A numerical study of a two-layer model for the growth of granular matter in a silo

The problem of filling a silo of given bounded cross-section with granular matter can be described by the two-layer model of Hadeler and Kuttler [8]. In this paper we discuss how similarity quasi-static solutions for this model can be numerically characterized by the direct finite element solution of a semidefinite elliptic Neumann problem. We also discuss a finite difference scheme for the dynamical model through which we can show that the growing profiles of the heaps in the silo evolve in finite time towards such similarity solutions.Comment: Submitted to Proceedings of the MASCOT2015 - IMACS/ISGG Workshop, Rome, Ital

Do we need N3^3LO Parton Distributions?

We discuss the uncertainty on processes computed using next-to-next-to leading (NNLO) parton distributions (PDFs) due to the neglect of higher order perturbative corrections in the PDF determination, in the specific case of Higgs production in gluon fusion. By studying the behaviour of the perturbative series for this process, we show that this uncertainty is negligible in comparison to the theoretical uncertainty on the matrix element. We then take this as a case study for the use of the Cacciari-Houdeau method for the estimate of theoretical uncertainties, and show that the method provides an effective way of treating theoretical uncertainties on the matrtix element and the PDF on the same footing.Comment: 10 pages 5 figures. Final version, to be published in Phys. Lett. B. Comparison with top production (figs 4-5) added. Several typos corrected and references updated. Grant info adde

Boundary regularity estimates in H\"older spaces with variable exponent

We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in H\"older spaces with variable exponent. The procedure allows to extend the estimates up to a portion of the boundary where Dirichlet or Neumann boundary conditions are prescribed and produces an interior Schauder theory for partial derivatives of solutions of any order $k\in\mathbb{N}$. The strategy relies on the construction of a class of suitable regularizing problems and an approximation argument. The estimates we obtain are sharp with respect to the regularity or integrability conditions on variable coefficients, boundaries, boundary data and right hand sides respectively in H\"older and Lebesgue spaces, both with variable exponentComment: 29 page

On s-harmonic functions on cones

We deal with non negative functions which are s-harmonic on a given cone of the n-dimensional Euclidean space with vertex at zero, vanishing on the complementary. We consider the case when the parameter s approaches 1, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions

A numerical study of a two-layer model for the growth of granular matter in a silo

The problem of filling a silo of given bounded cross-section with granular matter can be described by the two-layer model of Hadeler and Kuttler. In this paper we discuss how similarity quasi-static solutions for this model can be numerically characterized by the direct finite element solution of a semidefinite elliptic Neumann problem. We also discuss a finite difference scheme for the dynamical model through which we can show that the growing profiles of the heaps in the silo evolve in finite time towards such similarity solutions

Master integrals for the NNLO virtual corrections to qqˉ→ttˉq \bar{q} \rightarrow t \bar{t} scattering in QCD: the non-planar graphs

We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are determined from their differential equations, which are cast into a canonical form using the Magnus exponential. The analytic expressions of the Laurent series coefficients of the integrals are expressed as combinations of generalized polylogarithms, which we validate with several numerical checks. We discuss the analytic continuation of the planar and the non-planar master integrals, which contribute to $q {\bar q} \to t {\bar t}$ in QCD, as well as to the companion QED scattering processes $e e \to \mu \mu$ and $e \mu \to e \mu$.Comment: 1+26 pages, 4 figures, 1 table, 3 ancillary files. v2: references added, text partly reworded, results unmodifie

Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a WW pair and to the triple gauge couplings ZWWZWW and γ∗WW\gamma^*WW

We compute the two-loop master integrals required for the leading QCD corrections to the interaction vertex of a massive neutral boson $X^0$, e.g. $H,Z$ or $\gamma^{*}$, with a pair of $W$ bosons, mediated by a $SU(2)_L$ quark doublet composed of one massive and one massless flavor. All the external legs are allowed to have arbitrary invariant masses. The Magnus exponential is employed to identify a set of master integrals that, around $d=4$ space-time dimensions, obey a canonical system of differential equations. The canonical master integrals are given as a Taylor series in $\epsilon = (4-d)/2$, up to order four, with coefficients written as combination of Goncharov polylogarithms, respectively up to weight four. In the context of the Standard Model, our results are relevant for the mixed EW-QCD corrections to the Higgs decay to a $W$ pair, as well as to the production channels obtained by crossing, and to the triple gauge boson vertices $ZWW$ and $\gamma^*WW$.Comment: 42 pages, 5 figures, 2 ancillary file

Ciudades medias, escalas intermedias y planificación. Procesos potenciales e instrumentos ausentes en Brescia

The ongoing phase of transition, led by processes of globalization and world crisis, has been encouraging the demographic and economic re-centralization towards major and largest cities. This trend urges the analysis of socio-economic and spatial dynamics in medium-sized cities which are historically characterized by manufacturing and entrepreneurial culture. This is the case of Brescia (one of the urban hubs of the North Italy city-region), where a strategic agenda (up to now, missing) could foster the management of trans-scalar urban issues, as well as the development of multi-level governance and planning solutions.La fase de transición en curso, dirigida por procesos de globalización y crisis mundial, ha venido alentando la recentralización demográfica y económica hacia las ciudades más grandes e importantes. Esta tendencia urge a analizar la dinámica socioeconómica y espacial de las ciudades de tamaño medio que se caracterizan históricamente por su cultura manufacturera y empresarial. Este es el caso de Brescia (uno de los nodos urbanos de la ciudad-región del norte de Italia), donde un programa estratégico (hasta ahora inexistente) podría fomentar la gestión de los retos urbanos transescalares, así como el desarrollo de soluciones de gobernanza y planificación multinivel

Three-loop master integrals for ladder-box diagrams with one massive leg

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six. The considered integrals enter the next-to-next-to-next-to-leading order virtual corrections to scattering processes like the three-jet production mediated by vector boson decay, V* -> jjj, as well as the Higgs plus one-jet production in gluon fusion, pp -> Hj.Comment: 44 pages, 5 figures, 2 ancillary file

Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

We present the calculation of the master integrals needed for the two-loop QCDxEW corrections to $q + \bar{q} \to l^- + l^+$ and $q + \bar{q}' \to l^- + \overline{\nu} \, ,$ for massless external particles. We treat W and Z bosons as degenerate in mass. We identify three types of diagrams, according to the presence of massive internal lines: the no-mass type, the one-mass type, and the two-mass type, where all massive propagators, when occurring, contain the same mass value. We find a basis of 49 master integrals and evaluate them with the method of the differential equations. The Magnus exponential is employed to choose a set of master integrals that obeys a canonical system of differential equations. Boundary conditions are found either by matching the solutions onto simpler integrals in special kinematic configurations, or by requiring the regularity of the solution at pseudo-thresholds. The canonical master integrals are finally given as Taylor series around d=4 space-time dimensions, up to order four, with coefficients given in terms of iterated integrals, respectively up to weight four.Comment: 1+45 pages, 6 figures, 1 table, 5 ancillary file