiano e del pensiero visuale

In L. Cremonesi, G. Magnani et F. Migliorati (sous la direction de), Remo Pasetto. Dignità del lavoro, Presentarsì, Castiglione d/S, 2014, ISBN 978-88-97730-54-5.The text attempts to analyze the poetics of the painter Remo Pasette.Il testo rappresenta un tentativo di analisi della poetica del pittore Remo Pasetto