13,130 research outputs found
Model Reduction for Multiscale Lithium-Ion Battery Simulation
In this contribution we are concerned with efficient model reduction for
multiscale problems arising in lithium-ion battery modeling with spatially
resolved porous electrodes. We present new results on the application of the
reduced basis method to the resulting instationary 3D battery model that
involves strong non-linearities due to Buttler-Volmer kinetics. Empirical
operator interpolation is used to efficiently deal with this issue.
Furthermore, we present the localized reduced basis multiscale method for
parabolic problems applied to a thermal model of batteries with resolved porous
electrodes. Numerical experiments are given that demonstrate the reduction
capabilities of the presented approaches for these real world applications
Grand Canonical Adaptive Resolution Simulation for Molecules with Electrons: A Theoretical Framework based on Physical Consistency
A theoretical scheme for the treatment of an open molecular system with
electrons and nuclei is proposed. The idea is based on the Grand Canonical
description of a quantum region embedded in a classical reservoir of molecules.
Electronic properties of the quantum region are calculated at constant
electronic chemical potential equal to that of the corresponding (large) bulk
system treated at full quantum level. Instead, the exchange of molecules
between the quantum region and the classical environment occurs at the chemical
potential of the macroscopic thermodynamic conditions. T he Grand Canonical
Adaptive Resolution Scheme is proposed for the treatment of the classical
environment; such an approach can treat the exchange of molecules according to
first principles of statistical mechanics and thermodynamic. The overall scheme
is build on the basis of physical consistency, with the corresponding
definition of numerical criteria of control of the approximations implied by
the coupling. Given the wide range of expertise required, this work has the
intention of providing guiding principles for the construction of a well
founded computational protocol for actual multiscale simulations from the
electronic to the mesoscopic scale.Comment: Computer Physics Communications (2017), in pres
Adaptive multiscale detection of filamentary structures in a background of uniform random points
We are given a set of points that might be uniformly distributed in the
unit square . We wish to test whether the set, although mostly
consisting of uniformly scattered points, also contains a small fraction of
points sampled from some (a priori unknown) curve with -norm
bounded by . An asymptotic detection threshold exists in this problem;
for a constant , if the number of points sampled from the
curve is smaller than , reliable detection
is not possible for large . We describe a multiscale significant-runs
algorithm that can reliably detect concentration of data near a smooth curve,
without knowing the smoothness information or in advance,
provided that the number of points on the curve exceeds
. This algorithm therefore has an optimal
detection threshold, up to a factor . At the heart of our approach is
an analysis of the data by counting membership in multiscale multianisotropic
strips. The strips will have area and exhibit a variety of lengths,
orientations and anisotropies. The strips are partitioned into anisotropy
classes; each class is organized as a directed graph whose vertices all are
strips of the same anisotropy and whose edges link such strips to their ``good
continuations.'' The point-cloud data are reduced to counts that measure
membership in strips. Each anisotropy graph is reduced to a subgraph that
consist of strips with significant counts. The algorithm rejects
whenever some such subgraph contains a path that connects many consecutive
significant counts.Comment: Published at http://dx.doi.org/10.1214/009053605000000787 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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