Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

The MINERν\nuA Data Acquisition System and Infrastructure

MINER$\nu$A (Main INjector ExpeRiment $\nu$-A) is a new few-GeV neutrino cross section experiment that began taking data in the FNAL NuMI (Fermi National Accelerator Laboratory Neutrinos at the Main Injector) beam-line in March of 2010. MINER$\nu$A employs a fine-grained scintillator detector capable of complete kinematic characterization of neutrino interactions. This paper describes the MINER$\nu$A data acquisition system (DAQ) including the read-out electronics, software, and computing architecture.Comment: 34 pages, 16 figure

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Measurement of Muon Antineutrino Quasi-Elastic Scattering on a Hydrocarbon Target at E_{\nu} ~ 3.5 GeV

We have isolated muon anti-neutrino charged-current quasi-elastic interactions occurring in the segmented scintillator tracking region of the MINERvA detector running in the NuMI neutrino beam at Fermilab. We measure the flux-averaged differential cross-section, d{\sigma}/dQ^2, and compare to several theoretical models of quasi-elastic scattering. Good agreement is obtained with a model where the nucleon axial mass, M_A, is set to 0.99 GeV/c^2 but the nucleon vector form factors are modified to account for the observed enhancement, relative to the free nucleon case, of the cross-section for the exchange of transversely polarized photons in electron-nucleus scattering. Our data at higher Q^2 favor this interpretation over an alternative in which the axial mass is increased.Comment: 8 pages, 5 figures. Added correlation between neutrino and anti-neutrino results in ancillary text files (CSV

Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on polarized 3He target

Inclusive 3He(e,e') and exclusive 3He(e,e'n) processes with polarized electrons and 3He have been theoretically analyzed and values for the magnetic and electric neutron form factors have been extracted. In both cases the form factor values agree well with the ones extracted from processes on the deuteron. Our results are based on Faddeev solutions, modern NN forces and partially on the incorporation of mesonic exchange currents.Comment: 28 pages, 29 Postscript figure

Hardy's inequality for functions vanishing on a part of the boundary

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8 allowing to relax the assumptions in the main results. Final version published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-