Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems

In this paper we develop adaptive iterative coupling schemes for the Biot system modeling coupled poromechanics problems. We particularly consider the space-time formulation of the fixed-stress iterative scheme, in which we first solve the problem of flow over the whole space-time interval, then exploiting the space-time information for solving the mechanics. Two common discretizations of this algorithm are then introduced based on two coupled mixed finite element methods in-space and the backward Euler scheme in-time. Therefrom, adaptive fixed-stress algorithms are build on conforming reconstructions of the pressure and displacement together with equilibrated flux and stresses reconstructions. These ingredients are used to derive a posteriori error estimates for the fixed-stress algorithms, distinguishing the different error components, namely the spatial discretization, the temporal discretization, and the fixed-stress iteration components. Precisely, at the iteration $k\geq 1$ of the adaptive algorithm, we prove that our estimate gives a guaranteed and fully computable upper bound on the energy-type error measuring the difference between the exact and approximate pressure and displacement. These error components are efficiently used to design adaptive asynchronous time-stepping and adaptive stopping criteria for the fixed-stress algorithms. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive iterative coupling algorithms

Performance Of A Liquid Argon Time Projection Chamber Exposed To The WANF Neutrino Beam

We present the results of the first exposure of a Liquid Argon TPC to a multi-GeV neutrino beam. The data have been collected with a 50 liters ICARUS-like chamber located between the CHORUS and NOMAD experiments at the CERN West Area Neutrino Facility (WANF). We discuss both the instrumental performance of the detector and its capability to identify and reconstruct low multiplicity neutrino interactions.Comment: 14 pages, 12 figures. Submitted for publication to Physical Review

Quasar Tomography: Unification of Echo Mapping and Photoionisation Models

Reverberation mapping uses time-delayed variations in photoionised emission lines to map the geometry and kinematics of emission-line gas in active galactic nuclei. In previous work, the light travel time delay tau=R(1+cos(theta))/c and Doppler shift v give a 2-d map Psi(tau,v) for each emission line. Here we combine the velocity-delay information with photoionisation physics in a maximum entropy fit to the full reverberating spectrum F_lam(lam,t) to recover a 5-d map of the differential covering fraction f(R,theta,n,N,v), with n and N the density and column density of the gas clouds. We test the method for a variety of geometries (shells, rings, disks, clouds, jets) by recovering a 3-d map f(R,theta,n) from reverberations in 7 uv emission lines. The best test recovers a hollow shell geometry, defining R to 0.15 dex, n to 0.3 dex, and ionisation parameter U ~ 1/(n R^2) to 0.1 dex. The results are sensitive to the adopted distance and luminosity, suggesting that these parameters may be measurable as well.Comment: Accepted 4 Sep 2002 for publication in MNRA

Deep shower interpretation of the cosmic ray events observed in excess of the Greisen-Zatsepin-Kuzmin energy

We consider the possibility that the ultra-high-energy cosmic ray flux has a small component of exotic particles which create showers much deeper in the atmosphere than ordinary hadronic primaries. It is shown that applying the conventional AGASA/HiRes/Auger data analysis procedures to such exotic events results in large systematic biases in the energy spectrum measurement. SubGZK exotic showers may be mis-reconstructed with much higher energies and mimick superGZK events. Alternatively, superGZK exotic showers may elude detection by conventional fluorescence analysis techniques.Comment: 22 pages, 5 figure

Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems

International audienceWe derive a posteriori error estimates for a class of second-order monotone quasi-linear diffusion-type problems approximated by piecewise affine, continuous finite elements. Our estimates yield a guaranteed and fully computable upper bound on the error measured by the dual norm of the residual, as well as a global error lower bound, up to a generic constant independent of the nonlinear operator. They are thus fully robust with respect to the nonlinearity, thanks to the choice of the error measure. They are also locally efficient, albeit in a different norm, and hence suitable for adaptive mesh refinement. Moreover, they allow to distinguish, estimate separately, and compare the discretization and linearization errors. Hence, the iterative (Newton--Raphson, quasi-Newton) linearization can be stopped whenever the linearization error drops to the level at which it does not affect significantly the overall error. This can lead to important computational savings, as performing an excessive number of unnecessary linearization iterations can be avoided. Numerical experiments for the $p$-Laplacian illustrate the theoretical developments

Well-balanced finite volume schemes for hydrodynamic equations with general free energy

Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system, given by its free energy, allows for a characterization of the stationary states by its variation. An analog property at the discrete level enables us to preserve stationary states at machine precision while keeping the dissipation of the discrete free energy. These schemes allow for analysing accurately the stability properties of stationary states in challeging problems such as: phase transitions in collective behavior, generalized Euler-Poisson systems in chemotaxis and astrophysics, and models in dynamic density functional theories; having done a careful validation in a battery of relevant test cases.Comment: Videos from the simulations of this work are available at https://sergioperezresearch.wordpress.com/well-balance

Limits to the muon flux from WIMP annihilation in the center of the Earth with the AMANDA detector

A search for nearly vertical up-going muon-neutrinos from neutralino annihilations in the center of the Earth has been performed with the AMANDA-B10 neutrino detector. The data sample collected in 130.1 days of live-time in 1997, ~10^9 events, has been analyzed for this search. No excess over the expected atmospheric neutrino background is oberved. An upper limit at 90% confidence level on the annihilation rate of neutralinos in the center of the Earth is obtained as a function of the neutralino mass in the range 100 GeV-5000 GeV, as well as the corresponding muon flux limit.Comment: 14 pages, 11 figures. Version accepted for publication in Physical Review