2,477 research outputs found
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
In this paper we formulate and test numerically a fully-coupled discontinuous
Galerkin (DG) method for incompressible two-phase flow with discontinuous
capillary pressure. The spatial discretization uses the symmetric interior
penalty DG formulation with weighted averages and is based on a wetting-phase
potential / capillary potential formulation of the two-phase flow system. After
discretizing in time with diagonally implicit Runge-Kutta schemes the resulting
systems of nonlinear algebraic equations are solved with Newton's method and
the arising systems of linear equations are solved efficiently and in parallel
with an algebraic multigrid method. The new scheme is investigated for various
test problems from the literature and is also compared to a cell-centered
finite volume scheme in terms of accuracy and time to solution. We find that
the method is accurate, robust and efficient. In particular no post-processing
of the DG velocity field is necessary in contrast to results reported by
several authors for decoupled schemes. Moreover, the solver scales well in
parallel and three-dimensional problems with up to nearly 100 million degrees
of freedom per time step have been computed on 1000 processors
On rates of convergence for the overlap in the Hopfield model
We consider the Hopfield model with neurons and an increasing number
of randomly chosen patterns and use Stein's method to obtain rates of
convergence for the central limit theorem of overlap parameters, which holds
for every fixed choice of the overlap parameter for almost all realisations of
the random patterns.Comment: 19 page
Ambiguities in gravitational lens models: impact on time delays of the source position transformation
The central ambition of the modern time delay cosmography consists in
determining the Hubble constant with a competitive precision. However,
the tension with obtained from the Planck satellite for a spatially-flat
CDM cosmology suggests that systematic errors may have been
underestimated. The most critical one probably comes from the degeneracy
existing between lens models that was first formalized by the well-known
mass-sheet transformation (MST). In this paper, we assess to what extent the
source position transformation (SPT), a more general invariance transformation
which contains the MST as a special case, may affect the time delays predicted
by a model. To this aim we use pySPT, a new open-source python package fully
dedicated to the SPT that we present in a companion paper. For axisymmetric
lenses, we find that the time delay ratios between a model and its SPT-modified
counterpart simply scale like the corresponding source position ratios, , regardless of the mass profile
and the isotropic SPT. Similar behavior (almost) holds for non-axisymmetric
lenses in the double image regime and for opposite image pairs in the quadruple
image regime. In the latter regime, we also confirm that the time delay ratios
are not conserved. In addition to the MST effects, the SPT-modified time delays
deviate in general no more than a few percent for particular image pairs,
suggesting that its impact on time-delay cosmography seems not be as crucial as
initially suspected. We also reflected upon the relevance of the SPT validity
criterion and present arguments suggesting that it should be reconsidered. Even
though a new validity criterion would affect the time delays in a different
way, we expect from numerical simulations that our conclusions will remain
unchanged.Comment: 15 pages, 14 figure
Effect of mechanical soil treatment in blueberry orchards
From June 2004 onwards a trial was conducted on a blueberry farm in the Lüneburg
Heath, Northern Germany, in which methods of mechanical soil cultivation were compared
with mulching. The aim was to determine how far the mechanical methods and equipment
established for soil management in viniculture and pomiculture can be adapted to
blueberry cultivation, and can be improved. The results showed a clear advantage of the
methods based on mulch technology in the shape of increased yields. Whilst the
mechanical treatments provided acceptable weed control, they cannot be recommended
for routine use at present because of strong yield reductions associated with damage to
the shallow root system of highbush blueberry shrubs
- …